https://wiki.ubc.ca/api.php?action=feedcontributions&feedformat=atom&user=PierreUBC Wiki - User contributions [en]2026-05-07T21:14:20ZUser contributionsMediaWiki 1.43.7https://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=211880Course:CHEM5292013-01-02T19:03:13Z<p>Pierre: </p>
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<div><br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2012W-2), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]]<br><br />
3. [[Ground State Spectroscopic Methods]]<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
You will note that the wiki already includes some materials included from previous iterations of this course. We will be cleaning this up as we go along, removing examples that we feel are not appropriate and adding new ones that we feel are particularly relevant... stay tuned.<br />
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[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=211879Course:CHEM5292013-01-02T19:02:54Z<p>Pierre: </p>
<hr />
<div><br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2011W-1), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]]<br><br />
3. [[Ground State Spectroscopic Methods]]<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
You will note that the wiki already includes some materials included from previous iterations of this course. We will be cleaning this up as we go along, removing examples that we feel are not appropriate and adding new ones that we feel are particularly relevant... stay tuned.<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113328Symmetry and Group Theory2011-09-13T19:11:04Z<p>Pierre: /* Symmetry Point Groups */</p>
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<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
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Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
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<br />
== Lecture Notes for Group Theory ==<br />
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[[File:2009W2-C529-S012.pdf|thumb|test]]<br />
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== Symmetry Elements and Symmetry Operations ==<br />
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'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
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The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
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<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
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Remember that operations are performed sequentially from right to left!<br />
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In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
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== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
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{| class="wikitable sortable"<br />
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! Point Group !! Category !! Molecular Structure !! User !! Details<br />
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| C<sub>1</sub> || Low Symmetry || [[File:badexample.png|100px|Caption: CFClBrI]] || [[User:Pierre|PK]] || Add specific text that describes any restrictions placed on the molecule (none in this case). Also include reference here if appropriate - use DOI links wherever possible (e.g. [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]).<br />
|-<br />
| C<sub>s</sub> || Low Symmetry || insert structure || username || more stuff<br />
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| C<sub>i</sub> || Low Symmetry || insert structure || username || more stuff<br />
|-<br />
| C<sub>2</sub> || Rotational || insert structure || username || more stuff<br />
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| D<sub>2</sub> || Dihedral || insert structure || username || more stuff<br />
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| T<sub>d</sub> || High Symmetry || insert structure || username || more stuff<br />
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|}<br />
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== Properties of a Mathematical Group ==<br />
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'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
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'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
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'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
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'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
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== Representations of Groups: Character Tables ==<br />
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[http://symmetry.jacobs-university.de/ Character Tables]<br />
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Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
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<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
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<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
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<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
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<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
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<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
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<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
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<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
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Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
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Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
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== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
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* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
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<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
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"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
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"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
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"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
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"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
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“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
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''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
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"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
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This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
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“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
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"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
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''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
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"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
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''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
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''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
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''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
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"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
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"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
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<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
<br />
<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113327Symmetry and Group Theory2011-09-13T19:09:05Z<p>Pierre: /* Symmetry Point Groups */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
[[File:2009W2-C529-S012.pdf|thumb|test]]<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
<br />
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{| class="wikitable sortable"<br />
|-<br />
! Point Group !! Category !! Molecular Structure !! User !! Details<br />
|-<br />
| Point Group || Category || insert structure || username || more stuff<br />
|-<br />
| C<sub>1</sub> || Low Symmetry || [[File:badexample.png|100px|Caption: CFClBrI]] || [[User:Pierre|PK]] || Add specific text that describes any restrictions placed on the molecule (none in this case). Also include reference here if appropriate - use DOI links wherever possible (e.g. [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]).<br />
|}<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
<br />
''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
<br />
"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
<br />
"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
<br />
''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
<br />
''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
<br />
<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
<br />
''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
<br />
''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
<br />
<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
<br />
<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
<br />
<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113326Symmetry and Group Theory2011-09-13T19:04:44Z<p>Pierre: /* Symmetry Point Groups */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
[[File:2009W2-C529-S012.pdf|thumb|test]]<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
<br />
{| class="wikitable sortable"<br />
|-<br />
! Point Group !! Category !! Molecular Structure !! User !! Details<br />
|-<br />
| Point Group || Category || insert structure || type '[[User:Pierre|PK]]' here || more stuff<br />
|-<br />
| C<sub>1</sub> || Low Symmetry || [[File:badexample.png|100px|Caption: CFClBrI]] || [[User:Pierre|PK]] || Add specific text that describes any restrictions placed on the molecule (none in this case). Also include reference here if appropriate - use DOI links wherever possible (e.g. [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]).<br />
|}<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
<br />
"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
<br />
"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
<br />
''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
<br />
''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
<br />
<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
<br />
''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
<br />
''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
<br />
<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
<br />
<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
<br />
<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113325Symmetry and Group Theory2011-09-13T19:03:03Z<p>Pierre: /* Symmetry Point Groups */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
[[File:2009W2-C529-S012.pdf|thumb|test]]<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
<br />
{| class="wikitable sortable"<br />
|-<br />
! Point Group !! Classification !! Molecular Structure !! User !! Details<br />
|-<br />
| C<sub>1</sub> || Low Symmetry || [[File:badexample.png|100px|Caption: CFClBrI]] || [[User:Pierre|PK]] || Add specific text that describes any restrictions placed on the molecule (none in this case). Also include reference here if appropriate - use DOI links wherever possible (e.g. [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]).<br />
|-<br />
| Point Group || Example || Example || Example || Example<br />
|}<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
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<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
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"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
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"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
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''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
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"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
<br />
''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
<br />
<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
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''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
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<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
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<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
<br />
<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113324Symmetry and Group Theory2011-09-13T19:02:31Z<p>Pierre: /* Symmetry Point Groups */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
[[File:2009W2-C529-S012.pdf|thumb|test]]<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
<br />
{| class="wikitable sortable"<br />
|-<br />
! Point Group !! Classification !! Molecular Structure !! User !! Details<br />
|-<br />
| C<sub>1</sub> || Low Symmetry || [[File:badexample.png|100px|Caption: CFClBrI]] || || Add specific text that describes any restrictions placed on the molecule (none in this case). Also include reference here if appropriate - use DOI links wherever possible (e.g. [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]).<br />
|-<br />
| Point Group || Example || Example || Example || Example<br />
|}<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
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"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
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"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
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''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
<br />
<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
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''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
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<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
<br />
<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
<br />
<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113323Symmetry and Group Theory2011-09-13T19:01:02Z<p>Pierre: /* Symmetry Point Groups */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
[[File:2009W2-C529-S012.pdf|thumb|test]]<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
<br />
{| class="wikitable sortable"<br />
|-<br />
! Point Group !! Classification !! Molecular Structure !! Details<br />
|-<br />
| C<sub>1</sub> || Low Symmetry || [[File:badexample.png|100px|Caption: CFClBrI]] || || Add specific text that describes any restrictions placed on the molecule (none in this case). Also include reference here if appropriate.<br />
|-<br />
| Point Group || Example || Example || Example || Example<br />
|}<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
<br />
''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
<br />
"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
<br />
"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
<br />
''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
<br />
''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
<br />
<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
<br />
''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
<br />
''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
<br />
<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
<br />
<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
<br />
<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113322Symmetry and Group Theory2011-09-13T18:59:23Z<p>Pierre: /* Low Symmetry Point Groups */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
[[File:2009W2-C529-S012.pdf|thumb|test]]<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
<br />
=== Low Symmetry Point Groups ===<br />
These are molecules with no associated symmetry elements (other than the identity, E).<br />
{| class="wikitable sortable"<br />
|-<br />
! Point Group !! Classification !! Molecular Structure !! Details<br />
|-<br />
| C<sub>1</sub> || Low Symmetry || [[File:badexample.png|100px|Caption: CFClBrI]] || Add specific text that describes any restrictions placed on the molecule (none in this case). Also include reference here if appropriate.<br />
|-<br />
| Example || Example || Example || Example<br />
<br />
|}<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
<br />
"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
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''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
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"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
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''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
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<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
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''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
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<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
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"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
<br />
<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=File:Badexample.png&diff=113321File:Badexample.png2011-09-13T18:52:06Z<p>Pierre: </p>
<hr />
<div></div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113320Symmetry and Group Theory2011-09-13T18:51:45Z<p>Pierre: /* Low Symmetry Point Groups */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
[[File:2009W2-C529-S012.pdf|thumb|test]]<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
<br />
=== Low Symmetry Point Groups ===<br />
These are molecules with no associated symmetry elements (other than the identity, E).<br />
<br />
C<sub>1</sub> <br />
[[File:badexample.png]]<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
<br />
"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
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"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
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''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
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<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
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''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
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<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
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<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
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<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
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"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113319Symmetry and Group Theory2011-09-13T18:50:41Z<p>Pierre: /* Lecture Notes for Group Theory */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
[[File:2009W2-C529-S012.pdf|thumb|test]]<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
<br />
=== Low Symmetry Point Groups ===<br />
These are molecules with no associated symmetry elements (other than the identity, E).<br />
<br />
C<sub>1</sub> <br />
<gallery><br />
File:badexample.png|CFClBrI<br />
</gallery><br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
<br />
"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
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"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
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''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
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<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
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''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
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<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
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<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
<br />
<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
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"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113318Symmetry and Group Theory2011-09-13T18:50:17Z<p>Pierre: </p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
File:2009W2-C529-S012.pdf|thumb|test<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
<br />
=== Low Symmetry Point Groups ===<br />
These are molecules with no associated symmetry elements (other than the identity, E).<br />
<br />
C<sub>1</sub> <br />
<gallery><br />
File:badexample.png|CFClBrI<br />
</gallery><br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
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"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
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''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
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"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
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''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
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''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
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''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
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<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
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<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
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<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
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"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
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"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113317Symmetry and Group Theory2011-09-13T18:49:54Z<p>Pierre: </p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
[File:2009W2-C529-S012.pdf|thumb|test]<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
<br />
=== Low Symmetry Point Groups ===<br />
These are molecules with no associated symmetry elements (other than the identity, E).<br />
<br />
C<sub>1</sub> <br />
<gallery><br />
[File:badexample.png|CFClBrI]<br />
</gallery><br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
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"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
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"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
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"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
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"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
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“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
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''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
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"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
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This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
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“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
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"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
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''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
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"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
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''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
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''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
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''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
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"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
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: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
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"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
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: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
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"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
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: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
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"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
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: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
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"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
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: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
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[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
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"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
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: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113316Symmetry and Group Theory2011-09-13T18:49:17Z<p>Pierre: </p>
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<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
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Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
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== Lecture Notes for Group Theory ==<br />
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[[File:2009W2-C529-S012.pdf|thumb|test]]<br />
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== Symmetry Elements and Symmetry Operations ==<br />
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'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
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The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
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<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
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Remember that operations are performed sequentially from right to left!<br />
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In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
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== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
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=== Low Symmetry Point Groups ===<br />
These are molecules with no associated symmetry elements (other than the identity, E).<br />
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C<sub>1</sub> <br />
<gallery><br />
[[File:badexample.jpg|CFClBrI]]<br />
</gallery><br />
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== Properties of a Mathematical Group ==<br />
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'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
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'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
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'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
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'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
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== Representations of Groups: Character Tables ==<br />
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[http://symmetry.jacobs-university.de/ Character Tables]<br />
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Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
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<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
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<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
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<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
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<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
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<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
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<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
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<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
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Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
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Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
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== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
<br />
"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
<br />
"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
<br />
''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
<br />
<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
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''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
<br />
<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
<br />
<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
<br />
<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113315Symmetry and Group Theory2011-09-13T18:48:32Z<p>Pierre: </p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
[[File:2009W2-C529-S012.pdf|thumb|test]]<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups ==<br />
Molecules can be classified based on their symmetry point groups. Although there are a large number of different point groups, they are generally classified in four general classes depending on the number and type of rotational elements that can be used to describe a particular molecular geometry:<br />
<br />
=== Low Symmetry Point Groups ===<br />
These are molecules with no associated symmetry elements (other than the identity, E).<br />
<br />
C<sub>1</sub> <br />
<gallery><br />
File:badexample.jpg|CFClBrI<br />
</gallery><br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
<br />
"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
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''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
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"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
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''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
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"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
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''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
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<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
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''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
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<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
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<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
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<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113313Symmetry and Group Theory2011-09-13T18:41:07Z<p>Pierre: </p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Symmetry and Group Theory are an effective way of simplifying complex problems and determining how best to evaluate a particular spectroscopic problem. The uses of group theory are very general but our focus will be on the application of group theoretical principals to help us evaluate and utilize spectroscopy in inorganic chemistry.<br />
<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
[[File:2009W2-C529-S012.pdf|thumb|test]]<br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups and Space Groups ==<br />
<br />
<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
<br />
"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
<br />
"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
<br />
''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
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<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
<br />
''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
<br />
<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
<br />
<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
<br />
<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113312Symmetry and Group Theory2011-09-13T18:37:57Z<p>Pierre: </p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
== Lecture Notes for Group Theory ==<br />
<br />
[[File:2009W2-C529-S012.pdf]]<br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups and Space Groups ==<br />
<br />
<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
<br />
''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
<br />
"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
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"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
<br />
''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
<br />
<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
<br />
''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
<br />
<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
<br />
<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
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"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113311Symmetry and Group Theory2011-09-13T18:37:17Z<p>Pierre: </p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Lecture Notes for Group Theory: [[File:2009W2-C529-S012.pdf]]<br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups and Space Groups ==<br />
<br />
<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
<br />
''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
<br />
"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
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''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
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"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
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''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
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''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
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''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
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"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
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<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
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<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
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"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
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"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113310Symmetry and Group Theory2011-09-13T18:36:40Z<p>Pierre: /* Examples in Chemistry where Symmetry and Group Theory are commonly utilized */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
Lecture Notes for Group Theory: [[File:2009W2-C529-S012.pdf | thumb | Preliminary lecture notes, copyright Pierre Kennepohl, all rights reserved]]<br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups and Space Groups ==<br />
<br />
<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
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"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
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"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
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"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
<br />
"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
<br />
''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
<br />
''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
<br />
<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
<br />
''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
<br />
''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
<br />
<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
<br />
<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
<br />
<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=113309Symmetry and Group Theory2011-09-13T18:36:16Z<p>Pierre: </p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
[[File:2009W2-C529-S012.pdf | thumb | Preliminary lecture notes, copyright Pierre Kennepohl, all rights reserved]]<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups and Space Groups ==<br />
<br />
<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
<br />
''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
<br />
"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
<br />
"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
<br />
"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
<br />
''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
<br />
''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
<br />
<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
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''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
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''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
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<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
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<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
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"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=File:CHEM529-Syllabus.pdf&diff=112957File:CHEM529-Syllabus.pdf2011-09-08T15:56:26Z<p>Pierre: uploaded a new version of &quot;File:CHEM529-Syllabus.pdf&quot;</p>
<hr />
<div></div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=112956Course:CHEM5292011-09-08T15:55:58Z<p>Pierre: </p>
<hr />
<div>[[File:CHEM529-Syllabus.pdf|200px|thumb|2011W1 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2011W-1), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]]<br><br />
3. [[Ground State Spectroscopic Methods]]<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
You will note that the wiki already includes some materials included from previous iterations of this course. We will be cleaning this up as we go along, removing examples that we feel are not appropriate and adding new ones that we feel are particularly relevant... stay tuned.<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=112955Course:CHEM5292011-09-08T15:55:32Z<p>Pierre: </p>
<hr />
<div>[[File:CHEM529-Syllabus.pdf|200px|thumb|2010W2 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2011W-1), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]]<br><br />
3. [[Ground State Spectroscopic Methods]]<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
You will note that the wiki already includes some materials included from previous iterations of this course. We will be cleaning this up as we go along, removing examples that we feel are not appropriate and adding new ones that we feel are particularly relevant... stay tuned.<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=112954Symmetry and Group Theory2011-09-08T15:52:58Z<p>Pierre: /* Literature examples of the use of symmetry/group theory in inorganic chemistry */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
[[File:2009W2-C529-S012.pdf|thumb|Preliminary lecture notes, copyright Pierre Kennepohl, all rights reserved]]<br />
<br />
* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
<br />
== Symmetry Elements and Symmetry Operations ==<br />
<br />
'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
<br />
The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
<br />
<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
<br />
Remember that operations are performed sequentially from right to left!<br />
<br />
In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
<br />
== Symmetry Point Groups and Space Groups ==<br />
<br />
<br />
<br />
== Properties of a Mathematical Group ==<br />
<br />
'''Identity:''' There is an element <math> e </math> of the group such that <math> a </math> • <math> e </math> = <math> e </math> • <math> a </math> = <math> e </math>, for any element of the group.<br />
<br />
'''Closure:''' If <math> a </math> and <math> b </math> are in the group then the result of <math> a </math> • <math> b </math> is also a member of the group.<br />
<br />
'''Inverse:''' For any element <math> a </math> of the group, there is an <math> a^-</math><math>^1</math> such that <math> a </math> • <math> a^- </math><math>^1</math> = <math> a^-</math><math>^1</math> • <math> a </math> = <math> e </math>.<br />
<br />
'''Associativity:''' If <math> a </math> , <math> b </math> and <math>c</math> are in the group then <math>(a</math> • <math>b)</math> • <math>c</math> = <math>a</math> • <math>(b</math> • <math>c)</math>.<br />
<br />
== Representations of Groups: Character Tables ==<br />
<br />
[http://symmetry.jacobs-university.de/ Character Tables]<br />
<br />
Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
<br />
<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
<br />
<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
<br />
<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
<br />
<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
<br />
<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
<br />
<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
<br />
<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
<br />
Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
<br />
Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l]. [[User:Pierre|PK]]<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
<br />
"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
<br />
"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
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"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
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"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
<br />
"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
<br />
''"Hangman Corroles: Efficient Synthesis and Oxygen ReactionChemistry"'', Dilek K. Dogutan, Sebastian A. Stoian, Robert McGuire, Jr., Matthias Schwalbe, Thomas S. Teets, Daniel G. Nocera ''J. Am. Chem. Soc.'', '''2011''', 133(1), 131-140, [http://pubs.acs.org/doi/full/10.1021/ja108904s doi:10.1021/ja108904s].<br />
: This paper discusses a new synthesis of Hangman Corroles,a type of corrin macrocycle, and the reactivity of the resultant cobalt complexes towards oxygen. Symmetry and group theory are prevalent throughout this paper from the discussion of crystallography to EPR transitions. In particular, DFT calculations were preformed with symmetry constraints and then further optimized without symmetry constraints. The symmetry constraints allows for faster initial optimization, and the fact that the calculations generate the same results when symmetry constraints were removed suggests that these symmetry elements are present in the molecule. [[User:FraserPick|FraserPick]]<br />
<br />
''"Vibrational frequencies and structural determination of phosphorus tricyanide"'', James O. Jensen, ''Spectrochemica Acta Part A'', '''2004''', 60, 2537-2540, [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNG-4CS4SK5-5&_user=1022551&_coverDate=09%2F30%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050484&_version=1&_urlVersion=0&_userid=1022551&md5=54f8d866fee55062ac202140ef0e4696&searchtype=a doi:10.1016/j.saa.2003.12.032].<br />
: This paper describes the use of theoretical calculations of the vibrational frequencies of phosphorus tricyanide, and how these calculated values were used to assign the experimental values to the corresponding stretch. The calculations were performed using the C3v symmetry of phosphorus tricyanide. [[User:AndrewPriegert|AndrewPriegert]]<br />
<br />
<br />
''"Phthalocyanine as a Chemically Inert, Redox-Active Ligand: Structural and Electronic Properties of a Nb(IV)-Oxo Complex Incorporating a Highly Reduced Phthalocyanine(4-) Anion"'', Edwin W.Y. Wong, Charles J. Walsby, Tim Storr, Daniel Leznoff ''Inorg. Chem.'', '''2010''', 49, 3343-3350, [http://pubs.acs.org/doi/pdf/10.1021/ic902409n]. <br />
:This paper investigates the electronic structure of a reduced niobium(V) phthalocyanine complex. The electronic structures of the parent complex and reduced forms were compared via UV-Vis absorption, X-ray crystallography, EPR, ENDOR, and TD-DFT. The symmetry of each complex was used to predict changes in the UV-Vis spectra from parent to reduced forms, and the line shape of the EPR spectra was predicted by the observed symmetry of the complexes. [[User:CaterinaRamogida|CaterinaRamogida]] <br />
<br />
''"New C2v- and Chiral C2-Symmetric Olefin Polymerization Catalysts Based on Nickel(II) and Palladium(II) Diimine Complexes Bearing 2,6-Diphenyl Aniline Moieties: Synthesis, Structural Characterization, and First Insight into Polymerization Properties"'', Markus Schmid, Robert Eberhardt, Martti Klinga, Markku Leskela and Bernhard Rieger<br />
''Organometallics'', '''2001''', 20,2321-2330, [http://pubs.acs.org/doi/pdf/10.1021/om010001f].<br />
: The paper discusses the synthesis and characterization of Novel olefin polymerization catalysts with C2v and C2 symmetry. The discussion indicates how sterics affect the geometry and the symmetry of metal complexes. [[User:DineshAluthge|DineshAluthge]] <br />
<br />
''"Activation of Methane by Zinc: Gas-Phase Synthesis, Structure, and Bonding of HZnCH<sub>3</sub>"'', Michael A. Flory, Aldo J. Apponi, Lindsay N. Zack, and Lucy M. Ziurys.<br />
''J. Am. Chem. Soc.'', '''2010''', ''132'', 17186–17192, [http://pubs.acs.org/doi/full/10.1021/ja106121v doi:10.1021/ja106121v].<br />
: The authors synthesized MeZnH in the gas phase and identified it using rotational spectroscopy. Its spectral features, particularly the existence of a K-ladder, indicate that the molecule has <math>C_{3v}</math> symmetry; analysis of the rotational constants of the isotopologues allowed determination of its bond lengths and angles. [[User:CatherineChow|CatherineChow]] <br />
<br />
<br />
"''LiCoO2 Concaved Cuboctahedrons from Symmetry-Controlled Topological Reactions''" Chen, H.; Wu, L.; Zhang, L.; Zhu, Y. Grey, C. ''J. Am. Chem. Soc.'' 2010, 133, 262-270. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
<br />
: The growth of novel [http://en.wikipedia.org/wiki/Cuboctahedron cuboctahedron] nanoparticles is presented. The unique structure adopted by these nanoparticles is controlled using symmetry as a synthetic tool. X-ray diffraction and other analytical methods are employed in order to determine how and why these marvelous crystals form. [[Peter Christensen]] <br />
<gallery><br />
File:Cuboctahedron.jpg|Chen et al. [http://pubs.acs.org/doi/abs/10.1021/ja104852q?from=jhp]<br />
</gallery> <br />
<br />
<br />
"''Molecular Dials: Hindered Rotations in Mono- andDiferrocenyl Anthracenes and Triptycenes''" Nikitin,K; Muller-Bunz, H; Ortin, Y; Muldoon, J; McGlinchey, M. J. ''J. Am. Chem. Soc.'' '''2010''', ''132'', 17617-17622. [http://pubs.acs.org/doi/full/10.1021/ja108226p]<br />
<br />
: Interesting mono- and diferrocenyl anthracenes and triptycenes have been synthesized. NMR methods (including 2D-EXSY NMR) are employed to probe into the hindered rotational behaviors of these complexes under different temperatures, on the basis that molecules with certain symmetry (e.g. <math>C_{2v}</math> and <math>C_{2}</math>) yield specific signals. [[Yang Cao]]<br />
<br />
<br />
"''A New Set of Structurally Related Enantiopure Polypyrazolyl Ligands of Varying Rotational Symmetry: Synthesis, Metal Complexation, and Comparison of Asymmetric Induction''" Michael C. Keyes, Bradley M. Chamberlain, Scott A. <br />
Caltagirone, Jason A. Halfen, and William B. Tolman. ''Oragnometallics.'' '''1998''', ''17'', 1984-1992. [http://pubs.acs.org/doi/abs/10.1021/om9801047]<br />
<br />
: This paper discusses the synthesis of various enantiomerically pure ligands with C1, C2, or C3 symmetry. These ligands were used to form copper complexes to perform cyclopropanation of styrene. Their study showed that the complexes with C3 symmetry had significantly higher enantioselectivity compared to the ligands with C1 or C2 symmetry. [[User:PhillipTaylor|PhillipTaylor]]<br />
<br />
<br />
"''Arylene Imine Macrocycles of C-3h and C-3 Symmetry from Reductive Imination of Nitroformylarenes''" Andrew L. Korich and Thomas S. Hughes. ''ORGANIC LETTERS'' '''2008''', ''23'', 5405-5408. [http://pubs.acs.org/doi/full/10.1021/ol802302x]<br />
<br />
: The author synthesized some kinds of Schiff base macrocycles starting from nitroaldehyde precursors. In this method, each imine macrocycle can be traced back to a single fragment that contains both the amine and the carbonyl moieties. All of those kinds of macrocycles are in C3 symmetry, which is evident by the simplicity of the 1H NMR spectra. [[Zhengyu Chen]]<br />
<br />
"''Identification of a Novel η 2 -Se2 Bonding Mode in Cu(I) Complexes of the Dimeric Selenocarbonyl Dianions, [(EPh2P)2CSeSeC(PPh2E)2 [ 2- (E = S, Se)''" Maarit Risto, Jari Konu, and Tristram Chivers ''INORGANIC CHEMISTRY'' '''2011''', ''50'', 406-408. [http://pubs.acs.org/doi/pdf/10.1021/ic101866v]<br />
<br />
: The author synthesized and characterized some Cu(I) complexes with novel η 2 -Se2 bonding mode. X-ray crystallography shows different symmetry operations among three different complexes: 1-x,1-y,1-z, 2-x,1-y,1-z, and 1-x,1-y,1-z, respectively. [[Jiazhang Wang]]<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]<br />
<br />
"''Nanocrystal Materials with Modified Symmetry''" A. M. Zheltikov ''Laser Physics'' '''2001''', ''11(9)'', 1024-1028. []<br />
<br />
: The author provides a qualitative analysis of birefringence and changes in linear and nonlinear-optical properties of porous materials based on crystal symmetry considerations. [[Joanna De Witt]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=The_Role_of_Spectroscopy_in_Inorganic_Chemistry&diff=112953The Role of Spectroscopy in Inorganic Chemistry2011-09-08T15:52:12Z<p>Pierre: /* Some examples of the use of spectroscopy in Inorganic Chemistry */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
[[File:Raman.jpg|frame|An incident 532nm laser used during a resonance Raman experiment. (c) Pierre Kennepohl]]<br />
<br />
This page is designed to list the important roles that spectroscopy plays in the field of inorganic chemistry. Please be specific and include examples from the literature if possible. Remember that this is an interactive page and that all members of the course should be participating! You should consider this page as your first introduction to the use of the wiki environment so play around, include some links (for references), some graphics, an equation maybe?<br />
<br />
Remember to use the 'discussion' page (see tabs above) to discuss items before finalizing them on this page. Also remember that Pierre will be tracking who inserts what on this page, and this information will be used (qualitatively) to help determine the participation part of your mark for Chem 529. <br />
<br />
<br />
<br />
--[[User:Pierre|Pierre]] 16:54, 5 January 2010 (UTC)<br />
<br />
<br />
== The role of spectroscopy in Inorganic Chemistry ==<br />
<br />
(Generally, spectroscopy can be used to characterize inorganic materials in various ways.<br />
Such as:<br />
*Determination of geometric structure of inorganic compounds.<br />
*Determination of electronic structure of inorganic compounds.<br />
*Determination of the elemental composition of a sample.<br />
*Determination of protein secondary and tertiary structure.<br />
*Determination of kinetic parameters during a reaction.<br />
*Determination of relative concentrations of different species present at any time during a reaction.<br />
*Determination of the functional groups of a compound.)<br />
<br />
== Some examples of the use of spectroscopy in Inorganic Chemistry ==<br />
<br />
((<br />
===Elucidation of structure===<br />
* NMR: indicates degree of symmetry of a ligand around a metal center as well as the electron environment of the nucleus being probed.<br />
* Mass spectrometry: mass of compound, composition of a compound or mixture of compounds<br />
* EPR: determination of properties and spin resonance of paramagnetic metal complexes.<br />
* Linear Dichroism: provide orientation data of anisotropic inorganic materials. <br />
* Circular Dichroism: provides fingerprint information for the structure of various large biological molecules such as peptides (which can be coordinated with metals)<br />
* NMR: J-coupling constants are used to derive to dihedral (torsion) angles and therefore enable determination of protein structure<br />
* IR/UV-Vis/Raman: can be used to identify certain functional groups in a sample<br />
* UV-Vis Spectroscopy: Used to determine electronic structure of compounds (Band structures)<br />
* X-Ray Crystallography: can be used to elucidate structure of crystalline materials<br />
* NMR Titrations: can be used to track variations in structure (nmr signal) under the influence of some external stimulus (pH for example)<br />
* Atomic Absorption Spectroscopy: Analysis of the concentration of a metal element.<br />
<br />
===Kinetics===<br />
<br />
* IR, UV-Vis and Raman spectroscopy: can all be used to monitor kinetics by tracking a molecular vibration which is unique to either the product, or reactant. <br />
* NMR can also be used in kinetic studies. <br />
* Auger electron spectroscopy: A surface specific technique used to determine the composition of the surface layers of a sample.<br />
* Energy Dispersive X-Ray Spectroscopy: Typically used in conjunction with scanning electron microscopy to characterize the elemental composition of a sample. <br />
* Moessbauer Spectroscopy: Helps determine electron configuration<br />
* NMR: can be used to monitor the reaction by the analysis of nuclei other than <sup>1</sup>H and <sup>13</sup>C<br />
*Fluorescence spectroscopy: used to measure the fluorescence of a sample<br />
))<br />
<br />
<br />
<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Role of Spectroscopy]][[Category:Chemistry]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=The_Role_of_Spectroscopy_in_Inorganic_Chemistry&diff=112952The Role of Spectroscopy in Inorganic Chemistry2011-09-08T15:51:51Z<p>Pierre: /* Elucidation of structure */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
[[File:Raman.jpg|frame|An incident 532nm laser used during a resonance Raman experiment. (c) Pierre Kennepohl]]<br />
<br />
This page is designed to list the important roles that spectroscopy plays in the field of inorganic chemistry. Please be specific and include examples from the literature if possible. Remember that this is an interactive page and that all members of the course should be participating! You should consider this page as your first introduction to the use of the wiki environment so play around, include some links (for references), some graphics, an equation maybe?<br />
<br />
Remember to use the 'discussion' page (see tabs above) to discuss items before finalizing them on this page. Also remember that Pierre will be tracking who inserts what on this page, and this information will be used (qualitatively) to help determine the participation part of your mark for Chem 529. <br />
<br />
<br />
<br />
--[[User:Pierre|Pierre]] 16:54, 5 January 2010 (UTC)<br />
<br />
<br />
== The role of spectroscopy in Inorganic Chemistry ==<br />
<br />
(Generally, spectroscopy can be used to characterize inorganic materials in various ways.<br />
Such as:<br />
*Determination of geometric structure of inorganic compounds.<br />
*Determination of electronic structure of inorganic compounds.<br />
*Determination of the elemental composition of a sample.<br />
*Determination of protein secondary and tertiary structure.<br />
*Determination of kinetic parameters during a reaction.<br />
*Determination of relative concentrations of different species present at any time during a reaction.<br />
*Determination of the functional groups of a compound.)<br />
<br />
== Some examples of the use of spectroscopy in Inorganic Chemistry ==<br />
<br />
(<br />
===Elucidation of structure===<br />
* NMR: indicates degree of symmetry of a ligand around a metal center as well as the electron environment of the nucleus being probed.<br />
* Mass spectrometry: mass of compound, composition of a compound or mixture of compounds<br />
* EPR: determination of properties and spin resonance of paramagnetic metal complexes.<br />
* Linear Dichroism: provide orientation data of anisotropic inorganic materials. <br />
* Circular Dichroism: provides fingerprint information for the structure of various large biological molecules such as peptides (which can be coordinated with metals)<br />
* NMR: J-coupling constants are used to derive to dihedral (torsion) angles and therefore enable determination of protein structure<br />
* IR/UV-Vis/Raman: can be used to identify certain functional groups in a sample<br />
* UV-Vis Spectroscopy: Used to determine electronic structure of compounds (Band structures)<br />
* X-Ray Crystallography: can be used to elucidate structure of crystalline materials<br />
* NMR Titrations: can be used to track variations in structure (nmr signal) under the influence of some external stimulus (pH for example)<br />
* Atomic Absorption Spectroscopy: Analysis of the concentration of a metal element.<br />
<br />
===Kinetics===<br />
<br />
* IR, UV-Vis and Raman spectroscopy: can all be used to monitor kinetics by tracking a molecular vibration which is unique to either the product, or reactant. <br />
<br />
* NMR can also be used in kinetic studies. <br />
<br />
* Auger electron spectroscopy: A surface specific technique used to determine the composition of the surface layers of a sample.<br />
<br />
* Energy Dispersive X-Ray Spectroscopy: Typically used in conjunction with scanning electron microscopy to characterize the elemental composition of a sample. <br />
<br />
* Moessbauer Spectroscopy: Helps determine electron configuration<br />
<br />
* NMR: can be used to monitor the reaction by the analysis of nuclei other than <sup>1</sup>H and <sup>13</sup>C<br />
<br />
*Fluorescence spectroscopy: used to measure the fluorescence of a sample)<br />
<br />
<br />
<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Role of Spectroscopy]][[Category:Chemistry]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=The_Role_of_Spectroscopy_in_Inorganic_Chemistry&diff=112951The Role of Spectroscopy in Inorganic Chemistry2011-09-08T15:51:17Z<p>Pierre: /* Some examples of the use of spectroscopy in Inorganic Chemistry */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
[[File:Raman.jpg|frame|An incident 532nm laser used during a resonance Raman experiment. (c) Pierre Kennepohl]]<br />
<br />
This page is designed to list the important roles that spectroscopy plays in the field of inorganic chemistry. Please be specific and include examples from the literature if possible. Remember that this is an interactive page and that all members of the course should be participating! You should consider this page as your first introduction to the use of the wiki environment so play around, include some links (for references), some graphics, an equation maybe?<br />
<br />
Remember to use the 'discussion' page (see tabs above) to discuss items before finalizing them on this page. Also remember that Pierre will be tracking who inserts what on this page, and this information will be used (qualitatively) to help determine the participation part of your mark for Chem 529. <br />
<br />
<br />
<br />
--[[User:Pierre|Pierre]] 16:54, 5 January 2010 (UTC)<br />
<br />
<br />
== The role of spectroscopy in Inorganic Chemistry ==<br />
<br />
(Generally, spectroscopy can be used to characterize inorganic materials in various ways.<br />
Such as:<br />
*Determination of geometric structure of inorganic compounds.<br />
*Determination of electronic structure of inorganic compounds.<br />
*Determination of the elemental composition of a sample.<br />
*Determination of protein secondary and tertiary structure.<br />
*Determination of kinetic parameters during a reaction.<br />
*Determination of relative concentrations of different species present at any time during a reaction.<br />
*Determination of the functional groups of a compound.)<br />
<br />
== Some examples of the use of spectroscopy in Inorganic Chemistry ==<br />
<br />
(<br />
===Elucidation of structure===<br />
<br />
* NMR: indicates degree of symmetry of a ligand around a metal center as well as the electron environment of the nucleus being probed.<br />
<br />
* Mass spectrometry: mass of compound, composition of a compound or mixture of compounds<br />
<br />
* EPR: determination of properties and spin resonance of paramagnetic metal complexes.<br />
<br />
* Linear Dichroism: provide orientation data of anisotropic inorganic materials. <br />
<br />
* Circular Dichroism: provides fingerprint information for the structure of various large biological molecules such as peptides (which can be coordinated with metals)<br />
<br />
* NMR: J-coupling constants are used to derive to dihedral (torsion) angles and therefore enable determination of protein structure<br />
<br />
* IR/UV-Vis/Raman: can be used to identify certain functional groups in a sample<br />
<br />
* UV-Vis Spectroscopy: Used to determine electronic structure of compounds (Band structures)<br />
<br />
* X-Ray Crystallography: can be used to elucidate structure of crystalline materials<br />
<br />
* NMR Titrations: can be used to track variations in structure (nmr signal) under the influence of some external stimulus (pH for example)<br />
<br />
* Atomic Absorption Spectroscopy: Analysis of the concentration of a metal element.<br />
<br />
===Kinetics===<br />
<br />
* IR, UV-Vis and Raman spectroscopy: can all be used to monitor kinetics by tracking a molecular vibration which is unique to either the product, or reactant. <br />
<br />
* NMR can also be used in kinetic studies. <br />
<br />
* Auger electron spectroscopy: A surface specific technique used to determine the composition of the surface layers of a sample.<br />
<br />
* Energy Dispersive X-Ray Spectroscopy: Typically used in conjunction with scanning electron microscopy to characterize the elemental composition of a sample. <br />
<br />
* Moessbauer Spectroscopy: Helps determine electron configuration<br />
<br />
* NMR: can be used to monitor the reaction by the analysis of nuclei other than <sup>1</sup>H and <sup>13</sup>C<br />
<br />
*Fluorescence spectroscopy: used to measure the fluorescence of a sample)<br />
<br />
<br />
<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Role of Spectroscopy]][[Category:Chemistry]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=The_Role_of_Spectroscopy_in_Inorganic_Chemistry&diff=112950The Role of Spectroscopy in Inorganic Chemistry2011-09-08T15:50:57Z<p>Pierre: /* Some examples of the use of spectroscopy in Inorganic Chemistry */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
[[File:Raman.jpg|frame|An incident 532nm laser used during a resonance Raman experiment. (c) Pierre Kennepohl]]<br />
<br />
This page is designed to list the important roles that spectroscopy plays in the field of inorganic chemistry. Please be specific and include examples from the literature if possible. Remember that this is an interactive page and that all members of the course should be participating! You should consider this page as your first introduction to the use of the wiki environment so play around, include some links (for references), some graphics, an equation maybe?<br />
<br />
Remember to use the 'discussion' page (see tabs above) to discuss items before finalizing them on this page. Also remember that Pierre will be tracking who inserts what on this page, and this information will be used (qualitatively) to help determine the participation part of your mark for Chem 529. <br />
<br />
<br />
<br />
--[[User:Pierre|Pierre]] 16:54, 5 January 2010 (UTC)<br />
<br />
<br />
== The role of spectroscopy in Inorganic Chemistry ==<br />
<br />
(Generally, spectroscopy can be used to characterize inorganic materials in various ways.<br />
Such as:<br />
*Determination of geometric structure of inorganic compounds.<br />
*Determination of electronic structure of inorganic compounds.<br />
*Determination of the elemental composition of a sample.<br />
*Determination of protein secondary and tertiary structure.<br />
*Determination of kinetic parameters during a reaction.<br />
*Determination of relative concentrations of different species present at any time during a reaction.<br />
*Determination of the functional groups of a compound.)<br />
<br />
== Some examples of the use of spectroscopy in Inorganic Chemistry ==<br />
<br />
(===Elucidation of structure===<br />
<br />
* NMR: indicates degree of symmetry of a ligand around a metal center as well as the electron environment of the nucleus being probed.<br />
<br />
* Mass spectrometry: mass of compound, composition of a compound or mixture of compounds<br />
<br />
* EPR: determination of properties and spin resonance of paramagnetic metal complexes.<br />
<br />
* Linear Dichroism: provide orientation data of anisotropic inorganic materials. <br />
<br />
* Circular Dichroism: provides fingerprint information for the structure of various large biological molecules such as peptides (which can be coordinated with metals)<br />
<br />
* NMR: J-coupling constants are used to derive to dihedral (torsion) angles and therefore enable determination of protein structure<br />
<br />
* IR/UV-Vis/Raman: can be used to identify certain functional groups in a sample<br />
<br />
* UV-Vis Spectroscopy: Used to determine electronic structure of compounds (Band structures)<br />
<br />
* X-Ray Crystallography: can be used to elucidate structure of crystalline materials<br />
<br />
* NMR Titrations: can be used to track variations in structure (nmr signal) under the influence of some external stimulus (pH for example)<br />
<br />
* Atomic Absorption Spectroscopy: Analysis of the concentration of a metal element.<br />
<br />
===Kinetics===<br />
<br />
* IR, UV-Vis and Raman spectroscopy: can all be used to monitor kinetics by tracking a molecular vibration which is unique to either the product, or reactant. <br />
<br />
* NMR can also be used in kinetic studies. <br />
<br />
* Auger electron spectroscopy: A surface specific technique used to determine the composition of the surface layers of a sample.<br />
<br />
* Energy Dispersive X-Ray Spectroscopy: Typically used in conjunction with scanning electron microscopy to characterize the elemental composition of a sample. <br />
<br />
* Moessbauer Spectroscopy: Helps determine electron configuration<br />
<br />
* NMR: can be used to monitor the reaction by the analysis of nuclei other than <sup>1</sup>H and <sup>13</sup>C<br />
<br />
*Fluorescence spectroscopy: used to measure the fluorescence of a sample)<br />
<br />
<br />
<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Role of Spectroscopy]][[Category:Chemistry]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=The_Role_of_Spectroscopy_in_Inorganic_Chemistry&diff=112949The Role of Spectroscopy in Inorganic Chemistry2011-09-08T15:50:36Z<p>Pierre: /* The roles of spectroscopy in Inorganic Chemistry */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
[[File:Raman.jpg|frame|An incident 532nm laser used during a resonance Raman experiment. (c) Pierre Kennepohl]]<br />
<br />
This page is designed to list the important roles that spectroscopy plays in the field of inorganic chemistry. Please be specific and include examples from the literature if possible. Remember that this is an interactive page and that all members of the course should be participating! You should consider this page as your first introduction to the use of the wiki environment so play around, include some links (for references), some graphics, an equation maybe?<br />
<br />
Remember to use the 'discussion' page (see tabs above) to discuss items before finalizing them on this page. Also remember that Pierre will be tracking who inserts what on this page, and this information will be used (qualitatively) to help determine the participation part of your mark for Chem 529. <br />
<br />
<br />
<br />
--[[User:Pierre|Pierre]] 16:54, 5 January 2010 (UTC)<br />
<br />
<br />
== The role of spectroscopy in Inorganic Chemistry ==<br />
<br />
(Generally, spectroscopy can be used to characterize inorganic materials in various ways.<br />
Such as:<br />
*Determination of geometric structure of inorganic compounds.<br />
*Determination of electronic structure of inorganic compounds.<br />
*Determination of the elemental composition of a sample.<br />
*Determination of protein secondary and tertiary structure.<br />
*Determination of kinetic parameters during a reaction.<br />
*Determination of relative concentrations of different species present at any time during a reaction.<br />
*Determination of the functional groups of a compound.)<br />
<br />
== Some examples of the use of spectroscopy in Inorganic Chemistry ==<br />
<br />
===Elucidation of structure===<br />
<br />
* NMR: indicates degree of symmetry of a ligand around a metal center as well as the electron environment of the nucleus being probed.<br />
<br />
* Mass spectrometry: mass of compound, composition of a compound or mixture of compounds<br />
<br />
* EPR: determination of properties and spin resonance of paramagnetic metal complexes.<br />
<br />
* Linear Dichroism: provide orientation data of anisotropic inorganic materials. <br />
<br />
* Circular Dichroism: provides fingerprint information for the structure of various large biological molecules such as peptides (which can be coordinated with metals)<br />
<br />
* NMR: J-coupling constants are used to derive to dihedral (torsion) angles and therefore enable determination of protein structure<br />
<br />
* IR/UV-Vis/Raman: can be used to identify certain functional groups in a sample<br />
<br />
* UV-Vis Spectroscopy: Used to determine electronic structure of compounds (Band structures)<br />
<br />
* X-Ray Crystallography: can be used to elucidate structure of crystalline materials<br />
<br />
* NMR Titrations: can be used to track variations in structure (nmr signal) under the influence of some external stimulus (pH for example)<br />
<br />
* Atomic Absorption Spectroscopy: Analysis of the concentration of a metal element.<br />
<br />
===Kinetics===<br />
<br />
* IR, UV-Vis and Raman spectroscopy: can all be used to monitor kinetics by tracking a molecular vibration which is unique to either the product, or reactant. <br />
<br />
* NMR can also be used in kinetic studies. <br />
<br />
* Auger electron spectroscopy: A surface specific technique used to determine the composition of the surface layers of a sample.<br />
<br />
* Energy Dispersive X-Ray Spectroscopy: Typically used in conjunction with scanning electron microscopy to characterize the elemental composition of a sample. <br />
<br />
* Moessbauer Spectroscopy: Helps determine electron configuration<br />
<br />
* NMR: can be used to monitor the reaction by the analysis of nuclei other than <sup>1</sup>H and <sup>13</sup>C<br />
<br />
*Fluorescence spectroscopy: used to measure the fluorescence of a sample<br />
<br />
<br />
<br />
<br />
<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Role of Spectroscopy]][[Category:Chemistry]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=112948Course:CHEM5292011-09-08T15:48:05Z<p>Pierre: </p>
<hr />
<div>[[File:CHEM529-Syllabus.pdf|200px|thumb|2010W2 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2009W-2), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]]<br><br />
3. [[Ground State Spectroscopic Methods]]<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
By the end of this course, pages associated with this wiki will have hopefully become a useful reference for all physical methods and topics discussed during the course. The overall quality of the final product depends on active participation from all students in the class!<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=82620Course:CHEM5292011-03-14T14:49:56Z<p>Pierre: </p>
<hr />
<div>[[File:CHEM529-Syllabus.pdf|200px|thumb|2010W2 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2009W-2), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]], Problem Set #1:<br><br />
3. [[Ground State Spectroscopic Methods]], Problem Set #2: [[File:2010W2-C529-PS02.pdf]] (due date: March 14th, 2011)<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
By the end of this course, pages associated with this wiki will have hopefully become a useful reference for all physical methods and topics discussed during the course. The overall quality of the final product depends on active participation from all students in the class!<br />
<br />
Project Template: must be emailed to you (???)<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=82619Course:CHEM5292011-03-14T14:47:11Z<p>Pierre: </p>
<hr />
<div>[[File:CHEM529-Syllabus.pdf|200px|thumb|2010W2 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2009W-2), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]], Problem Set #1:<br><br />
3. [[Ground State Spectroscopic Methods]], Problem Set #2: [[File:2010W2-C529-PS02.pdf]] (due date: March 14th, 2011)<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
By the end of this course, pages associated with this wiki will have hopefully become a useful reference for all physical methods and topics discussed during the course. The overall quality of the final product depends on active participation from all students in the class!<br />
<br />
Project Template: [[File:2010W2-C529-project.ppt]]<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=79904Course:CHEM5292011-03-02T15:39:46Z<p>Pierre: </p>
<hr />
<div>[[File:CHEM529-Syllabus.pdf|200px|thumb|2010W2 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2009W-2), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]], Problem Set #1:[[File:2010W2-C529-PS01.pdf]]<br><br />
3. [[Ground State Spectroscopic Methods]], Problem Set #2: [[File:2010W2-C529-PS02.pdf]] (due date: March 14th, 2011)<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
By the end of this course, pages associated with this wiki will have hopefully become a useful reference for all physical methods and topics discussed during the course. The overall quality of the final product depends on active participation from all students in the class!<br />
<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=71973Course:CHEM5292011-01-24T23:12:03Z<p>Pierre: </p>
<hr />
<div>[[File:CHEM529-Syllabus.pdf|200px|thumb|2010W2 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2009W-2), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]], Problem Set #1:[[File:2010W2-C529-PS01.pdf]]<br><br />
3. [[Ground State Spectroscopic Methods]]<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
By the end of this course, pages associated with this wiki will have hopefully become a useful reference for all physical methods and topics discussed during the course. The overall quality of the final product depends on active participation from all students in the class!<br />
<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=71969Course:CHEM5292011-01-24T23:09:47Z<p>Pierre: </p>
<hr />
<div>[[File:CHEM529-Syllabus.pdf|200px|thumb|2010W2 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2009W-2), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]] - [[File:2010W2-C529-PS01.pdf|Problem Set 1 due Feb 04]]<br><br />
3. [[Ground State Spectroscopic Methods]]<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
By the end of this course, pages associated with this wiki will have hopefully become a useful reference for all physical methods and topics discussed during the course. The overall quality of the final product depends on active participation from all students in the class!<br />
<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=71965Course:CHEM5292011-01-24T23:05:38Z<p>Pierre: </p>
<hr />
<div>[[File:CHEM529-Syllabus.pdf|200px|thumb|2010W2 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2009W-2), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]] - [[File:2010W2-C529-PS01.pdf | Problem Set #1 (due Feb 04, 2011)]]<br><br />
3. [[Ground State Spectroscopic Methods]]<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
By the end of this course, pages associated with this wiki will have hopefully become a useful reference for all physical methods and topics discussed during the course. The overall quality of the final product depends on active participation from all students in the class!<br />
<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=71963Course:CHEM5292011-01-24T23:04:22Z<p>Pierre: </p>
<hr />
<div>[[File:CHEM529-Syllabus.pdf|200px|thumb|2010W2 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2009W-2), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]] - [[File:2010W2-C529-PS01.pdf|Problem Set #1 (due Feb 04, 2011)]]<br><br />
3. [[Ground State Spectroscopic Methods]]<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
By the end of this course, pages associated with this wiki will have hopefully become a useful reference for all physical methods and topics discussed during the course. The overall quality of the final product depends on active participation from all students in the class!<br />
<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=71961Course:CHEM5292011-01-24T23:02:29Z<p>Pierre: </p>
<hr />
<div>[[File:CHEM529-Syllabus.pdf|200px|thumb|2010W2 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2009W-2), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]] - [[File:2010W2-C529-PS01|Problem Set #1 (due Feb 04, 2011)]]<br><br />
3. [[Ground State Spectroscopic Methods]]<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
By the end of this course, pages associated with this wiki will have hopefully become a useful reference for all physical methods and topics discussed during the course. The overall quality of the final product depends on active participation from all students in the class!<br />
<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Ground_State_Spectroscopic_Methods&diff=69152Ground State Spectroscopic Methods2011-01-11T17:08:08Z<p>Pierre: </p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 Chem 529] <> [http://wiki.ubc.ca/Ground_State_Spectroscopic_Methods Ground State Spectroscopic Methods]<br />
<br />
==Vibrational Spectroscopy==<br />
[[File:2009W2-C529-S013.pdf|thumb|Preliminary lecture notes, copyright Pierre Kennepohl, all rights reserved]]There are two distinct approaches to vibrational spectroscopy: infrared absorption spectroscopy (a single photon technique) and Raman spectroscopy (a two photon inelastic scattering technique). Each carries its own set of selection rules, thus each can give complementary information regarding the vibrational modes of a molecule.<br />
<br />
===Infrared spectroscopy===<br />
<br />
===Raman spectroscopy===<br />
<br />
=== Literature examples of the use of vibrational spectroscopy in inorganic chemistry ===<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
<br />
''"Imaging of single GaN nanowires by tip-enhanced Raman spectroscopy"'', N. Marquestaut, D. Talaga, L. Servant, P. Yang, P. Pauzauskie, F. Lagugné-Labarthet, ''Journal of Raman Spectroscopy'', '''2009''', 40(10), 1441-1445, [http://dx.doi.org/10.1002/jrs.2404 doi:10.1002/jrs.2404].<br />
: This article demonstrates the use of an AFM microscopy used in tandem with a Raman spectroscopy to determine the physical dimensions of a GaN nanowire. Typically well defined objects of sizes on the order of (lambda/2) can be observed by raman, but by using tip-enhanced Raman spectroscopy (TERS) this spatial resolution can be enhanced. The GaN nanowire analyzed in this paper was on the order of ~200 nm. [[User:EricPrice|EricPrice]]<br />
<br />
"Effect of high external pressure on the vibrational spectra of crystalline dichloro(1.5-cycloctadiene)platinum(II)", JA Baldwin, IS Butler and DFR Gilson, "Inorganica Chimica Acta", 2006, 359, 3079-3083, [http://dx.doi.org/10.1016/j.ica.2006.02.003 doi:10.1016/j.ica.2006.02.003].<br />
: This article used high pressure IR and Raman spectroscopy to investigate the bonding in a dichloro-COD platinum complex. They assign the IR and Raman bands based on previous work and use the pressure dependencies of certain bands in the spectra to make conclusions about structural deformations at high pressure and how they can influence the strength of pi-backbonding in this molecule. [[User:Kimosten|Kimosten]]<br />
<br />
"A two-dimensional IR correlation spectroscopic study of the conformational changes in syndiotactic polypropylene during crystallization", K. Zheng, R. Liu, Y. Huang, "Polymer Journal", "2010", 42, 81-85 [http://dx.doi.org/10.1038/pj.2009.304 doi:10.1038/pj.2009.304].<br />
: This article examines the melting/crystallization of syndiotactic polypropylene by using FTIR and 2D correlation analysis. The changes are seen through the intensities of peaks known to be associated with the crystalline and amorphous forms of the polymer. The 2D correlation analysis gives insight to the order of change within the polymer during these two processes (melting, crystallization). [[User:AmberJuilfs|AmberJuilfs]]<br />
<br />
''"Isolation of Dysprosium and Yttrium Complexes of a Three-Electron Reduction Product in the Activation of Dinitrogen, the (N<sub>2</sub>)<sup>3-</sup> Radical"'', William J. Evans, Ming Fang, Gael Zucchi, Filipp Furche, Joseph W. Ziller, Ryan M. Hoekstra, Jeffrey I. Zink, ''J. Am. Chem. Soc.'', '''2009''', ''131'', 11195-11202, [http://dx.doi.org/10.1021/ja9036753 doi:10.1021/ja9036753].<br />
: This article concentrates on synthesis of N<sub>2</sub> complexes involving yttrium and dysprosium, and analysis of the N-N bond order using Raman spectroscopy. Data is compared to computational values, and <sup>15</sup>N isotopic substitution experiments were conducted. [[User:Lwence|Lwence]]<br />
<br />
'''Spectroscopic Properties and Quantum Chemistry-Based Normal Coordinate Analysis (QCB-NCA) of a Dinuclear Tantalum complex Exhibiting the Novel Side-On End-On Bridging Geometry of N<sub>2</sub>: Correlation to Electronic Structure and Reactivity"'', Felix Studt, Bruce A. MacKay, Michael D. Fryzuk, Felix Tuczek, ''J. Am. Chem. Soc.'', '''2003''', ''126'', 280-290, [http://dx.doi.org/10.1021/ja036997y doi:10.1021/ja036997y]. [[User:TrumanWambach|TrumanWambach]]<br />
: IR, Raman, isotopic substitution and computations are used in concert to throughly describe the bonding in a dimeric tantalum N<sub>2</sub> compound. IR and Raman spectra are calculated, and assigned to a molecular vibration. Computations are then compared to experimental values. Force constants are assigned to the bonds of interest.<br />
<br />
''"Probing thin-film morphology of conjugated polymers by Raman spectroscopy"'', Jessica M. Winfield, Carrie L. Donley, Richard H. Friend, Ji-Seon Kim, ''J. Appl. Phys.'', '''2010''', ''107'', 024902, [http://dx.doi.org/10.1063/1.3276257 doi:10.1063/1.3276257].<br />
: This article demonstrates how Raman spectroscopy can be used to compare the thin-film morphology of conjugated polymers at the polymer-substrate interface versus that in the bulk polymer. It is shown that near the substrate interface[poly(9,9-di-n-octylfluorene-alt-benzothiadiazole (F8BT)] adopts a more planar conformation (has a lower torsion angle between the alternating units). The morphology of conjugated polymers at interfaces is very important in light-emitting diode and field-effect transistor applications where charge transport occurs near the polymer-substrate interface. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
''"Resonance Raman Scattering from Solutions of C<sub>60</sub>"'', S.H. Gallagher, R.S. Armstrong, W.A. Clucas, P.A. Lay, C.A. Reed, ''J. Phys. Chem. A.'', '''1997''', 101''(16)'', 2960-2968. [http://dx.doi.org/10.1021/jp970232t doi:10.1021/jp970232t].<br />
: The resonance raman excitation spectrum of fullerene (C<sub>60</sub>) is studied at eight excitation wavelengths. Raman excitation calculations were performed on the five most intense resonance bands to correlate the bands with the vibrational modes of fullerene. Rare (D-type) scattering is observed. It is determined that the symmetry of C<sub>60</sub> is distorted by solvent, as there are Raman-silent vibrational modes present. The symmetry of the distorted excited state of fullerene is D<sub>5h</sub>. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Photoinduced Orientation of Azobenzene Chromophores in Amorphous Polymer As Studied by Real-Time Visible and FTIR Spectroscpies"'', T. Buffeteau, F. Lagugne-Labarthet, M. Pezolet, and C. Sourisseau, ''Macromolecules'', '''1998''', 31(21), 7312-7320, [http://dx.doi.org/10.1021/ma980843z doi:10.1021/ma980843z].<br />
: This article shows the use of visible (birefringent studies) and infrared (polarization modulated FTIR) spectroscopy to study the dynamics of photoinduced orientation of doped and co-polymers of azobenzenes. Polarization modulated infrared spectroscopy (PM-FTIR)is a form of IR which allows the observation of the amount of order in a given anisotropic sample. The authors used this technique to observe the orientation (by photoinduction) and relaxation of DR1 in a matrix of PMMA. [[User:JackyYim|JackyYim]]<br />
<br />
''"Charging effects on bonding and catalyzed oxidation of CO on Au-8 clusters on MgO"'', Yoon B, Hakkinen H, Landman U, Worz AS, Antonietti JM, Abbet S, Judai K, Heiz U, ''SCIENCE'', '''2005''', 307(5708), 403-407, [http://dx.doi.org/10.1126/science.1104168 doi:10.1126/science.1104168].<br />
: This article investigates on how gold octamers bound to oxygen-vacancy F-center defects on MgO(001) activate adsorbed CO and O2 and catalyze the oxidation of CO. The authors use infrared spectroscopy to measure the stretch vibration of CO and it shows a red shift by 25 to 50 cm-1. This shift is caused by enhanced backdonation from the gold nanocluster into the antibonding 2pi* orbital of the CO. All the experimental results agree with quantum calculations. [[User:CuilingXu|CuilingXu]]<br />
<br />
<br />
''"Real-time monitoring of microwave-promoted organometallic ligand-substitution reactions using ''in situ'' Raman spectroscopy"'', T. M. Barnard and N. E. Leadbeater, ''Chem. Commun.'', '''2006''', 3615.<br />
[http://dx.doi.org/10.1039/b608793k doi:10.1039/b608793k].<br />
<br />
: The article demonstrates an application of Raman spectroscopy in monitoring progress in organometallic ligand-substitution reactions ''in situ'', while using microwave irradiation to facilitate the reaction. This allows reaction conditions to be easily optimized and does not require much trial and error, but requires the help of some literature data. The theory is tested with the substitution of a CO ligand with some ligands in Mo(CO)<sub>6</sub>, where the course of substitution is monitored with Raman spectroscopy without aliquots removed and conserves time. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Synthesis, Crystal Structure, and Vibrational Spectroscopy of K<sub>2</sub>Ca<sub>4</sub>Si<sub>8</sub>O<sub>21</sub>—An Unusual Single-Layer Silicate Containing Q2 and Q3 Units"'', E. Arroyabe, R. Kaindl, D.M. Tbbens and V. Kahlenberg, ''Inorg. Chem.'', '''2009''', ''48'', 11929–11934., [http://dx.doi.org/10.1021/ic901762u doi:10.1021/ic901762u].<br />
<br />
: The author synthesized a novel silicate, and determined its crystal structure. Confocal Raman spectrum of a single crystal of this silicate was also studied in this article. The author assigned the fequencies to specific vibrational modes, and concluded that K<sub>2</sub>Ca<sub>4</sub>Si<sub>8</sub>O<sub>21</sub> is a silicate based on loop-branched chains. [[User:JiazhangWang|JiazhangWang]]<br />
<br />
''"Comparison of the Structures and Wetting Properties of Self-Assembled Monolayers of n-Alkanethiols on the Coinage Metal Surfaces, Cu, Ag, Au."'', P. Laibinis, G. Whitesides, D. Allara, Y. Tao, A. Parikh, R. Nuzzo, ''Journal of the American Chemical Society'', '''1991''', 113, 7152-7167, [http://dx.doi.org/10.1021/ja00019a011 doi:10.1021/ja00019a011].<br />
<br />
:Reflection-absorption infrared spectroscopy (RAIRS) is used to determine the crystallinity and cant angle of straight-chain alkanethiols adsorbed on Cu and Ag. These measurements are then compared to the well-studied system of alkanethiols adsorbed on Au. RAIRS uses p-polarized incident light to take advantage of the "surface selection rule," which states that only vibrations with a transition-dipole moment component perpendicular to the plane of the metal substrate can be observed. The intensity of a particular vibration is compared to that of a bulk spectrum and the orientation of the vibration relative to the substrate can be determined. [[User:BrianSahli|BrianSahli]]<br />
<br />
==Nuclear Magnetic Resonance Spectroscopy==<br />
[[File:2009W2-C529-S021a.pdf|thumb|Preliminary lecture notes, copyright Pierre Kennepohl, all rights reserved]]<br />
Nuclear magnetic resonance spectroscopy is probably the most widely used spectroscopic technique in modern chemistry. It allows for rapid and accurate characterization of organic molecules as well as more in-depth studies of electronic and geometric structure of a wide range of molecules.The technique relies on the quantum mechanical behaviour of atomic nuclei, most particularly their ground state angular momentum (<math>I_g</math>). NMR active nuclei must have <math>I_g>0</math> such that they have more than one magnetic state (# of states = <math>2I+1</math>). NMR uses the Zeeman effect, the splitting of angular momentum states in a magnetic field, to create a situation where one can probe the nuclear states with electromagnetic radiation.<br />
<br />
=== Common uses of NMR in inorganic chemistry ===<br />
<br />
* identification of compounds<br />
* help with mechanism elucidation<br />
* kinetics studies<br />
* isotopic labelling experiments<br />
* solid state identification<br />
* paramagnetic/diamagnetic verification<br />
<br />
=== Literature examples of NMR in inorganic chemistry ===<br />
<br />
<!-- Note: Remember to sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
''"Neutral-Ligand Complexes of Bis(imino)pyridine Iron: Synthesis, Strucutre, and Spectrososcopy"'', S.C. Bart, E. Lobkovsky, E. Bill, K. Wieghardt, P.J. Chirik, "Inorg. Chem.", '''2007''', 46, 7055-7063, http://dx.doi.org/10.1021/ic700869h <br />
: A series of bis(imino)pyridine (PDI) iron complexes are synthesized and characterized using I.R. NMR, and Mossbauer spectroscopy. It is found that temperature independent paramagnetism occurs (TIP). TIP if found to be a function of donor strength. Upon two electron reduction of the system the ligand displays redox activity. Weak field ligands stabilize the S=0 ground state, where the redox active ligand (S=1) is antiferromagnetically coupled to the Fe(II) high spin iron center (S=1). Stronger field ligands stabilize the excited state (S=1).[[User:TrumanWambach|TrumanWambach]]Truman <br />
<br />
<br />
"Synthesis, Structures, Bonding, and Redox Chemistry of Ditungsten Butadiyne Complexes with WCCW Backbones", J. Sun, E. Shaner, M.K. Jones, D.C. O'Hanlon, J.S. Mugridge, and M.D. Hopkins, <i>Inorganic Chem.</i>, <b>2010</b>, 49, 1687-1698, [http://dx.doi.org/10.1021/ic902088x doi:10.1021/ic902088x].<br />
: This article reports the synthesis of a new Tungsten-Carbon triply bonded species of the form XL<sub>4</sub>WCCWL<sub>4</sub>X, where L = 1/2 dmpe, 1/2 depe, P(OMe)<sub>3</sub> and X = Cl, OTf. They used both X-ray crystallography and NMR to observe the molecule. They also performed DFT calculations to observe the bonding of the species. Through <sup>31</sup>P NMR they were able to observe the degradation of the molecule by seeing the formation of free ligands. [[User:AmberJuilfs|AmberJuilfs]]<br />
<br />
''"Na-Y Zeolite as a Highly Active Catalyst for the Hydroamination of α,β-Unsaturated Compounds with Aromatic Amines"'', K. Komura, R. Hongo, J. Tsutsui, and Y. Sugi, ''Catal. Lett.'', '''2009''', 128, 203-209, [http://dx.doi.org/10.1007/s10562-008-9738-4 doi:10.1007/s10562-008-9738-4].<br />
: This article reports the use of Zeolite as a reusable, green solid catalyst for hydroamination to produce fine chemicals. The authors use the hydroamination of aniline with methyl acrylate as a their test reaction and found Na-Y shows high catalytic activity and mono-product selectivity. To study the mechanism by which this transformation occurs, <sup>13</sup>C MAS NMR and solution <sup>13</sup>C NMR of methyl acrylate adsorpted Na-Y zeolite were compared. It was found that Na-Y activates methyl acrylate through a Lewis-acid interaction between the carbonyl and sodium ion. [[User:JackyYim|JackyYim]]<br />
<br />
''"Insertion Reactions of trans-Mo(dmpe)<sub>2</sub>(H)(NO) with Imines"'', F. Liang, H. W. Schmalle, and H. Berke, ''Inorg. Chem.'', '''2004''', 43, 993-999, [http://dx.doi.org/10.1021/ic030139l doi:10.1021/ic0301391].<br />
: The insertion of a disubstituted aromatic imine into the metal-hydrogen bond of a molybdenum hydride complex is studied using variable temperature <sup>1</sup>H NMR. By comparing the relative peak intensities of product and reactant at different temperatures the standard enthalpy and entropy of reaction are determined. This is done using a van't Hoff plot, which plots ln K vs. 1/T. The calculated change in enthalpy and entropy were -48.8 kJ/mol and -33 J/(K mol), respectively. [[User:BrianSahli|BrianSahli]]<br />
<br />
''"Structural and thermodynamical properties of CuII amyloid-beta16/28 complexes associated with Alzheimer's disease"". Guilloreau, L.; Damian, L.; Coppel, Y.; Mazarguil, H.; Winterhalter, M.; Faller, P. Journal Of Biological Inorganic Chemistry: JBIC: A Publication Of The Society Of Biological Inorganic Chemistry 2006, 11, 1024-1038, [http://dx.doi.org/10.1007/s00775-006-0154-1 doi:10.1007].<br />
: Amyloid-beta peptide interaction with the paramagnetic metal Cu(II) is investigated by 1D proton NMR. The paramagnetic shift/broading that occurs in the NMR signals of amino acid residues that are bound with Cu(II) are used to identify them as ligands. The signals from other residues are also broadened and shifted due to the influence of the paramagnetic metal, and so substoichiometric amounts of Cu(II) are used in order to see the most dramatic broadening occur at the coordinated amino acids.[[User:EricPrice|EricPrice]]<br />
<br />
''"Diphenylphosphino- or Dicyclohexylphosphino-Tethered Boryl Pincer Ligands: Synthesis of PBP Iridium(III) Complexes and Their Conversion to Iridium-Ethylene Complexes"'', Y. Segawa, M. Yamashita, and K. Nozaki, ''Organometallics'', '''2009''', ''28'', 6234-6242, [http://dx.doi.org/10.1021/om9006455 doi:10.1021].<br />
:This article focuses on synthesis and characterization of various Ir PBP pincer complex derivatives. NMR studies are of interest as up to 4 different NMR active nuclei (<sup>31</sup>P, <sup>11</sup>B, <sup>1</sup>H, and <sup>13</sup>C) may be bound to the metal centre at once.[[User:Lwence|Lwence]]<br />
<br />
"Characterization of wurtzite indium nitride synthesized from indium oxide by In-115 MAS NMR spectroscopy", W.S. Jung, O.H. Han and S.A. Chae, Materials Letters, 2007, 61, 3413-3415, [http://dx.doi.org/10.1016/j.matlet.2006.11.083 doi:10.1016/j.matlet.2006.11.083].<br />
: This article outlines the characterization of wurtzite indium nitride (w-InN) samples made using different conditions using 115-In MAS NMR spectroscopy. The authors used this technique, in addition to XRD, to identify the different phases present in each sample and found that samples made using higher temperatures had a w-InN structure with extra In incorporated, due to thermal decomposition. [[User:Kimosten|Kimosten]]<br />
<br />
''"29Si NMR Relaxation of Silicated Nanoparticles in Tetraethoxysilane-Tetrapropylammonium Hydroxide-Water System (TEOS-TPAOH-H2O)"'', M. Haouas, D. Petry, M. Anderson, F. Taulelle, ''J. Phys. Chem. C'', '''2009''', ''113'', 10838-10841, [http://dx.doi.org/10.1021/jp903454f doi:10.1021/jp903454f].<br />
:In an attempt to understand how zeolites nucleate and grow, silicon-29 NMR relaxation times are measured from a silicalite-1 precursor solution. Nanoparticles and silicate oligomers in the solution all give rise to observable resonances. From these resonances the Qn distribution of nanoparticles in the solution can be measured and therefore the progressive connectivity of the nanoparticles to form zeolites can be followed. ([[User:AshleeJHowarth|AshleeJHowarth]])<br />
<br />
''"Multiple Functional Groups of Varying Ratios in Metal-Organic Frameworks"'', Hexiang Deng, Christian J. Doonan, Hiroyasu Furukawa, Ricardo B. Ferreira, John Towne, Carolyn B. Knobler, Bo Wang, Omar M. Yaghi, ''Science'', '''2010''', 327, 846-850, [http://dx.doi.org/10.1126/science.1181761 doi:10.1126/science.1181761].<br />
: This article reports a set of synthesized multivariate metal-organic frameworks (MTV-MOF). The frameworks are composed of metal-oxide joints and 1,4-benzenedicarboxylate and its derivatives links and a "complex" secondary structure formed by multivaried arrangements of many functional groups. The structures is ordered, and highly porous. They can achieve better capacity and selectivity in gas storage. <sup>13</sup>C CP/MAS NMR study indicates the presence of multi functional organic links in the MOF backbone without unbound link in crystals. <sup>1</sup>H NMR spectra indicates the link ratio of their crystals. [[User:Jiazhang|Jiazhang]]<br />
<br />
''"Rhodium(0) Metalloradicals in Binuclear C-H Activation"'', F. F. Puschmann, H. Grutzmacher, B. de Bruin, ''J. Am. Chem. Soc.'' '''2010''', ''132'', 73-75, [http://dx.doi.org/10.1021/ja909022p].<br />
:The paper uses <sup>1</sup>H NMR to monitor the C-H activation reaction of a 17-electron Rhodium(0) species into two 16-electron complexes. As the reaction proceeds, the broad paramagnetic peaks disappear and the signals corresponding to the dimagnetic products grow. The growth of peaks allows monitoring of the reaction, hence kinetic studies can be performed. [[User:ReneeMan|ReneeMan]]<br />
<br />
<br />
''"Crystal-Structure Determination of Powdered Paramagnetic Lanthanide Complexes by Proton NMR Spectroscopy'', Gwendal Kervern, Anthony D'Aleo, Loic Toupet, Olivier Maury, Lyndon Emsley, and Guido Pintacuda, ''Angew. Chem. Int. Ed.'', '''2009''', ''48'', 3082-3086, [http://dx.doi.org/10.1002/anie.200805302 doi: 10.1002/anie.200805302] <br />
: Solid-state NMR spectroscopy can be used for structure determination of microcrystalline paramagnetic solids at natural isotopic abundance. The protocol makes use of paramagnetic effects, measured on suitably recorded <sup>1</sup>H NMR spectra, to define the conformation of a molecule in the lattice and the intermolecular packing in the solid phase. [[User:CuilingXu|CuilingXu]]<br />
<br />
==Electron Paramagnetic Resonance Spectroscopy==<br />
[[File:2009W2-C529-S022.pdf|thumb|Preliminary lecture notes, copyright Pierre Kennepohl, all rights reserved]]<br />
<br />
Electron Paramagnetic Resonance (EPR) spectroscopy is a technique that uses the same principles as those in NMR, but applied to the angular momentum states of electrons rather than nuclei. EPR is also sometime called electron spin resonance (ESR) although this terminology is somewhat outdated. As with NMR, the Zeeman effect only applies if there exists more than one angular momentum state of the system, therefore unparied electrons (such that <math>S>0</math>) are required to observe an EPR signal. Given that the gyromagnetic ratio of an electron is approximately <math>10^3</math> times larger than that of a proton, the Zeeman splitting requires much larger photon energies for similar magnetic fields. EPR therefore generally uses microwaves rather than radiowaves. Although the technique is essentially identical to NMR, the information content of the technique is quite different in many respects given that the origin of observed chemical shifts are very different.<br />
<br />
===Common uses of EPR in inorganic chemistry===<br />
<br />
* determining the spin state of a compound<br />
<br />
=== Literature examples of EPR in inorganic chemistry ===<br />
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<!-- Note: Remember to sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
<br />
''" EPR Studies of SiBNC Preceramic Polymers and Ceramic Employing Isotope Labeling"'', Y.H. Sehlleier, Y. Akdogan, A. Verhoeven, E. Roduner, and M. Jansen, ''Chem. Mater.'', '''2008''', 20, 7563-7569. [http://dx.doi.org/10.1021/cm801889w doi:10.1021/cm801889w].<br />
: This article examines the pyrolysis process of preceramic polymers to ceramic materials. They use isotope labeled EPR, SQUID and NMR to look at the polymers after pyrolysis at a variety of temperatures. It was shown that the unpaired electron spends some time around the <sup>13</sup>C nuclei as well as the <sup>15</sup>N nuclei from the broadening of the EPR spectra. [[User:AmberJuilfs|AmberJuilfs]]<br />
<br />
''" EPR Study of the Low-Sping [d<sup>3</sup>; S=1/2], Jahn-Teller-Active, Dinitrogen Complex of a Molybdenum Trisamido Amine"'', R.L. McNaughton, J.M. Chin, W.W. Weare, R.R. Schrock, and B.M. Hoffman, ''J. Am. Chem. Soc.'', '''2007''', 129, 3480-3482. [http://dx.doi.org/10.1021/ja068546u doi:1021/ja068546u].<br />
: This article explores the Mo-N<sub>2</sub> complex which is capable of catalytic turn over, forming ammonia. The Mo-N<sub>2</sub> complex exists as an extremely rare low spin d<sup>3</sup> complex, S=1/2. The electronic and vibronic strucutre of the Mo-N<sub>2</sub> complex are described using EPR. [[User:TrumanWambach|TrumanWambach]]<br />
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''"Synthesis and Characterization of V<sup>V</sup>(3,6-DBSQ)(3,6-DBCat)<sub>2</sub>, a d<sup>0</sup> Metal Complex with Dioxygenase Catalytic Activity"'', A.M. Morris, C.G. Pierpont, and R.G. Finke, ''Inorg. Chem.'', '''2009''', 48, 3496-3498, [http://dx.doi.org/10.1021/ic802122q doi:10.1021/ic802122q].<br />
: This article reports the synthesis of V<sup>V</sup>(3,6-DBSQ)(3,6-DBCat)<sub>2</sub> (3,6-DBSQ = 3,6-di-''tert''-butylsemiquinone, 3,6-DBCat = 3,6-di-''tert''-butylcatechol), which is characterized with X-ray crystallography, UV-Vis and EPR spectroscopy. It was also found that this complex had catalytic activity towards dioxygenase. Using EPR, it was shown that the 3,6-DBSQ radical couples to the <sup>51</sup>V center as well as two protons form the SQ ring, which provides supporting evidence of chemical structure. [[User:JackyYim|JackyYim]]<br />
<br />
''"Hopping of Thiolate Ligands between Au Nanoparticles Revealed by EPR Spectroscopy"'', M. Zachary and V. Chechik, ''Angew. Chem. Int. Ed.'' '''2007''', ''46'', 3304-3307, [http://dx.doi.org/10.1002/anie.200604070 doi.10.1002/anie.200604070] .<br />
: The use of EPR spectroscopy in monitoring the exchange of stabilizing ligands between Au nanoparticles is explored in this article. One set of nanoparticle was functionalized by nitroxide spin label, and the particles are left overnight with another set of octanethiol-protected nanoparticles for the ligand exchange to occur. The EPR spectrum of the reaction mixture changes from a broad line to a triplet, as the nitroxide ligands exchange with the octanethiol ligands. Kinetic studies using the EPR spectra have shown that the maximum conversion of the reaction is independent of the initial concentrations, indicating that the rate-determining step of the reaction is the slow desorption of the nitroxide ligand from the surface of the Au nanoparticle. [[User:ReneeMan|ReneeMan]]<br />
<br />
''"Isolation of Dysprosium and Yttrium Complexes of a Three-Electron Reduction Product in the Activation of Dinitrogen, the (N<sub>2</sub>)<sup>3-</sup> Radical"'', William J. Evans, Ming Fang, Gael Zucchi, Filipp Furche, Joseph W. Ziller, Ryan M. Hoekstra, Jeffrey I. Zink, ''J. Am. Chem. Soc.'', '''2009''', ''131'', 11195-11202, [http://dx.doi.org/10.1021/ja9036753 doi:10.1021/ja9036753].<br />
: EPR spectroscopy is used to show a radical electron existing on a dinitrogen ligand, verifying that the synthesized side-on bridged yttrium complex is indeed the first example of a (N<sub>2</sub>)<sup>3-</sup> compound. EPR spectroscopy studies were furthered with <sup>15</sup>N<sub>2</sub> coordination, resulting in altered splitting patterns.[[User:Lwence|Lwence]]<br />
<br />
''"Spin Trapping of Au-H Intermediate in the Alcohol Oxidation by Supported and Unsupported Gold Catalysts"'', M. Conte, H. Miyamura, S. Kobayashi, and V. Chechik, ''J. Am. Chem. Soc.'', '''2009''', 131, 7189-7196. [http://dx.doi.org/10.1021/ja809883c doi:10.1021/ja809883c].<br />
: The mechanism of alcohol oxidation by supported and unsupported gold catalysts is studied using electron paramagnetic resonance (EPR) spectroscopy and spin trapping. The spin traps DMPO and PBN are nitrones that react with short-lived radicals to produce a more stable spin adduct that is itself a radical. The spin adduct can then be detected using EPR spectroscopy, allowing reaction intermediates to be identified. Isotopic labelling and anaeorbic oxidation experiments are also performed; the authors conclude that the reaction proceeds through a Au-H intermediate, and that the role of O<sub>2</sub> is to regenerate the catalyst as opposed to oxidizing the alcohol. [[User:BrianSahli|BrianSahli]]<br />
<br />
"In Vitro Monitoring of Poly(ortho ester) Degradation by Electron Paramagnetic Resonance Imaging", S. Capancioni et al., Macromolecules, 2003, 36, 6135-6141. [http://dx.doi.org/10.1021/ma034365q doi:10.1021/ma034365q].<br />
: This paper outlines the use of EPR techniques to track the degradation of biodegradable polymers in the body. The polymers were used as drug delivery systems and EPR was used on nitroxide radical labeled polymers to track changes in pH over time during the degradation process. [[User:Kimosten|Kimosten]]<br />
<br />
<br />
''"Two conformations in the human kinesin power stroke defined by X-ray crystallography and EPR spectroscopy"'', C.V. Sincdelar, M.J. Budny, S. Rice, N. Naber, ''Nature Structural Biology'', '''2002''', 9, 844. [http://dx.doi.org/10.1021/jmsb852 doi:10.1021/jmsb852]. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
<br />
''" A Stable and Crystalline Triarylgermyl Radical: Structure and EPR Spectra"'', Christian Drost, Jan Griebel, Reinhard Kirmse, Peter L�nnecke, and Joachim Reinhold, ''Angew. Chem. Int. Ed.'', '''2009''', ''48'', 1962-1965. [http://dx.doi.org/10.1002/anie.200805328 doi:10.1002/anie.200805328].<br />
: In this paper, the author showed the synthesis of the first stable triarylgermyl radical: Ge[3,5-''t''Bu<sub>2</sub>-2,6-(EtO)<sub>2</sub>C<sub>6</sub>H]<sub>3</sub>. X-ray crystallography and EPR were used to determine the structure of the radical both in solid state and solution. Studies showed that the radical is planar in solid state and pyramidal in solution. <br />
[[User:CuilingXu|CuilingXu]]<br />
<br />
==Mössbauer Spectroscopy==<br />
[[File:2009W2-C529-S023.pdf|thumb|Preliminary lecture notes, copyright Pierre Kennepohl, all rights reserved]]<br />
<br />
<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 Chem 529] <> [http://wiki.ubc.ca/Ground_State_Spectroscopic_Methods Ground State Spectroscopic Methods]<br />
[[Category:Ground State Spectroscopies]]<br />
[[Category:Chemistry]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Ground_State_Spectroscopic_Methods&diff=69151Ground State Spectroscopic Methods2011-01-11T17:06:55Z<p>Pierre: </p>
<hr />
<div>[http://wiki.ubc.ca/Course:Chem529 Chem 529] <> [http://wiki.ubc.ca/Ground_State_Spectroscopic_Methods Ground State Spectroscopic Methods]<br />
<br />
==Vibrational Spectroscopy==<br />
[[File:2009W2-C529-S013.pdf|thumb|Preliminary lecture notes, copyright Pierre Kennepohl, all rights reserved]]There are two distinct approaches to vibrational spectroscopy: infrared absorption spectroscopy (a single photon technique) and Raman spectroscopy (a two photon inelastic scattering technique). Each carries its own set of selection rules, thus each can give complementary information regarding the vibrational modes of a molecule.<br />
<br />
===Infrared spectroscopy===<br />
<br />
===Raman spectroscopy===<br />
<br />
=== Literature examples of the use of vibrational spectroscopy in inorganic chemistry ===<br />
<br />
<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
<br />
''"Imaging of single GaN nanowires by tip-enhanced Raman spectroscopy"'', N. Marquestaut, D. Talaga, L. Servant, P. Yang, P. Pauzauskie, F. Lagugné-Labarthet, ''Journal of Raman Spectroscopy'', '''2009''', 40(10), 1441-1445, [http://dx.doi.org/10.1002/jrs.2404 doi:10.1002/jrs.2404].<br />
: This article demonstrates the use of an AFM microscopy used in tandem with a Raman spectroscopy to determine the physical dimensions of a GaN nanowire. Typically well defined objects of sizes on the order of (lambda/2) can be observed by raman, but by using tip-enhanced Raman spectroscopy (TERS) this spatial resolution can be enhanced. The GaN nanowire analyzed in this paper was on the order of ~200 nm. [[User:EricPrice|EricPrice]]<br />
<br />
"Effect of high external pressure on the vibrational spectra of crystalline dichloro(1.5-cycloctadiene)platinum(II)", JA Baldwin, IS Butler and DFR Gilson, "Inorganica Chimica Acta", 2006, 359, 3079-3083, [http://dx.doi.org/10.1016/j.ica.2006.02.003 doi:10.1016/j.ica.2006.02.003].<br />
: This article used high pressure IR and Raman spectroscopy to investigate the bonding in a dichloro-COD platinum complex. They assign the IR and Raman bands based on previous work and use the pressure dependencies of certain bands in the spectra to make conclusions about structural deformations at high pressure and how they can influence the strength of pi-backbonding in this molecule. [[User:Kimosten|Kimosten]]<br />
<br />
"A two-dimensional IR correlation spectroscopic study of the conformational changes in syndiotactic polypropylene during crystallization", K. Zheng, R. Liu, Y. Huang, "Polymer Journal", "2010", 42, 81-85 [http://dx.doi.org/10.1038/pj.2009.304 doi:10.1038/pj.2009.304].<br />
: This article examines the melting/crystallization of syndiotactic polypropylene by using FTIR and 2D correlation analysis. The changes are seen through the intensities of peaks known to be associated with the crystalline and amorphous forms of the polymer. The 2D correlation analysis gives insight to the order of change within the polymer during these two processes (melting, crystallization). [[User:AmberJuilfs|AmberJuilfs]]<br />
<br />
''"Isolation of Dysprosium and Yttrium Complexes of a Three-Electron Reduction Product in the Activation of Dinitrogen, the (N<sub>2</sub>)<sup>3-</sup> Radical"'', William J. Evans, Ming Fang, Gael Zucchi, Filipp Furche, Joseph W. Ziller, Ryan M. Hoekstra, Jeffrey I. Zink, ''J. Am. Chem. Soc.'', '''2009''', ''131'', 11195-11202, [http://dx.doi.org/10.1021/ja9036753 doi:10.1021/ja9036753].<br />
: This article concentrates on synthesis of N<sub>2</sub> complexes involving yttrium and dysprosium, and analysis of the N-N bond order using Raman spectroscopy. Data is compared to computational values, and <sup>15</sup>N isotopic substitution experiments were conducted. [[User:Lwence|Lwence]]<br />
<br />
'''Spectroscopic Properties and Quantum Chemistry-Based Normal Coordinate Analysis (QCB-NCA) of a Dinuclear Tantalum complex Exhibiting the Novel Side-On End-On Bridging Geometry of N<sub>2</sub>: Correlation to Electronic Structure and Reactivity"'', Felix Studt, Bruce A. MacKay, Michael D. Fryzuk, Felix Tuczek, ''J. Am. Chem. Soc.'', '''2003''', ''126'', 280-290, [http://dx.doi.org/10.1021/ja036997y doi:10.1021/ja036997y]. [[User:TrumanWambach|TrumanWambach]]<br />
: IR, Raman, isotopic substitution and computations are used in concert to throughly describe the bonding in a dimeric tantalum N<sub>2</sub> compound. IR and Raman spectra are calculated, and assigned to a molecular vibration. Computations are then compared to experimental values. Force constants are assigned to the bonds of interest.<br />
<br />
''"Probing thin-film morphology of conjugated polymers by Raman spectroscopy"'', Jessica M. Winfield, Carrie L. Donley, Richard H. Friend, Ji-Seon Kim, ''J. Appl. Phys.'', '''2010''', ''107'', 024902, [http://dx.doi.org/10.1063/1.3276257 doi:10.1063/1.3276257].<br />
: This article demonstrates how Raman spectroscopy can be used to compare the thin-film morphology of conjugated polymers at the polymer-substrate interface versus that in the bulk polymer. It is shown that near the substrate interface[poly(9,9-di-n-octylfluorene-alt-benzothiadiazole (F8BT)] adopts a more planar conformation (has a lower torsion angle between the alternating units). The morphology of conjugated polymers at interfaces is very important in light-emitting diode and field-effect transistor applications where charge transport occurs near the polymer-substrate interface. ([[User:AshleeHowarth|AshleeHowarth]])<br />
<br />
''"Resonance Raman Scattering from Solutions of C<sub>60</sub>"'', S.H. Gallagher, R.S. Armstrong, W.A. Clucas, P.A. Lay, C.A. Reed, ''J. Phys. Chem. A.'', '''1997''', 101''(16)'', 2960-2968. [http://dx.doi.org/10.1021/jp970232t doi:10.1021/jp970232t].<br />
: The resonance raman excitation spectrum of fullerene (C<sub>60</sub>) is studied at eight excitation wavelengths. Raman excitation calculations were performed on the five most intense resonance bands to correlate the bands with the vibrational modes of fullerene. Rare (D-type) scattering is observed. It is determined that the symmetry of C<sub>60</sub> is distorted by solvent, as there are Raman-silent vibrational modes present. The symmetry of the distorted excited state of fullerene is D<sub>5h</sub>. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Photoinduced Orientation of Azobenzene Chromophores in Amorphous Polymer As Studied by Real-Time Visible and FTIR Spectroscpies"'', T. Buffeteau, F. Lagugne-Labarthet, M. Pezolet, and C. Sourisseau, ''Macromolecules'', '''1998''', 31(21), 7312-7320, [http://dx.doi.org/10.1021/ma980843z doi:10.1021/ma980843z].<br />
: This article shows the use of visible (birefringent studies) and infrared (polarization modulated FTIR) spectroscopy to study the dynamics of photoinduced orientation of doped and co-polymers of azobenzenes. Polarization modulated infrared spectroscopy (PM-FTIR)is a form of IR which allows the observation of the amount of order in a given anisotropic sample. The authors used this technique to observe the orientation (by photoinduction) and relaxation of DR1 in a matrix of PMMA. [[User:JackyYim|JackyYim]]<br />
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''"Charging effects on bonding and catalyzed oxidation of CO on Au-8 clusters on MgO"'', Yoon B, Hakkinen H, Landman U, Worz AS, Antonietti JM, Abbet S, Judai K, Heiz U, ''SCIENCE'', '''2005''', 307(5708), 403-407, [http://dx.doi.org/10.1126/science.1104168 doi:10.1126/science.1104168].<br />
: This article investigates on how gold octamers bound to oxygen-vacancy F-center defects on MgO(001) activate adsorbed CO and O2 and catalyze the oxidation of CO. The authors use infrared spectroscopy to measure the stretch vibration of CO and it shows a red shift by 25 to 50 cm-1. This shift is caused by enhanced backdonation from the gold nanocluster into the antibonding 2pi* orbital of the CO. All the experimental results agree with quantum calculations. [[User:CuilingXu|CuilingXu]]<br />
<br />
<br />
''"Real-time monitoring of microwave-promoted organometallic ligand-substitution reactions using ''in situ'' Raman spectroscopy"'', T. M. Barnard and N. E. Leadbeater, ''Chem. Commun.'', '''2006''', 3615.<br />
[http://dx.doi.org/10.1039/b608793k doi:10.1039/b608793k].<br />
<br />
: The article demonstrates an application of Raman spectroscopy in monitoring progress in organometallic ligand-substitution reactions ''in situ'', while using microwave irradiation to facilitate the reaction. This allows reaction conditions to be easily optimized and does not require much trial and error, but requires the help of some literature data. The theory is tested with the substitution of a CO ligand with some ligands in Mo(CO)<sub>6</sub>, where the course of substitution is monitored with Raman spectroscopy without aliquots removed and conserves time. [[User:ReneeMan|ReneeMan]]<br />
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''"Synthesis, Crystal Structure, and Vibrational Spectroscopy of K<sub>2</sub>Ca<sub>4</sub>Si<sub>8</sub>O<sub>21</sub>—An Unusual Single-Layer Silicate Containing Q2 and Q3 Units"'', E. Arroyabe, R. Kaindl, D.M. Tbbens and V. Kahlenberg, ''Inorg. Chem.'', '''2009''', ''48'', 11929–11934., [http://dx.doi.org/10.1021/ic901762u doi:10.1021/ic901762u].<br />
<br />
: The author synthesized a novel silicate, and determined its crystal structure. Confocal Raman spectrum of a single crystal of this silicate was also studied in this article. The author assigned the fequencies to specific vibrational modes, and concluded that K<sub>2</sub>Ca<sub>4</sub>Si<sub>8</sub>O<sub>21</sub> is a silicate based on loop-branched chains. [[User:JiazhangWang|JiazhangWang]]<br />
<br />
''"Comparison of the Structures and Wetting Properties of Self-Assembled Monolayers of n-Alkanethiols on the Coinage Metal Surfaces, Cu, Ag, Au."'', P. Laibinis, G. Whitesides, D. Allara, Y. Tao, A. Parikh, R. Nuzzo, ''Journal of the American Chemical Society'', '''1991''', 113, 7152-7167, [http://dx.doi.org/10.1021/ja00019a011 doi:10.1021/ja00019a011].<br />
<br />
:Reflection-absorption infrared spectroscopy (RAIRS) is used to determine the crystallinity and cant angle of straight-chain alkanethiols adsorbed on Cu and Ag. These measurements are then compared to the well-studied system of alkanethiols adsorbed on Au. RAIRS uses p-polarized incident light to take advantage of the "surface selection rule," which states that only vibrations with a transition-dipole moment component perpendicular to the plane of the metal substrate can be observed. The intensity of a particular vibration is compared to that of a bulk spectrum and the orientation of the vibration relative to the substrate can be determined. [[User:BrianSahli|BrianSahli]]<br />
<br />
==Nuclear Magnetic Resonance Spectroscopy==<br />
[[File:2009W2-C529-S021a.pdf|thumb|Preliminary lecture notes, copyright Pierre Kennepohl, all rights reserved]]<br />
Nuclear magnetic resonance spectroscopy is probably the most widely used spectroscopic technique in modern chemistry. It allows for rapid and accurate characterization of organic molecules as well as more in-depth studies of electronic and geometric structure of a wide range of molecules.The technique relies on the quantum mechanical behaviour of atomic nuclei, most particularly their ground state angular momentum (<math>I_g</math>). NMR active nuclei must have <math>I_g>0</math> such that they have more than one magnetic state (# of states = <math>2I+1</math>). NMR uses the Zeeman effect, the splitting of angular momentum states in a magnetic field, to create a situation where one can probe the nuclear states with electromagnetic radiation.<br />
<br />
=== Common uses of NMR in inorganic chemistry ===<br />
<br />
* identification of compounds<br />
* help with mechanism elucidation<br />
* kinetics studies<br />
* isotopic labelling experiments<br />
* solid state identification<br />
* paramagnetic/diamagnetic verification<br />
<br />
=== Literature examples of NMR in inorganic chemistry ===<br />
<br />
<!-- Note: Remember to sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
''"Neutral-Ligand Complexes of Bis(imino)pyridine Iron: Synthesis, Strucutre, and Spectrososcopy"'', S.C. Bart, E. Lobkovsky, E. Bill, K. Wieghardt, P.J. Chirik, "Inorg. Chem.", '''2007''', 46, 7055-7063, http://dx.doi.org/10.1021/ic700869h <br />
: A series of bis(imino)pyridine (PDI) iron complexes are synthesized and characterized using I.R. NMR, and Mossbauer spectroscopy. It is found that temperature independent paramagnetism occurs (TIP). TIP if found to be a function of donor strength. Upon two electron reduction of the system the ligand displays redox activity. Weak field ligands stabilize the S=0 ground state, where the redox active ligand (S=1) is antiferromagnetically coupled to the Fe(II) high spin iron center (S=1). Stronger field ligands stabilize the excited state (S=1).[[User:TrumanWambach|TrumanWambach]]Truman <br />
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"Synthesis, Structures, Bonding, and Redox Chemistry of Ditungsten Butadiyne Complexes with WCCW Backbones", J. Sun, E. Shaner, M.K. Jones, D.C. O'Hanlon, J.S. Mugridge, and M.D. Hopkins, <i>Inorganic Chem.</i>, <b>2010</b>, 49, 1687-1698, [http://dx.doi.org/10.1021/ic902088x doi:10.1021/ic902088x].<br />
: This article reports the synthesis of a new Tungsten-Carbon triply bonded species of the form XL<sub>4</sub>WCCWL<sub>4</sub>X, where L = 1/2 dmpe, 1/2 depe, P(OMe)<sub>3</sub> and X = Cl, OTf. They used both X-ray crystallography and NMR to observe the molecule. They also performed DFT calculations to observe the bonding of the species. Through <sup>31</sup>P NMR they were able to observe the degradation of the molecule by seeing the formation of free ligands. [[User:AmberJuilfs|AmberJuilfs]]<br />
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''"Na-Y Zeolite as a Highly Active Catalyst for the Hydroamination of α,β-Unsaturated Compounds with Aromatic Amines"'', K. Komura, R. Hongo, J. Tsutsui, and Y. Sugi, ''Catal. Lett.'', '''2009''', 128, 203-209, [http://dx.doi.org/10.1007/s10562-008-9738-4 doi:10.1007/s10562-008-9738-4].<br />
: This article reports the use of Zeolite as a reusable, green solid catalyst for hydroamination to produce fine chemicals. The authors use the hydroamination of aniline with methyl acrylate as a their test reaction and found Na-Y shows high catalytic activity and mono-product selectivity. To study the mechanism by which this transformation occurs, <sup>13</sup>C MAS NMR and solution <sup>13</sup>C NMR of methyl acrylate adsorpted Na-Y zeolite were compared. It was found that Na-Y activates methyl acrylate through a Lewis-acid interaction between the carbonyl and sodium ion. [[User:JackyYim|JackyYim]]<br />
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''"Insertion Reactions of trans-Mo(dmpe)<sub>2</sub>(H)(NO) with Imines"'', F. Liang, H. W. Schmalle, and H. Berke, ''Inorg. Chem.'', '''2004''', 43, 993-999, [http://dx.doi.org/10.1021/ic030139l doi:10.1021/ic0301391].<br />
: The insertion of a disubstituted aromatic imine into the metal-hydrogen bond of a molybdenum hydride complex is studied using variable temperature <sup>1</sup>H NMR. By comparing the relative peak intensities of product and reactant at different temperatures the standard enthalpy and entropy of reaction are determined. This is done using a van't Hoff plot, which plots ln K vs. 1/T. The calculated change in enthalpy and entropy were -48.8 kJ/mol and -33 J/(K mol), respectively. [[User:BrianSahli|BrianSahli]]<br />
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''"Structural and thermodynamical properties of CuII amyloid-beta16/28 complexes associated with Alzheimer's disease"". Guilloreau, L.; Damian, L.; Coppel, Y.; Mazarguil, H.; Winterhalter, M.; Faller, P. Journal Of Biological Inorganic Chemistry: JBIC: A Publication Of The Society Of Biological Inorganic Chemistry 2006, 11, 1024-1038, [http://dx.doi.org/10.1007/s00775-006-0154-1 doi:10.1007].<br />
: Amyloid-beta peptide interaction with the paramagnetic metal Cu(II) is investigated by 1D proton NMR. The paramagnetic shift/broading that occurs in the NMR signals of amino acid residues that are bound with Cu(II) are used to identify them as ligands. The signals from other residues are also broadened and shifted due to the influence of the paramagnetic metal, and so substoichiometric amounts of Cu(II) are used in order to see the most dramatic broadening occur at the coordinated amino acids.[[User:EricPrice|EricPrice]]<br />
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''"Diphenylphosphino- or Dicyclohexylphosphino-Tethered Boryl Pincer Ligands: Synthesis of PBP Iridium(III) Complexes and Their Conversion to Iridium-Ethylene Complexes"'', Y. Segawa, M. Yamashita, and K. Nozaki, ''Organometallics'', '''2009''', ''28'', 6234-6242, [http://dx.doi.org/10.1021/om9006455 doi:10.1021].<br />
:This article focuses on synthesis and characterization of various Ir PBP pincer complex derivatives. NMR studies are of interest as up to 4 different NMR active nuclei (<sup>31</sup>P, <sup>11</sup>B, <sup>1</sup>H, and <sup>13</sup>C) may be bound to the metal centre at once.[[User:Lwence|Lwence]]<br />
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"Characterization of wurtzite indium nitride synthesized from indium oxide by In-115 MAS NMR spectroscopy", W.S. Jung, O.H. Han and S.A. Chae, Materials Letters, 2007, 61, 3413-3415, [http://dx.doi.org/10.1016/j.matlet.2006.11.083 doi:10.1016/j.matlet.2006.11.083].<br />
: This article outlines the characterization of wurtzite indium nitride (w-InN) samples made using different conditions using 115-In MAS NMR spectroscopy. The authors used this technique, in addition to XRD, to identify the different phases present in each sample and found that samples made using higher temperatures had a w-InN structure with extra In incorporated, due to thermal decomposition. [[User:Kimosten|Kimosten]]<br />
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''"29Si NMR Relaxation of Silicated Nanoparticles in Tetraethoxysilane-Tetrapropylammonium Hydroxide-Water System (TEOS-TPAOH-H2O)"'', M. Haouas, D. Petry, M. Anderson, F. Taulelle, ''J. Phys. Chem. C'', '''2009''', ''113'', 10838-10841, [http://dx.doi.org/10.1021/jp903454f doi:10.1021/jp903454f].<br />
:In an attempt to understand how zeolites nucleate and grow, silicon-29 NMR relaxation times are measured from a silicalite-1 precursor solution. Nanoparticles and silicate oligomers in the solution all give rise to observable resonances. From these resonances the Qn distribution of nanoparticles in the solution can be measured and therefore the progressive connectivity of the nanoparticles to form zeolites can be followed. ([[User:AshleeJHowarth|AshleeJHowarth]])<br />
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''"Multiple Functional Groups of Varying Ratios in Metal-Organic Frameworks"'', Hexiang Deng, Christian J. Doonan, Hiroyasu Furukawa, Ricardo B. Ferreira, John Towne, Carolyn B. Knobler, Bo Wang, Omar M. Yaghi, ''Science'', '''2010''', 327, 846-850, [http://dx.doi.org/10.1126/science.1181761 doi:10.1126/science.1181761].<br />
: This article reports a set of synthesized multivariate metal-organic frameworks (MTV-MOF). The frameworks are composed of metal-oxide joints and 1,4-benzenedicarboxylate and its derivatives links and a "complex" secondary structure formed by multivaried arrangements of many functional groups. The structures is ordered, and highly porous. They can achieve better capacity and selectivity in gas storage. <sup>13</sup>C CP/MAS NMR study indicates the presence of multi functional organic links in the MOF backbone without unbound link in crystals. <sup>1</sup>H NMR spectra indicates the link ratio of their crystals. [[User:Jiazhang|Jiazhang]]<br />
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''"Rhodium(0) Metalloradicals in Binuclear C-H Activation"'', F. F. Puschmann, H. Grutzmacher, B. de Bruin, ''J. Am. Chem. Soc.'' '''2010''', ''132'', 73-75, [http://dx.doi.org/10.1021/ja909022p].<br />
:The paper uses <sup>1</sup>H NMR to monitor the C-H activation reaction of a 17-electron Rhodium(0) species into two 16-electron complexes. As the reaction proceeds, the broad paramagnetic peaks disappear and the signals corresponding to the dimagnetic products grow. The growth of peaks allows monitoring of the reaction, hence kinetic studies can be performed. [[User:ReneeMan|ReneeMan]]<br />
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''"Crystal-Structure Determination of Powdered Paramagnetic Lanthanide Complexes by Proton NMR Spectroscopy'', Gwendal Kervern, Anthony D'Aleo, Loic Toupet, Olivier Maury, Lyndon Emsley, and Guido Pintacuda, ''Angew. Chem. Int. Ed.'', '''2009''', ''48'', 3082-3086, [http://dx.doi.org/10.1002/anie.200805302 doi: 10.1002/anie.200805302] <br />
: Solid-state NMR spectroscopy can be used for structure determination of microcrystalline paramagnetic solids at natural isotopic abundance. The protocol makes use of paramagnetic effects, measured on suitably recorded <sup>1</sup>H NMR spectra, to define the conformation of a molecule in the lattice and the intermolecular packing in the solid phase. [[User:CuilingXu|CuilingXu]]<br />
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==Electron Paramagnetic Resonance Spectroscopy==<br />
[[File:2009W2-C529-S022.pdf|thumb|Preliminary lecture notes, copyright Pierre Kennepohl, all rights reserved]]<br />
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Electron Paramagnetic Resonance (EPR) spectroscopy is a technique that uses the same principles as those in NMR, but applied to the angular momentum states of electrons rather than nuclei. EPR is also sometime called electron spin resonance (ESR) although this terminology is somewhat outdated. As with NMR, the Zeeman effect only applies if there exists more than one angular momentum state of the system, therefore unparied electrons (such that <math>S>0</math>) are required to observe an EPR signal. Given that the gyromagnetic ratio of an electron is approximately <math>10^3</math> times larger than that of a proton, the Zeeman splitting requires much larger photon energies for similar magnetic fields. EPR therefore generally uses microwaves rather than radiowaves. Although the technique is essentially identical to NMR, the information content of the technique is quite different in many respects given that the origin of observed chemical shifts are very different.<br />
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===Common uses of EPR in inorganic chemistry===<br />
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* determining the spin state of a compound<br />
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=== Literature examples of EPR in inorganic chemistry ===<br />
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''" EPR Studies of SiBNC Preceramic Polymers and Ceramic Employing Isotope Labeling"'', Y.H. Sehlleier, Y. Akdogan, A. Verhoeven, E. Roduner, and M. Jansen, ''Chem. Mater.'', '''2008''', 20, 7563-7569. [http://dx.doi.org/10.1021/cm801889w doi:10.1021/cm801889w].<br />
: This article examines the pyrolysis process of preceramic polymers to ceramic materials. They use isotope labeled EPR, SQUID and NMR to look at the polymers after pyrolysis at a variety of temperatures. It was shown that the unpaired electron spends some time around the <sup>13</sup>C nuclei as well as the <sup>15</sup>N nuclei from the broadening of the EPR spectra. [[User:AmberJuilfs|AmberJuilfs]]<br />
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''" EPR Study of the Low-Sping [d<sup>3</sup>; S=1/2], Jahn-Teller-Active, Dinitrogen Complex of a Molybdenum Trisamido Amine"'', R.L. McNaughton, J.M. Chin, W.W. Weare, R.R. Schrock, and B.M. Hoffman, ''J. Am. Chem. Soc.'', '''2007''', 129, 3480-3482. [http://dx.doi.org/10.1021/ja068546u doi:1021/ja068546u].<br />
: This article explores the Mo-N<sub>2</sub> complex which is capable of catalytic turn over, forming ammonia. The Mo-N<sub>2</sub> complex exists as an extremely rare low spin d<sup>3</sup> complex, S=1/2. The electronic and vibronic strucutre of the Mo-N<sub>2</sub> complex are described using EPR. [[User:TrumanWambach|TrumanWambach]]<br />
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''"Synthesis and Characterization of V<sup>V</sup>(3,6-DBSQ)(3,6-DBCat)<sub>2</sub>, a d<sup>0</sup> Metal Complex with Dioxygenase Catalytic Activity"'', A.M. Morris, C.G. Pierpont, and R.G. Finke, ''Inorg. Chem.'', '''2009''', 48, 3496-3498, [http://dx.doi.org/10.1021/ic802122q doi:10.1021/ic802122q].<br />
: This article reports the synthesis of V<sup>V</sup>(3,6-DBSQ)(3,6-DBCat)<sub>2</sub> (3,6-DBSQ = 3,6-di-''tert''-butylsemiquinone, 3,6-DBCat = 3,6-di-''tert''-butylcatechol), which is characterized with X-ray crystallography, UV-Vis and EPR spectroscopy. It was also found that this complex had catalytic activity towards dioxygenase. Using EPR, it was shown that the 3,6-DBSQ radical couples to the <sup>51</sup>V center as well as two protons form the SQ ring, which provides supporting evidence of chemical structure. [[User:JackyYim|JackyYim]]<br />
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''"Hopping of Thiolate Ligands between Au Nanoparticles Revealed by EPR Spectroscopy"'', M. Zachary and V. Chechik, ''Angew. Chem. Int. Ed.'' '''2007''', ''46'', 3304-3307, [http://dx.doi.org/10.1002/anie.200604070 doi.10.1002/anie.200604070] .<br />
: The use of EPR spectroscopy in monitoring the exchange of stabilizing ligands between Au nanoparticles is explored in this article. One set of nanoparticle was functionalized by nitroxide spin label, and the particles are left overnight with another set of octanethiol-protected nanoparticles for the ligand exchange to occur. The EPR spectrum of the reaction mixture changes from a broad line to a triplet, as the nitroxide ligands exchange with the octanethiol ligands. Kinetic studies using the EPR spectra have shown that the maximum conversion of the reaction is independent of the initial concentrations, indicating that the rate-determining step of the reaction is the slow desorption of the nitroxide ligand from the surface of the Au nanoparticle. [[User:ReneeMan|ReneeMan]]<br />
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''"Isolation of Dysprosium and Yttrium Complexes of a Three-Electron Reduction Product in the Activation of Dinitrogen, the (N<sub>2</sub>)<sup>3-</sup> Radical"'', William J. Evans, Ming Fang, Gael Zucchi, Filipp Furche, Joseph W. Ziller, Ryan M. Hoekstra, Jeffrey I. Zink, ''J. Am. Chem. Soc.'', '''2009''', ''131'', 11195-11202, [http://dx.doi.org/10.1021/ja9036753 doi:10.1021/ja9036753].<br />
: EPR spectroscopy is used to show a radical electron existing on a dinitrogen ligand, verifying that the synthesized side-on bridged yttrium complex is indeed the first example of a (N<sub>2</sub>)<sup>3-</sup> compound. EPR spectroscopy studies were furthered with <sup>15</sup>N<sub>2</sub> coordination, resulting in altered splitting patterns.[[User:Lwence|Lwence]]<br />
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''"Spin Trapping of Au-H Intermediate in the Alcohol Oxidation by Supported and Unsupported Gold Catalysts"'', M. Conte, H. Miyamura, S. Kobayashi, and V. Chechik, ''J. Am. Chem. Soc.'', '''2009''', 131, 7189-7196. [http://dx.doi.org/10.1021/ja809883c doi:10.1021/ja809883c].<br />
: The mechanism of alcohol oxidation by supported and unsupported gold catalysts is studied using electron paramagnetic resonance (EPR) spectroscopy and spin trapping. The spin traps DMPO and PBN are nitrones that react with short-lived radicals to produce a more stable spin adduct that is itself a radical. The spin adduct can then be detected using EPR spectroscopy, allowing reaction intermediates to be identified. Isotopic labelling and anaeorbic oxidation experiments are also performed; the authors conclude that the reaction proceeds through a Au-H intermediate, and that the role of O<sub>2</sub> is to regenerate the catalyst as opposed to oxidizing the alcohol. [[User:BrianSahli|BrianSahli]]<br />
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"In Vitro Monitoring of Poly(ortho ester) Degradation by Electron Paramagnetic Resonance Imaging", S. Capancioni et al., Macromolecules, 2003, 36, 6135-6141. [http://dx.doi.org/10.1021/ma034365q doi:10.1021/ma034365q].<br />
: This paper outlines the use of EPR techniques to track the degradation of biodegradable polymers in the body. The polymers were used as drug delivery systems and EPR was used on nitroxide radical labeled polymers to track changes in pH over time during the degradation process. [[User:Kimosten|Kimosten]]<br />
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''"Two conformations in the human kinesin power stroke defined by X-ray crystallography and EPR spectroscopy"'', C.V. Sincdelar, M.J. Budny, S. Rice, N. Naber, ''Nature Structural Biology'', '''2002''', 9, 844. [http://dx.doi.org/10.1021/jmsb852 doi:10.1021/jmsb852]. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
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''" A Stable and Crystalline Triarylgermyl Radical: Structure and EPR Spectra"'', Christian Drost, Jan Griebel, Reinhard Kirmse, Peter L�nnecke, and Joachim Reinhold, ''Angew. Chem. Int. Ed.'', '''2009''', ''48'', 1962-1965. [http://dx.doi.org/10.1002/anie.200805328 doi:10.1002/anie.200805328].<br />
: In this paper, the author showed the synthesis of the first stable triarylgermyl radical: Ge[3,5-''t''Bu<sub>2</sub>-2,6-(EtO)<sub>2</sub>C<sub>6</sub>H]<sub>3</sub>. X-ray crystallography and EPR were used to determine the structure of the radical both in solid state and solution. Studies showed that the radical is planar in solid state and pyramidal in solution. <br />
[[User:CuilingXu|CuilingXu]]<br />
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==Mössbauer Spectroscopy==<br />
[[File:2009W2-C529-S023.pdf|thumb|Preliminary lecture notes, copyright Pierre Kennepohl, all rights reserved]]<br />
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<br />
[http://wiki.ubc.ca/Chem_529_-_Physical_Methods_in_Inorganic_Chemistry back to main CHEM 529 page]<br />
[[Category:Ground State Spectroscopies]]<br />
[[Category:Chemistry]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Talk:Symmetry_and_Group_Theory&diff=69150Talk:Symmetry and Group Theory2011-01-11T17:05:16Z<p>Pierre: Blanked the page</p>
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<div></div>Pierrehttps://wiki.ubc.ca/index.php?title=Symmetry_and_Group_Theory&diff=69147Symmetry and Group Theory2011-01-11T17:04:46Z<p>Pierre: </p>
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<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
== Examples in Chemistry where Symmetry and Group Theory are commonly utilized ==<br />
[[File:2009W2-C529-S012.pdf|thumb|Preliminary lecture notes, copyright Pierre Kennepohl, all rights reserved]]<br />
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* Crystallography<br />
* Isomers<br />
* NMR equivalency<br />
* Determining spectroscopic/photochemical selection rules (electronic, angular momentum etc.)<br />
** IR/Raman activity<br />
* Determining the nature of atomic and molecular orbitals<br />
** Symmetry labels in molecular orbital diagrams<br />
* Determining structures of compounds (e.g. tetrahedral, octahedral etc.)<br />
* Predicting reactivity: <br />
** e.g. forbidden and allowed transitions states for pericyclic reactions<br />
** predicting, or rationalizing stereochemical outcome of a reaction<br />
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== Symmetry Elements and Symmetry Operations ==<br />
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'''Improper Axis of Rotation ( <math>S_n^m</math> )'''<br />
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The improper axis of rotation is a combination of two simpler operations: a <math>C_n</math> rotation (about the appropriate axis) followed by a reflection through the plane ( <math>\sigma_h</math> ) that is perpendicular to the rotation axis (''need graphic here''). In the event where <math>m>1</math>, then operations are performed sequentially as follows:<br />
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<math>S_n^2=(\sigma_h \times C_n) \times (\sigma_h \times C_n)</math><br />
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Remember that operations are performed sequentially from right to left!<br />
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In an Abelian group (where operations are commutative as well as associative), we can see that the two <math>\sigma_h</math> operations will cancel themselves out, allowing us to easily determine that <math>S_n^2 \equiv C_n^2 </math>. We also find that although <math>C_n^2 \equiv C_{n}^{n+2} </math> in all cases, the same is not true for <math> n = odd </math> improper axes of rotation, ''i.e.'', <math>S_n^2 \not\equiv S_{n}^{n+2} </math>.<br />
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== Symmetry Point Groups and Space Groups ==<br />
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== Properties of a Mathematical Group ==<br />
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== Representations of Groups: Character Tables ==<br />
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[http://symmetry.jacobs-university.de/ Character Tables]<br />
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Simple Groups: <math>C_1</math>, <math>C_s</math>, <math>C_i</math>.<br />
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<math>C_n</math> Groups: <math>C_2</math>, <math>C_3</math>, <math>C_4</math>, <math>C_5</math>, <math>C_6</math>, <math>C_7</math>, <math>C_8</math>.<br />
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<math>C_{nv}</math> Groups: <math>C_{2v}</math>, <math>C_{3v}</math>, <math>C_{4v}</math>, <math>C_{5v}</math>, <math>C_{6v}</math>, <math>C_{7v}</math>, <math>C_{8v}</math>.<br />
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<math>C_{nh}</math> Groups: <math>C_{2h}</math>, <math>C_{3h}</math>, <math>C_{4h}</math>, <math>C_{5h}</math>, <math>C_{6h}</math>, <math>C_{7h}</math>, <math>C_{8h}</math>.<br />
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<math>D_n</math> Groups: <math>D_2</math>, <math>D_3</math>, <math>D_4</math>, <math>D_5</math>, <math>D_6</math>, <math>D_7</math>, <math>D_8</math>.<br />
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<math>D_{nd}</math> Groups: <math>D_{2d}</math>, <math>D_{3d}</math>, <math>D_{4d}</math>, <math>D_{5d}</math>, <math>D_{6d}</math>, <math>D_{7d}</math>, <math>D_{8d}</math>.<br />
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<math>D_{nh}</math> Groups: <math>D_{2h}</math>, <math>D_{3h}</math>, <math>D_{4h}</math>, <math>D_{5h}</math>, <math>D_{6h}</math>, <math>D_{7h}</math>, <math>D_{8h}</math>.<br />
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<math>S_n</math> Groups: <math>S_2</math>, <math>S_4</math>, <math>S_6</math>, <math>S_8</math>, <math>S_10</math>, <math>S_12</math>.<br />
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Cubic Groups: <math>T</math>, <math>T_h</math>, <math>T_d</math>, <math>O</math>, <math>O_h</math>, <math>I</math>, <math>I_h</math>.<br />
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Linear Groups: <math>C_{\infty v}</math>, <math>D_{\infty h}</math><br />
<br />
== Literature examples of the use of symmetry/group theory in inorganic chemistry ==<br />
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<!-- Note: Please use the following style for your references. You are welcome to add comments regarding articles that are not yours in subsequent indented paragraphs after the initial summary by the person who chose the article. You should sign your comments by using three consecutive tildes at the end of the paragraph (~~~), which will be modified by UBCWiki to give the User tag as shown in this example.--><br />
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''"Resonance Raman spectroscopy as a probe of the bis(mu-oxo)dicopper core"'', Holland PL, Cramer CJ, Wilkinson EC, Mahapatra S, Rodgers KR, Itoh S, Taki M, Fukuzumi S, Que L, Tolman WB, ''J. Am. Chem. Soc.'', '''2000''', 122(5), 792-802, [http://dx.doi.org/10.1021/ja992003l doi:10.1021/ja992003l].<br />
: This article explores the possible vibrational modes of dicopper bis(mu-oxo) complexes as a function of the symmetry of the complexes. Significant differences can be observed as a function of the symmetry of the dimetallic core, which can be easily explained by group theoretical analysis. [[User:Pierre|PK]]<br />
''"A multiplet analysis of Fe K-edge 1s->3d pre-edge features of iron complexes"'', Tami E. Westre, Pierre Kennepohl, Jane G. DeWitt, Britt Hedman, Keith O. Hodgson, and Edward I. Solomon, ''J. Am. Chem. Soc.'', '''1997''', 119(27), 6297-6314, [http://dx.doi.org/10.1021/ja964352a doi:10.1021/ja964352a].<br />
: This article develops a group theoretical and ligand field analysis of the pre-edge features for Fe K-edge X-ray sbsorption spectroscopy. The overall analysis is completely based on group theory to understand both the bonding and spectroscopic selection rules that apply for this spectroscopic method. [[User:Pierre|PK]]<br />
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"Transition Metal Containing Decatungstosilicate dimer [M(H2O)2-(SiW10O35)2]10- (M = Mn2+, Co2+, Ni2+)", Bassil BS, Dickman MH, Reicke M, Kortz U, Keita B and Nadjo L, "Dalton Trans.", "2006", 35, 4253-4259, [http://dx.doi.org/10.1039/b606911h doi:10.1039/b606911h].<br />
: These authors synthesized new tungstosilicate dimers with C2v point group symmetry. They talk about how the compounds with different metal ions were all the same symmetric C2v dimers and they all crystallized in the same space group as well. [[User:Kimosten|Kimosten]]<br />
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"Low-Valent Ruthenium Complexes of the Non-innocent 2,6-Bis(imino)pyridine Ligand", Gallager, M, Wieder NL, Dioumaev, VK, Carrol, PJ, Berry, DH. "Organometallics"<br />
[http://dx.doi.org/10.1021/om9009075 doi:10.1021/om9009075]<br />
: This article explores the synthesis and characterization of a Ru(0) 2,6-Bis(imino)pyridine dinitrogen compound. Group theory is used to geometrically describe the N2 compound. A Nujol IR spectrum is taken to attempt to characterize the degree of N2 activation. The IR stretch assigned to the N2 bond is observed as a weak signal at 1851 cm-1. The idealized geometry that the authors use to describe the compound (D2d) should not allow the N2 bond to be IR active. [[User:TrumanWambach|TrumanWambach]]<br />
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"''Construction of nano- and microporous frameworks from octahedral bubble clusters''", S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, ''Phys. Chem. Chem. Phys'', '''2009''', 11, 3176-3185, <br />
[http://dx.doi.org/10.1039/b902600b doi:10.1039/b902600b]<br />
: This article describes a method of constructing microporous frameworks using eight different high symmetry ZnO clusters as building blocks. The building blocks have either T, Td, Th or O point group symmetry. The lattice energies of the final structures are calculated using interatomic potentials and it is determined that the frameworks consisting of clusters with Th point group symmetry are much more stable than those with T, Td or O symmetry. ([[User:AshleeHowarth|AshleeHowarth]])<br />
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"''Synthesis of Pincer-Type Bis(benzimidazolin-2-ylidene) Palladium Complexes and Their Application in C-C Coupling Reactions''", F. Ekkehardt Hahn, Mareike C. Jahnke, Tania Pape, ''Organometallics'', '''2007''', ''26'', 150-154.<br />
[http://dx.doi.org/10.1021/om060882w doi:10.1021/om060882w]<br />
:This article focuses on the preparation and catalytic properties of palladium pincer N-heterocyclic carbene complexes. In the <sup>1</sup>H NMR spectroscopy analysis of the Pd compound, temperature dependent studies are undertaken to analyze the thermodynamic parameters of the atropisomerization process which the ligand backbone undergoes. At higher temperatures, an averaged structure with ''C<sub>2v</sub>'' symmetry is observed. [[User:Lwence|Lwence]]<br />
<br />
“''Why ‘spherical’ cyclophosphazenic dandelion dendrimers have a dipole moment?''” Fayet J-P, Sournies F, Crasnier F, Labarre M-C, Labarre J-F, ''Main Group Chem.'' '''1997''', 2(2), 107-110, [http://dx.doi.org/10.1080/10241229712331341224 doi:10.1080/10241229712331341224]<br />
:This article provides an explanation to why “spherical” cyclophosphazenic dendrimers consist of dipole moments when their geometrical morphology appears to be highly symmetrical. Peraminolysis of N<sub>3</sub>P<sub>3</sub>Cl<sub>6</sub> (which possesses D<sub>3h</sub> symmetry) by 1,6-diaminohexane generates dendrimers of C<sub>3</sub> symmetry, thus suggesting presence of a dipole moment. By molecular modeling and measurements in dipole moments, the decrease in symmetry of the dendrimer is found to be due to the non-symmetrical distribution of electron density of the nitrogen atoms of the amino groups, which is responsible for the significant dipole moments measured in the dendrimers. [[User:ReneeMan|ReneeMan]]<br />
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''"Application of Symmetry Operation Measures in Structural Inorganic Chemistry"'', Jorge Echeverria and Santiago Aivarez, ''Inorg. Chem.'', '''2008''', 47(23), 10965-10970, [http://dx.doi.org/10.1021/ic801264n doi:10.1021/ic801264n].<br />
: This article details the use of applying symmetry operation measures to describe distortions in octahedral and tetrahedral crystallographic sites, as well as, to show the Bailar and tetragonal Jahn-Teller distortions of molecular transition metal complexes. The symmetry operation measure (Z(R)) is a numerical indicator which shows if a certain structure has a given symmetry operation (R). The novelty prescribed in this paper is the use of only four symmetry operation (C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub> and i) to fully differentiate from different symmetry subgroups which corresponds to certain types of distortions. [[User:JackyYim|JackyYim]]<br />
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"''C<sub>60</sub>-derived nanobaskets: stability, vibrational signatures, and molecular trapping''", SG dos Santos, M S Pires, V Lemos, V N Freire, E W S Caetano, D S Galvao, F Sato and E L Albuquerque, ''Nanotechnology'', '''2009''',20 (39): 395701. [http://www.iop.org/EJ/abstract/0957-4484/20/39/395701/ doi 10.1088/0957-4484/20/39/395701]<br />
<br />
This article uses simulations to investigate C<sub>60</sub>-derived nanobaskets obtained by effecting planar cuts in the atomic cage of fullerene. Infrared selection rules for these baskets are used to predict their symmetries and thus provide a method of differentiating between the nanostructures. Three baskets with different molecular formulae are investigated: C<sub>40</sub>H<sub>10</sub>(C<sub>5v</sub>), C<sub>39</sub>H<sub>12</sub> (<sub>3v</sub>) and C<sub>46</sub>H<sub>12</sub> (C<sub>2v</sub>). [[User:SusanVickers|SusanVickers]]<br />
<br />
“''A novel hexachelating amino-thiol ligand and its complex with gallium(III)''” Dennis A. Moore, Phillip E. Fanwick, Michael J. Welch, ''Inorg. Chem.'' '''1990''', 29(4), 672-676, [http://dx.doi.org/10.1021/ic00329a022 DOI: 10.1021/ic00329a022]<br />
:This work describes the chelators I ,4,7-Tris( 2-mercaptoethy1)-1,4,7-triazacyclononane (TS-TACNH), and 1,4,7-Triazacyclononane-l,4,7-triaceticacid (NOTA) bound to gallium. Crystal structures are analyzed and found to be present in the centric P2<sub>1</sub>/n unit cell. Both the delta and lambda enantiomers are formed for reach ligand-metal complex. This is a simple paper describing the synthesis and characterization of these complexes and their potential use in radiochemistry and nuclear medicine. The binding of these ligands with gallium(III) was expected to be very similar to iron(III) (trigonal prismatic geometry); however the higher affinity of gallium(III) for nitrogen coordination resulted in closer to octahedral geometry.<br />
<br />
"''Structure and Vibrational Spectra of Ti(IV) Hydroxides and Their Clusters with Expanded Titanium Coordination. DFT Study''", Ignatyev IS, Montejo M, Gonzalez JJL, ''J. Phys. Chem. A.'', '''2007''', 111(32): 7973-7979. [http://dx.doi.org/10.1021/jp073423x DOI: 10.1021/jp073423x]<br />
: The most stable equilibrium structures of H<sub>4-n</sub>Ti(OH)<sub>n</sub> (n=2-4) molecules and Ti(OH)<sub>4</sub> clusters were determined using computational chemistry at the 6-31+G(d) basis set. Theoretical vibrational (IR) frequencies of TiO stretching modes were compared to experimental IR vibrational frequencies. The point groups of Ti(OH)<sub>4</sub> dimers, trimers and Ti<sub>3</sub>O<sub>12</sub> molecules are discussed along with their vibrational frequency & symmetry relationships. [[User:AlexandraAnderson|AlexandraAnderson]]<br />
<br />
''"Consideration on the symmetry of loop order in cuprates"'', A. Shekhter, C.M. Varma. Phys. Rev. B'', '''2009''', 80, 214501, [http://dx.doi.org/10.1103/PhysRevB.80.214501 doi:10.1103/PhysRevB.80.214501].<br />
: This article examines the effects of magnetic fields on the symmetry of cuprate. The changes in symmetry are then considered for the cuprates' psuedo gap phase and other parameters that make cuprates interesting. [[User:AmberJuilfs|AmberJuilfs]]<br />
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"''Symmetry: A guide to its application in 2D electron crystallography''", Landsberg MJ, Hankamer B. ''J. Struct. Biol.'', '''2007''', 160(3): 332-343, [http://dx.doi.org/10.1016/j.jsb.2007.07.002 doi:10.1016/j.jsb.2007.07.002].<br />
: This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It provides a solid basis allowing for the accurate identification of symmetry and the subsequent application of symmetry based averaging in structure refinement. [[User:CuilingXu|CuilingXu]]<br />
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[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Symmetry and Group Theory]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=The_Role_of_Spectroscopy_in_Inorganic_Chemistry&diff=69146The Role of Spectroscopy in Inorganic Chemistry2011-01-11T17:03:48Z<p>Pierre: </p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
[[File:Raman.jpg|frame|An incident 532nm laser used during a resonance Raman experiment. (c) Pierre Kennepohl]]<br />
<br />
This page is designed to list the important roles that spectroscopy plays in the field of inorganic chemistry. Please be specific and include examples from the literature if possible. Remember that this is an interactive page and that all members of the course should be participating! You should consider this page as your first introduction to the use of the wiki environment so play around, include some links (for references), some graphics, an equation maybe?<br />
<br />
Remember to use the 'discussion' page (see tabs above) to discuss items before finalizing them on this page. Also remember that Pierre will be tracking who inserts what on this page, and this information will be used (qualitatively) to help determine the participation part of your mark for Chem 529. <br />
<br />
<br />
<br />
--[[User:Pierre|Pierre]] 16:54, 5 January 2010 (UTC)<br />
<br />
<br />
== The roles of spectroscopy in Inorganic Chemistry ==<br />
<br />
Generally, spectroscopy can be used to characterize inorganic materials in various ways.<br />
<br />
Such as:<br />
<br />
*Determination of geometric structure of inorganic compounds.<br />
<br />
*Determination of electronic structure of inorganic compounds.<br />
<br />
*Determination of the elemental composition of a sample.<br />
<br />
*Determination of protein secondary and tertiary structure.<br />
<br />
*Determination of kinetic parameters during a reaction.<br />
<br />
*Determination of relative concentrations of different species present at any time during a reaction.<br />
<br />
*Determination of the functional groups of a compound.<br />
<br />
== Some examples of the use of spectroscopy in Inorganic Chemistry ==<br />
<br />
===Elucidation of structure===<br />
<br />
* NMR: indicates degree of symmetry of a ligand around a metal center as well as the electron environment of the nucleus being probed.<br />
<br />
* Mass spectrometry: mass of compound, composition of a compound or mixture of compounds<br />
<br />
* EPR: determination of properties and spin resonance of paramagnetic metal complexes.<br />
<br />
* Linear Dichroism: provide orientation data of anisotropic inorganic materials. <br />
<br />
* Circular Dichroism: provides fingerprint information for the structure of various large biological molecules such as peptides (which can be coordinated with metals)<br />
<br />
* NMR: J-coupling constants are used to derive to dihedral (torsion) angles and therefore enable determination of protein structure<br />
<br />
* IR/UV-Vis/Raman: can be used to identify certain functional groups in a sample<br />
<br />
* UV-Vis Spectroscopy: Used to determine electronic structure of compounds (Band structures)<br />
<br />
* X-Ray Crystallography: can be used to elucidate structure of crystalline materials<br />
<br />
* NMR Titrations: can be used to track variations in structure (nmr signal) under the influence of some external stimulus (pH for example)<br />
<br />
* Atomic Absorption Spectroscopy: Analysis of the concentration of a metal element.<br />
<br />
===Kinetics===<br />
<br />
* IR, UV-Vis and Raman spectroscopy: can all be used to monitor kinetics by tracking a molecular vibration which is unique to either the product, or reactant. <br />
<br />
* NMR can also be used in kinetic studies. <br />
<br />
* Auger electron spectroscopy: A surface specific technique used to determine the composition of the surface layers of a sample.<br />
<br />
* Energy Dispersive X-Ray Spectroscopy: Typically used in conjunction with scanning electron microscopy to characterize the elemental composition of a sample. <br />
<br />
* Moessbauer Spectroscopy: Helps determine electron configuration<br />
<br />
* NMR: can be used to monitor the reaction by the analysis of nuclei other than <sup>1</sup>H and <sup>13</sup>C<br />
<br />
*Fluorescence spectroscopy: used to measure the fluorescence of a sample<br />
<br />
<br />
<br />
<br />
<br />
<br />
[http://wiki.ubc.ca/Course:CHEM529 home]<br />
[[Category:Role of Spectroscopy]][[Category:Chemistry]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=The_Role_of_Spectroscopy_in_Inorganic_Chemistry&diff=69145The Role of Spectroscopy in Inorganic Chemistry2011-01-11T17:03:03Z<p>Pierre: /* Some examples of the use of spectroscopy in Inorganic Chemistry */</p>
<hr />
<div>[http://wiki.ubc.ca/Course:CHEM529 home]<br />
<br />
[[File:Raman.jpg|frame|An incident 532nm laser used during a resonance Raman experiment. (c) Pierre Kennepohl]]<br />
<br />
This page is designed to list the important roles that spectroscopy plays in the field of inorganic chemistry. Please be specific and include examples from the literature if possible. Remember that this is an interactive page and that all members of the course should be participating! You should consider this page as your first introduction to the use of the wiki environment so play around, include some links (for references), some graphics, an equation maybe?<br />
<br />
Remember to use the 'discussion' page (see tabs above) to discuss items before finalizing them on this page. Also remember that Pierre will be tracking who inserts what on this page, and this information will be used (qualitatively) to help determine the participation part of your mark for Chem 529. <br />
<br />
<br />
<br />
--[[User:Pierre|Pierre]] 16:54, 5 January 2010 (UTC)<br />
<br />
<br />
== The roles of spectroscopy in Inorganic Chemistry ==<br />
<br />
Generally, spectroscopy can be used to characterize inorganic materials in various ways.<br />
<br />
Such as:<br />
<br />
*Determination of geometric structure of inorganic compounds.<br />
<br />
*Determination of electronic structure of inorganic compounds.<br />
<br />
*Determination of the elemental composition of a sample.<br />
<br />
*Determination of protein secondary and tertiary structure.<br />
<br />
*Determination of kinetic parameters during a reaction.<br />
<br />
*Determination of relative concentrations of different species present at any time during a reaction.<br />
<br />
*Determination of the functional groups of a compound.<br />
<br />
== Some examples of the use of spectroscopy in Inorganic Chemistry ==<br />
<br />
===Elucidation of structure===<br />
<br />
* NMR: indicates degree of symmetry of a ligand around a metal center as well as the electron environment of the nucleus being probed.<br />
<br />
* Mass spectrometry: mass of compound, composition of a compound or mixture of compounds<br />
<br />
* EPR: determination of properties and spin resonance of paramagnetic metal complexes.<br />
<br />
* Linear Dichroism: provide orientation data of anisotropic inorganic materials. <br />
<br />
* Circular Dichroism: provides fingerprint information for the structure of various large biological molecules such as peptides (which can be coordinated with metals)<br />
<br />
* NMR: J-coupling constants are used to derive to dihedral (torsion) angles and therefore enable determination of protein structure<br />
<br />
* IR/UV-Vis/Raman: can be used to identify certain functional groups in a sample<br />
<br />
* UV-Vis Spectroscopy: Used to determine electronic structure of compounds (Band structures)<br />
<br />
* X-Ray Crystallography: can be used to elucidate structure of crystalline materials<br />
<br />
* NMR Titrations: can be used to track variations in structure (nmr signal) under the influence of some external stimulus (pH for example)<br />
<br />
* Atomic Absorption Spectroscopy: Analysis of the concentration of a metal element.<br />
<br />
===Kinetics===<br />
<br />
* IR, UV-Vis and Raman spectroscopy: can all be used to monitor kinetics by tracking a molecular vibration which is unique to either the product, or reactant. <br />
<br />
* NMR can also be used in kinetic studies. <br />
<br />
* Auger electron spectroscopy: A surface specific technique used to determine the composition of the surface layers of a sample.<br />
<br />
* Energy Dispersive X-Ray Spectroscopy: Typically used in conjunction with scanning electron microscopy to characterize the elemental composition of a sample. <br />
<br />
* Moessbauer Spectroscopy: Helps determine electron configuration<br />
<br />
* NMR: can be used to monitor the reaction by the analysis of nuclei other than <sup>1</sup>H and <sup>13</sup>C<br />
<br />
*Fluorescence spectroscopy: used to measure the fluorescence of a sample<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
[http://wiki.ubc.ca/Chem_529_-_Physical_Methods_in_Inorganic_Chemistry back to main CHEM 529 page]<br />
[[Category:Role of Spectroscopy]][[Category:Chemistry]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Talk:The_Role_of_Spectroscopy_in_Inorganic_Chemistry&diff=69144Talk:The Role of Spectroscopy in Inorganic Chemistry2011-01-11T17:02:15Z<p>Pierre: Replaced content with "This page is the discussion page for the actual wiki page, this should be used in preparation before including things on the 'real' page. This is the place where you can thro..."</p>
<hr />
<div>This page is the discussion page for the actual wiki page, this should be used in preparation before including things on the 'real' page. This is the place where you can throw ideas around and try things out before making it 'official'...</div>Pierrehttps://wiki.ubc.ca/index.php?title=File:CHEM529-Syllabus.pdf&diff=69143File:CHEM529-Syllabus.pdf2011-01-11T17:00:25Z<p>Pierre: uploaded a new version of &quot;File:CHEM529-Syllabus.pdf&quot;</p>
<hr />
<div></div>Pierrehttps://wiki.ubc.ca/index.php?title=File:CHEM529-Syllabus.pdf&diff=69142File:CHEM529-Syllabus.pdf2011-01-11T16:59:43Z<p>Pierre: </p>
<hr />
<div></div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=69141Course:CHEM5292011-01-11T16:53:06Z<p>Pierre: </p>
<hr />
<div>[[File:CHEM529-Syllabus.pdf|200px|thumb|2010W2 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2009W-2), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]]<br><br />
3. [[Ground State Spectroscopic Methods]]<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
By the end of this course, pages associated with this wiki will have hopefully become a useful reference for all physical methods and topics discussed during the course. The overall quality of the final product depends on active participation from all students in the class!<br />
<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierrehttps://wiki.ubc.ca/index.php?title=Course:CHEM529&diff=69140Course:CHEM5292011-01-11T16:50:46Z<p>Pierre: </p>
<hr />
<div>[[File:2009W2-C529-Syllabus.pdf|200px|thumb|2010W2 syllabus]]<br />
<br />
===Physical Methods in Inorganic Chemistry===<br />
<br />
This page is the official wiki for Chemistry 529 (2009W-2), an inorganic chemistry graduate course entitled "Physical Methods in Inorganic Chemistry". As the semester progresses, this wiki will become '''the''' reference page for all materials for the course. Topics to be discussed in the course will include:<br />
<br />
1. [[The Role of Spectroscopy in Inorganic Chemistry]]<br><br />
2. [[Symmetry and Group Theory]]<br><br />
3. [[Ground State Spectroscopic Methods]]<br><br />
4. [[Excited State Spectroscopic Methods]]<br><br />
<br />
By the end of this course, pages associated with this wiki will have hopefully become a useful reference for all physical methods and topics discussed during the course. The overall quality of the final product depends on active participation from all students in the class!<br />
<br />
<br />
[[Category:Chem529]][[Category: Chemistry]][[Category:CHEM]]</div>Pierre