32 votes
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What are t2g and eg in CFT?

As stated in both the links Geoff and Philipp have kindly commented (1, 2) they are to do with symmetry labels we chemists like to assign to orbitals. Knowing an orbitals symmetry class can lead to a ...
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28 votes

When is it true that more nodes equals higher energy?

General case There is indeed a mathematical theorem that deals with the number of nodes an eigenfunction corresponding to a certain eigenvalue can possess. It was laid down by Courant$^{[1, 2]}$ and ...
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27 votes
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What is the mathematical basis behind the Jahn-Teller effect?

1. Perturbations As already mentioned, the Jahn–Teller effect has its roots in group theory. The essence of the argument is that the energy of the compound is stabilised upon distortion to a lower-...
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26 votes
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Does trans-decalin really have a plane of symmetry?

It's not easy to see from a diagram, because it distorts bonds and angles. I recommend building it with a balls-and-sticks model set. You can also use a molecular viewer to model it; there are a ...
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22 votes
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How can I find the symmetry labels of atomic orbitals in a molecule?

First, you have to know the geometry of your compound. The complex $\ce{[PtCl4]^2-}$, for example, is square planar. The next step is to determine the point group of the compound from this geometry by ...
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20 votes
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Theoretical basis behind orbital correlation diagram for pericyclic reactions

Introduction Instead of the usual cycloadditions (which has some extra complications in terms of the reacting orbitals), let's consider the concerted reaction $\ce{H2 + D2 -> 2HD}$. We'll come ...
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18 votes

Symmetrize nearly symmetric molecule

I've done some work in both symmetry detection and in distance matrix methods. I think it's a great idea in concept, but the devil will be in the details for large, more complex molecules. The first ...
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17 votes
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Jahn-Teller Distortions in Square Planar Complexes?

Introduction Thank you for prompting me to look for square planar complexes that are not $\mathrm{d^8}$; I learnt some valuable stuff while researching the answer to this question! Do take this ...
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16 votes
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Relationship between the symmetry number of a molecule as used in rotational spectroscopy and point group

This is not in general true Consider molecules a point group not containing inversion symmetry, e.g. $C_2$ hydrogen peroxide The $C_2$ group has only two elements, $E$ and $C_2$, and the $C_2$ ...
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15 votes

Why is 2-methyl-2,3-pentadiene achiral (allene)?

I'll start by linking to Symmetry @ Otterbein, as it's a very useful tool for looking at various structures and seeing planes an axes of symmetry. If you're having issues visualising rotations and ...
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15 votes
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How are there two C3 rotation axes in ammonia?

In a character table for $C_{3v}$, $ 2C_3$, means that the element is actually 2 $C_3$ elements in the same conjugacy class. That means the two $C_3$ operations are related in some way. In fact, it ...
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14 votes
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Symmetry representations

Let's start with the basics: A representation is a set of matrices that fulfill the multiplication table for the point group. So I might be able to use a set of 3x3 matrices, since of course I can ...
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14 votes

What constraints are imposed on a wavefunction by the symmetry of the system?

I use quantum chemistry about as much as a lumberjack uses math (that is, just enough not to fell a tree on one's own head), so my answer will be short and hopefully useful as a tl;dr to someone else'...
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14 votes
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How do I show that a transition is magnetic dipole allowed with group theory/symmetry?

For a state-to-state transition coupled by an operator to be allowed, the direct product of the irreducible representations (irreps) of all three components must contain the completely symmetric irrep ...
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14 votes

How are there two C3 rotation axes in ammonia?

The top row of the character table does not refer to symmetry elements, but rather symmetry operations. (For the difference between the two, see Wikipedia:Molecular symmetry.) In this particular case, ...
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13 votes
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How do I find the ground state term symbol for transition metal complexes?

To find the ground state term symbol, you should be using symmetry and group theory arguments, you shouldn't have to resort to searching Tanabe-Sugano diagrams to get the answer. We'll start with ...
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13 votes
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Derivation of the Orgel diagram for octahedral d2 complexes

1. Weak-field and strong-field limits I will adopt the description used in Figgis and Hitchman's Ligand Field Theory and Its Applications (p 5), because I cannot really phrase it better: It is ...
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11 votes
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Why can anthracene, but not phenanthrene, take part in Diels–Alder reactions?

Have a look at the reaction mechanism of the Diels-Alder Reaction, e.g. at Wikipedia. We have talked about this reaction before on this site, and concluded that a sufficient explanation is only ...
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11 votes
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Is there a physical explanation why benzene's pi molecular orbitals in a Frost circle are degenerate but pyridine's are not?

My first thoughts are along the lines of your second-last paragraph. Here is a quick sketch of how to formalise it. From simple Hückel theory, you can obtain the coefficients of the AOs in the MOs: $$...
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10 votes

Why are square planar coordination compounds with four different ligands optically inactive?

Even though the central atom has 4 different ligands this does not necessarily mean that the compound is optically active. The condition for that rather the following (from Wikipedia): A molecule is ...
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10 votes
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What is difference between T1g and T2g?

Well, not quite. Here's the quick summary on subscripts in Mulliken notation for point group symmetry. “g” stands for "gerade" and refers to the symmetry around an inversion center. (That is, the ...
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10 votes
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AB5E type molecule

Why? Because there is no other choice. Starting from the AB6 octahedral configuration, all six vertices of the octahedron are symmetric, so it doesn't matter whichever one you “choose” to replace by ...
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9 votes
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Why doesn't 1,3-dichloro-2,4-dimethylcyclobutane have a plane of symmetry?

Ivan already stated quite briefly in the comments, that the planes you drew would transform an upward facing chlorine to a downward facing chlorine and vice versa, and that the same holds for the ...
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9 votes

Rule of mutual exclusion: is the converse true?

If there is a molecule of $O$ (as opposed to $O_h$) or $I$ (as opposed to $I_h$) symmetry, it would be such a counter example (no mode that is both IR and raman active, and not centrosymmetric). ...
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9 votes
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Rule of mutual exclusion: is the converse true?

Have a look at the point groups O (not $\ce{O_h}$) I, $\ce{D_{5h} and C_{5h}}$. A pic of an O point group molecule is shown below. The $\ce{c_2}$ axes are not shown. Taken from molecule-viewer.com web ...
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9 votes
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Why does the 31P{1H} NMR spectrum of cis-[Mo(CO)2(dppe)2] show two signals?

In this complex there are two different 31P environments which are not related by symmetry: The two green phosphorus nuclei can be interconverted by a $C_2$ rotation (the rotation axis bisects the OC–...
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8 votes
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How many peaks would there be in H1 NMR of ethene?

You need to consider whether the protons in ethene are chemically equivalent, magnetically equivalent, or both. The lewis structure of ethene: Because of the symmetry of the planar ethene molecule, ...
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8 votes
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How does B2Cl4 have two perpendicular c2' axes?

Diboron tetrachloride has the same symmetry as allene, which I will use to demonstrate the other two $\ce{C_2^{'}}$ axis. The back $\ce{CH_2}$ group is turned 90° in comparison to the front $\ce{CH_2}$...
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  • 6,053
8 votes
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How to get the reducible representations of the B-B and the B-Cl bond of B2Cl4

There seem to be two problems: the first is that your reducible representation for the $\ce{B-B}$ bond is wrong but your reducible representation for the $\ce{B-Cl}$ bonds seems to be correct and the ...
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8 votes
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Identifying the C3, C4, S4, and S6 symmetry operations in the Oh point group

At first I thought the character table was counting both positive and negative rotations, but then the order for the $C_2'$ and $C_2$ rotations should be doubled if that were the case ($12C_2'$ and $...
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