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30 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-...
orthocresol's user avatar
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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 ...
Martin - マーチン's user avatar
21 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 ...
orthocresol's user avatar
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16 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 ...
ninth_account's user avatar
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 $C_2$ ...
user213305's user avatar
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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 ...
user213305's user avatar
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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'...
Ivan Neretin's user avatar
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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 ...
pentavalentcarbon's user avatar
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, ...
orthocresol's user avatar
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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 ...
orthocresol's user avatar
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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 ...
orthocresol's user avatar
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12 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: $$...
orthocresol's user avatar
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11 votes
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Does 1,3-dichloroallene possess a C2 symmetry axis?

A $C_2$ axis is indeed here—although not the one that you are thinking of: your suggestion of a $C_4$ then $C_2$ rotation does not qualify as a $C_2$ symmetry operation. There is a true $C_2$ axis ...
andselisk's user avatar
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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 ...
F'x's user avatar
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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 ...
Martin - マーチン's user avatar
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 ...
porphyrin's user avatar
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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). ...
DavePhD's user avatar
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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–...
orthocresol's user avatar
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9 votes
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Example of an achiral molecule without a plane of symmetry or inversion center?

Part 1 Are there any molecules lacking plane of symmetry/center of inversion but that are achiral due to presence of an axis of improper rotation? Yes, although such examples are very rare. In ...
orthocresol's user avatar
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9 votes
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What's the relation between two symmetry groups, if one has all the symmetry of the other and some more?

What mathematical term describes the relationship between $C_s$ and $C_{2v}$? Is $C_{2v}$ a subgroup of $C_s$? Is it rather a subset of it? Should we rather say that $C_{2v}$ implies $C_s$? $C_\...
orthocresol's user avatar
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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 $...
Jan's user avatar
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8 votes
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Is there a possible distortion of XeF6 from Oh point group to reduced symmetry?

Now, there are a few things that must be stated very clearly. Firstly, it pays to be very careful when you are talking about point groups. It's careless (and confusing to others) to write $\mathrm{T_{...
orthocresol's user avatar
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8 votes
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Can a molecule be neither gerade nor ungerade?

g/u is not a property of a molecule; I assume you meant molecular orbital. All functions can be written as a linear combination of even + odd functions: there is a short explanation on Wikipedia. ...
orthocresol's user avatar
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8 votes
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Why is CO2 not in the C∞v point group?

Both are linear with a $C_{\infty}$ axis, but $D_{\infty h}$ has a center of inversion and $C_{\infty v}$ does not.
MaxW's user avatar
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8 votes
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Use of axis of symmetry

Alternating axes are not axes, much like a Guinea pig is not a pig. Having axes of symmetry is irrelevant to chirality. Having alternating axes is a necessary and sufficient condition of non-...
Ivan Neretin's user avatar
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8 votes
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Can the plane of symmetry for a compound be the plane of the paper?

In short: The presence of the $\sigma_h$ plane you see depends on the conformation of the methyl groups. If your example were either benzene or 1,4-dichlorobenzene, then you were be right, the ...
Buttonwood's user avatar
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8 votes

Chromium cyanide complexes

This doesn't appear to be a rare case and there are plenty $\ce{Cr^2+}$ square planar complexes. I found 15 square planar complexes with well-determined crystal structures $(R_\mathrm{int} < 10\%)$ ...
andselisk's user avatar
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8 votes

Stereo-isomerism in 7-methylbicyclo[2.2.1]hept-2-ene

7-Methylbicyclo[2.2.1]hex-2-ene exists as two diastereomers, anti-1 and syn-1, which differ by the relationship of the methyl group and the double bond. Both compounds are meso with the bridgehead ...
user55119's user avatar
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7 votes

XeF4 - why are there only 2 dihedral mirror planes?

This is a situation of coordinate systems. In the $D_\mathrm{4h}$ point group, as you've noticed, there are 4 $C_{2}$ rotation axes in the plane. The easiest way to set the coordinate system is to ...
Zhe's user avatar
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7 votes

How are these molecules chiral and achiral?

Regarding the first molecule: I understand that the simplistic Fischer projection - with all its bond depicted by solid lines - can be very confusing at first glance in determining optical activity. ...
Gaurang Tandon's user avatar

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