Questions tagged [group-theory]

The systematic discussion of molecular symmetry is known as group theory. Group theory is a systematic way of describing the symmetry of molecules using concepts/rules borrowed from mathematics. This tag should be applied to any question which involves the theory or application of point groups, symmetry elements, or character tables.

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Vanishing integral rule for two-electron integrals

I understand the vanishing integral rule for a one-electron integral to be: $$\langle i | \hat{O} | j \rangle = 0 \hspace{1cm} \mathrm{if} \hspace{0.2cm} \Gamma_O \neq \Gamma_i \otimes \Gamma_j$$ ...
6
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0answers
132 views

Equivalent Wyckoff position in different groups

I am not a chemist, I am a physicist, so please bare with me if what I am asking is rather obvious. If I have two symmetry groups ($P4/mmm$ and $P\!-\!1$), is there a way to find their respective ...
4
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179 views

Decomposition of axial vector and vector representions of C4v group

Let $R$ be the orthogonal matrix corresponding to an operation in $O(3)$. If R is a proper rotation, then both vectors $\vec{V}$ and axial vectors $\vec{A}$ are transformed in the same way $$ \vec{V} ...
3
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1answer
77 views

Is there a geometrically intuitive explanation of the equivalence of the numbers of irreducible representations and symmetry classes?

In group theory, as used in chemistry, we’re familiar with the idea that the number of irreducible representations of a symmetry group equals the number of classes of symmetry operations, e.g. three ...
3
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0answers
83 views

Reducible representations - choice of new basis

I was looking at this tutorial about reductions of representations. At first, the basis consists of four orbitals $(s_N, s_1, s_2, s_3)$ and the representations look like this and we want to reduce ...
3
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0answers
1k views

What is the symmetry of the cuboctahedron (FCC metal)?

The background to this is that I've recently given a tutorial wherein we had to go through the determination of point groups for atoms in various lattices (BCC, FCC/CCP and HCP). BCC and HCP, I have ...
2
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0answers
26 views

How to deal with non-symmorphic space groups for orbital/vibrational analysis?

I am learning about how to apply group theory analysis of MO diagrams and vibrational in the solid state context (not isolated molecules). I think the strategy for calculating representations and ...
2
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0answers
40 views

Character table and symmetry operations

It's been a while since I've dealt with these, but do character tables include all possible symmetry operations? I am looking at the $D_{\infty h}$ point group table and it lists $C_\infty$, $\...
2
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0answers
36 views

Misunderstanding about the spin part of the Jahn Teller effect

In the paper Stability if Polyatomic Molecules in Degenerate Electronic States II - Spin Degeneracy the author wrote: Thus a twofold degeneracy cannot produce instability for a molecule containing ...
2
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1answer
297 views

Whats the symmetric, anti-symmetric and non-symmetric part of the direct product of irreducible representations?

I am trying to understand how to see if a vibrational mode is Jahn-Teller active or not. According to the group theoretical description of the Jahn-Teller effect one needs to check if the symmetric ...
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0answers
11 views

Symmetry of glide planes

I am trying to understand the symmetry elements of space group number 194 (P$6_3$/mmc), which is hexagonal and has 24 symmetry operations. In the table of symmetry operations it says that it has ...
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0answers
32 views

Screw axis in P21c space group

I am having some trouble with understanding glide axis. The following is a question asking to reconstruct the full unit cell: And the following is the answer to the question: I have highlighted an ...
1
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0answers
58 views

Pncn space group diagram

I'm trying to make a diagram of the Pncn space group. Firstly, I know that this space group belongs to the orthorhombic system and derives from the point group (2/m 2/m 2/m). Therefore, although the ...
1
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0answers
546 views

N2 symmetry representation in higher symmetry groups (D3h…)

I'd like to describe the symmetry of the ground state of $N_2$ in the higher symmetry groups like $D_{3h}$ and $D_{\infty h}$. In this answer the topic is covered very good, but only for $D_{2h}$ ...
1
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0answers
462 views

Does Ni(H2O)6 have Oh symmetry or Th?

I optimized a geometry of $\ce{Ni(H2O)6}$ using quantum chemistry and got a molecule which is symmetrical for the $\ce{Ni-O}$ distances as shown here: In the literature it says that this complex has ...
0
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0answers
33 views

How to define axes if all rotation axes pass through the same number of atoms?

I was wondering how one can define the axes for a molecule with several equal axes of rotation, all of which pass through the same atom. I know that the $z$-axis is usually defined as the principal ...
0
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29 views

Symmetries and degeneracies of the s,p, and d orbitals

Consider the molecular AB_8 (complex with central atom A and 8 B ligands (coordination number 8), for which I determined the point group D_4d) and determine the symmetries and degeneracies of the s, p,...
0
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19 views

How can I determine the type of IR active mode on a complex molecule from molecular geometry arguments?

I am trying to synthesize 2,6,9,10-tetracyanoanthracene and I need to discriminate it from other regioisomers. I am hoping to take advantage of the C2h symmetry under an IR spectrometer. I like to ...