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# 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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42 views

### Why does dipole must lie parallel to a rotation symmetry axis?

While studying group theory, I've got confused by the following statement: For a molecule to have a permanent dipole moment, it must have an asymmetric charge distribution. The point group of the ...
16 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 ...
35 views

### What does “orthorhombic” actually mean?

I'm trying to understand what it means for a molecule to have orthorhombic symmetry. According to Di Lauro's "Rotational Structure in Molecular Infrared Spectra," a molecule is orthorhombic if the ...
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### 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 ...
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### C5v E1 SALC production using Full Projection

I have another SALC question. @Andrew and @user5713492 did a phenomenal job clarifying my previous confusion with Methane T2 SALC production, so I attempted to apply this to a new point group, and ...
85 views

### How do I interpret characters that are not 1 or -1 in a point group table?

When the character in a point group table is listed as 1 or -1, I understand how an object/orbital etc. transforms to give either itself or the negative of itself. When the character in a point ...
484 views

### Methane T2 SALCs

So I have a question on the form of the $T_2$ SALCs of methane. Below I show the $T_d$ character table and the accompanying reducible representation for the sigma framework (using, in the case of ...
101 views

### What happens when a symmetry element is added or removed from a point group? [closed]

What new point group is formed if symmetry element i is added to C3 point group?
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### How to get $\Gamma_{vib}$ for hexafluoroethane?

An exercise asks me to find $\Gamma_{vib}$ for that molecule. I know that: $$\Gamma_{cart}=\Gamma_{vib}+\Gamma_{translations}+\Gamma_{rot}$$ Since the molecule I'm considering belongs to the $D_{3d}$ ...
123 views

### Vibronic coupling: How do I determine the new point group after vibration?

So I was recently discussing the transitions in Egyptian Blue ($\ce{CaCu[Si4O10]}$) with some of my students, who had to prepare this compound. What I like in particular in this case is how, at least ...
75 views

### Does “higher symmetry” mean any symmetry group of higher order?

What is the precise definition of a higher symmetry in group theory? I see this term scattered around, such as in Cotton's Chemical Applications of Group Theory: ...In the cyclic groups each of the ...
140 views

### Cs Point Group's “Horizontal” Reflection Plane

Why is it that $C_s$ character tables always list a $\sigma_h$ operation despite the definition of $C_s$ not necessitating the reflection plane be horizontal? In fact, how can the reflection plane ...
174 views

### Vanishing integral rule for two-electron integrals

I understand the vanishing integral rule for a one-electron integral to be: $$\langle i | \hat{O} | j \rangle = 0 \hspace{1cm} \mathrm{if} \hspace{0.2cm} \Gamma_O \neq \Gamma_i \otimes \Gamma_j$$ ...
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### Why does benzene have 3 π–π* transitions in the UV range, but ethene, butadiene, and hexatriene each have only 1?

Are the π and π* orbitals of benzene much closer together in energy which allows for multiple transitions? Why is this not the case for hexatriene if they both contain the same number of pi bonds?
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### Are there any descent symmetry tables for character tables of linear structures?

I know about tables containing information about descending in symmetry, i.e. from larger point groups to their sub-groups. We can see such tables in this answer, or in this PDF. My question is - ...
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### 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 ...
279 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 $D_{2h}$ ...
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### How is group theory (and matrices) used in symmetry operations? [closed]

I am a high school IB student. For my 2-year math course, there is an internal assessment called "exploration" which should be max. 12 pages long. The goal of this assignment is for students to ...