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.

Filter by
Sorted by
Tagged with
2
votes
2answers
62 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 ...
2
votes
0answers
17 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 ...
1
vote
0answers
36 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 ...
0
votes
0answers
18 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 ...
2
votes
0answers
30 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 $C_\infty$, $\...
1
vote
0answers
43 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
vote
1answer
96 views

Molecular Orbitals (only pi system) of Allyl system using group theory

I have just started reading group theory and their applications in the MO theory. I tried to get the equations of the pi molecular orbitals of allyl system using group theory, but I am stuck at the ...
3
votes
1answer
127 views

MOs of Benzene using group theory

I am trying to analyze the $\sigma$ orbitals of benzene molecule using group theory, doing the same thing that is done to the $\pi$ orbitals. The symmetry group of benzene is the $D_{6h}$; considering ...
0
votes
0answers
55 views

Group theory and the orbitals of benzene

Can I apply group theory to the $\sigma$ orbitals of benzene? I have already seen it be applied to the $\pi$ orbitals, but I can't find an application to the $\sigma$ in literature. In this case, ...
7
votes
0answers
179 views

Vanishing integral rule for two-electron integrals

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

Point group from mono to bulk MoS2

Many articles say even numbers of layers or bulk crystal MoS2 have D6h point group and odd numbers of layers (including monolayer) MoS2 have D3h point group But whenever looking at the figure of ...
0
votes
1answer
237 views

How do I get irreducible representations?

I'm currently trying to do a problem where it asks me to "show that the irreducible representations spanned by the atomic x-, y-, and z- coordinates is independent of the choice of local coordinate ...
5
votes
1answer
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 ...
2
votes
0answers
35 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 ...
3
votes
1answer
133 views

What is a “symmetrical product” of an irreducible representation with itself?

In their classic paper outlining the Jahn–Teller theorem (Proc. R. Soc. Lond. A 1937, 161 (905), 220–235), the authors wrote "where $[\phi^2]$ denotes the representation of the symmetrical product of $...
2
votes
1answer
59 views

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 ...
2
votes
3answers
622 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 ...
0
votes
1answer
118 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?
3
votes
0answers
922 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 ...
5
votes
1answer
86 views

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 $D_{3d}$ ...
3
votes
1answer
148 views

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 - ...
18
votes
1answer
63k views

What are t2g and eg in CFT?

In the Crystal Field Theory, when the splitting of the d-orbital occurs, it gets divided into two parts... The upper part with higher Energy is the $t_{2g}$ and the lower part with lower Energy is ...
4
votes
2answers
137 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 ...
4
votes
1answer
78 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 ...
1
vote
1answer
148 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 ...
5
votes
1answer
363 views

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?
13
votes
2answers
2k views

Molecular orbital diagram and irreducible representations for dinitrogen

I'm trying to understand how to draw molecular orbital diagrams, since I'd like to use the molecular orbitals to determine the total state of the molecule (i.e. $A_1$, $B_1$ etc.), so I prefer the ...
3
votes
0answers
73 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 ...
1
vote
0answers
340 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 $D_{2h}$ ...
3
votes
1answer
262 views

Reducible representation of planar molecule N2H2 with bond lengths as a basis

I'm studying about molecular symmetry and its representations. Today I got a little confused about the planar $\ce{N2H2}$ molecule. It looks like this The basis in the example was chosen as $\Delta ...
5
votes
0answers
138 views

Finding the irreducible representation which an orbital transforms under [duplicate]

I have some major confusion on irreducible representations. An example of a problem I have is Based on the character table for the point group of each of the follwing molecules, which irreducible ...
13
votes
1answer
15k views

How can I find the symmetry labels of atomic orbitals in a molecule?

What are the symmetry labels for the p and d orbitals of platinum in $\ce{[PtCl4]^2-}$? I understand how to find the point group of a molecule, but am not sure how to use the character table to find ...
2
votes
2answers
3k views

Understanding Equivalent Wyckoff positions

I'm somewhat confused by the concept of Wyckoff positions in crystal structures. From Quantum Chemistry of Solids by Robert Evarestov, the definition of a Wyckoff position is "all the crystallographic ...
1
vote
1answer
207 views

Would an (NH3)2+ molecule be trigonal planar like BH3 rather than trigonal pyramidal?

I've been learning about using MO theory to explain why $\ce{BH3}$ and $\ce{NH3}$ have different geometries and by following the line of reasoning used to rationalise the differences in geometry I ...
2
votes
1answer
3k views

How to systematically find the reducible representation of a molecule? (eg: XeF4)

I am attempting to use the reduction formula to find the irreducible representation of $\ce{XeF4}$ to determine its IR stretching vibrations. I know the point group of $\ce{XeF4}$ is $D_{4h}$ and have ...
7
votes
1answer
154 views

Notation for excited states

I am reading some papers about quantum chemistry and in one I found a notation for excited states of a molecule that I don't understand at all. In the picture below you can see the potential curves ...
1
vote
0answers
218 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 ...
7
votes
1answer
197 views

Determining overtones bands of degenerate modes

I have a question of a more mathematical nature on the mathSE (Symmetric Direct Product Distributive?) that received a good answer, but I think an answer more oriented to chemists would be a useful ...
8
votes
1answer
284 views

How to dock aggregated structures comprised of “elementary” protein units like LEGO pieces?

There are proteins with intrinsic symmetries. For example: I was wondering how to use transformations such as: rotations, translation, replications to construct possible structures using 2 types of ...
5
votes
1answer
291 views

Why are there no dihedral mirror planes in the D3h point group?

Consider the molecule $\ce{BH3}$, which belongs to the $D_\mathrm{3h}$ point group. Why are the three mirror planes in this point group labelled as $\sigma_\mathrm v$ instead of $\sigma_\mathrm d$? ...
2
votes
1answer
237 views

D3d point group matrices

I am trying to construct all the matrices for the point group D3d operations. I find that the matrices of E, i, S6, inverse of S6, C3, and inverse of C3 are easy, but I do not know how to construct ...
34
votes
4answers
2k views

Why is the letter J omitted in the spdf… sequence?

Under spherical symmetry, the irreducible representations corresponding to $L = 0, 1, 2, \cdots$ are assigned the letters $\mathrm{S}, \mathrm{P}, \mathrm{D}, \mathrm{F}, \cdots$ after which the ...
10
votes
2answers
700 views

Irreducible representations and system states connection

Let's say I have the molecule $\ce{N2+}$. Its symmetry point group is clearly $D_{\infty\mathrm h}$. But I'm confused by its irreducible representations. I know there are 8 of them, but as I ...
9
votes
1answer
909 views

Why are there only two irreducible representations in the C3 group?

There are three elements in a $C_3$ group and there are three classes in this group cause it is an Abelian group. \begin{array}{c|ccc|cc} \hline C_3 & E & C_3 & C_3^2 & & \...
4
votes
1answer
653 views

How do we calculate a character table from its basis functions

This question is a actually a homework question, I'm given the basis functions of all the irreducible representations of $C_{2v}$ group, then I'm asked to complete the character table of $C_{2v}$ ...
6
votes
2answers
12k views

Identifying the C3, C4, S4, and S6 symmetry operations in the Oh point group

The Oh character table has ten symmetry classes. I am trying to identify them, but my stumbling block is in identifying the order of each class. I will use this diagram as a reference, from Sydney ...
7
votes
1answer
1k views

Is there a possible distortion of XeF6 from Oh point group to reduced symmetry?

Below the molecular orbital diagram for $\ce{XeF6}$ (from What is the molecular structure of xenon hexafluoride?) I am trying to figure out if a distortion from $O_h$ can take place and to which (...
8
votes
1answer
719 views

How do I show that a transition is magnetic dipole allowed with group theory/symmetry?

I am taking an introductory course in symmetry and bonding and have so far learnt about SALCs and various point groups etc... one of my problems asks me to show a $\mathrm{^{2}T_{2g}\rightarrow\ ^{2}...
2
votes
0answers
204 views

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 ...
12
votes
1answer
519 views

What is it that is “symmetry-adapted” about symmetry-adapted perturbation theory?

I think this is a fairly straightforward question which I should know the answer to, but surprisingly cannot find a discussion of online. Symmetry-adapted perturbation theory (SAPT) is a fairly ...