All Questions
Tagged with symmetry group-theory
70
questions
29
votes
1
answer
105k
views
What are t2g and eg in CFT?
In the crystal field theory (CFT), when the splitting of the d-orbital occurs, it gets divided into two parts.
The upper part with higher energy is the $\mathrm{e_g}$ and the lower part with lower ...
- 1,683
25
votes
1
answer
4k
views
What is the mathematical basis behind the Jahn-Teller effect?
Both first-order and second-order Jahn-Teller distortions play a very important role in chemistry.
It is often said that the Jahn-Teller effect is based on symmetry arguments, and hence nothing can ...
- 71.6k
17
votes
1
answer
25k
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 ...
- 944
11
votes
2
answers
8k
views
How does one recognized Td/Oh symmetry in molecules?
The identification of point groups of a molecule is usually done following a strict scheme, either manually or algorithmically. In all textbooks I could find, however, the first step of the scheme is ...
- 23.8k
10
votes
1
answer
2k
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}...
- 1,120
10
votes
1
answer
2k
views
Symmetry representations
I'm Having a real struggle trying to understand symmetry representations matrices and character tables. Is there anyone who would be kind enough to help me out here? I understand it is probably a ...
- 963
10
votes
0
answers
141
views
Using symmetry and group theory arguments to explain iron(II) in a tetrahedral crystal field
I am trying to figure out how to explain $1s \rightarrow 3d$ spectroscopic transitions for $\ce{Fe^{2+}}$ in $T_\mathrm{d}$ symmetry. These transitions make up the pre-edge region in K edge X-ray ...
- 101
9
votes
2
answers
34k
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 ...
- 1,648
8
votes
1
answer
7k
views
How to get the reducible representations of the B-B and the B-Cl bond of B2Cl4
I just can't seem to get the correct answer to this symmetry question in my book. "Introduction to molecular symmetry J.S.Ogden."
I am trying to find the reducible representations of both the $\ce{B-...
- 963
8
votes
1
answer
3k
views
Determination of +/- reflections in sigma molecular term symbols
This page, which depicts the molecular term symbols for the $\ce{O2}$ and $\ce{O2-}$ (Edit: Mistaken on $\ce{O2-}$) molecules, perhaps best summarizes the full scope of my questions. In general, I don'...
- 1,648
7
votes
3
answers
500
views
Why does (2z²-x²-y², x²-y²) have -1 trace in the character table of Td for C3 rotation?
I'm trying to understand the irreducible rep for $(2z^2-x^2-y^2, x^2-y^2)$ in the $T_\mathrm{d}$ point group. Specifically, for $C_3$ rotations, a trace of $-1$ is listed in the character table for ...
- 71
7
votes
1
answer
2k
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 (...
- 1,120
7
votes
1
answer
8k
views
How do I determine the crystal field splitting for an arbitrary point group?
How can I figure out the degeneracy of the d orbitals for a site that has a given point group? Specifically I'm interested in $D_{3d}$ and $D_{3h}$, but it would be good to know how to do it in the ...
- 917
7
votes
2
answers
101
views
Point group of harmonic oscillator
The book Molecular Quantum Mechanics by Atkins and Friedman [1] says the point group of a harmonic oscillator is $C_\mathrm{s},$ composed by the identity operator $E$ and a reflection $\sigma_\mathrm{...
- 461
7
votes
1
answer
960
views
Are these two space groups in a group–subgroup relationship?
Given two crystal space groups, how can one determine if they are in a group-subgroup relationship? The specific case at hand is P 21/m 2/m 2/a (aka P m m a, #51) and P m m 2 (#25), but knowing how to ...
- 23.8k