All Questions
Tagged with symmetry quantum-chemistry
25
questions
2
votes
2
answers
538
views
What does the 2 in t2g stand for?
I have read so far that it is about whether the d-Orbital is symmetric to a C2 element perpendicular to its main rotational axis. If all the given orbitals in a group are symmetric to that element, ...
- 83
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
1
vote
1
answer
81
views
What does it mean that a state belongin to a given irrep transforms like $Rx$, $Ry$ or $Rz$
The present question is related to this other question I did few days ago.
Given a point group and the list of the irreps (see for example here) the meaning of an irrep which transforms like $x$ or $x^...
- 267
7
votes
1
answer
412
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How do I show that a transition is electric dipole allowed with group theory/symmetry?
This is actually a follow up of this question
The follow-up is not because of the electric instead of magnetic dipole (this is trivial).
It is because I'm interested in extra info.
Suppose I have a ...
- 267
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
1
vote
0
answers
93
views
High symmetry points and x-coordinates
Is it possible to work out the x-coordinates related to high symmetry points?
The software I'm using doesn't provide me with that, so I was wondering if there is a way to manually figure it out, as I ...
- 11
3
votes
1
answer
178
views
Solution of the Roothaan Equations of H2 by Symmetry Arguments
FWIW my background is in physics and maths, but I am just starting a chemistry PhD (the last time I took a chemistry class was high school). I have only some background in representation theory, and ...
- 141
0
votes
0
answers
49
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are the exact and kohn-sham electron densities totally symmetric?
For any molecule with open or closed shells considering the electronic state to be the ground state:
Is the exact electron density totally symmetric?
is the Kohn-Sham electron density totally ...
2
votes
1
answer
91
views
How to find a symmetry group of a system if all the symmetry transformations do not obey closure and don't form a group?
For instance, consider a system with $p_x$ and $p_z$ orbitals at the vertices of a square (on xy-plane). A square by itself would have $D_4$ symmetry. However, because of the $p_x$ orbital; the $90^\...
- 21
1
vote
0
answers
42
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What is the link between the classical and quantum definition of the symmetry number?
From what I understand, the symmetry number for a molecule can be defined in 2 ways:
1. The quantum mechanical symmetry number corrects for overcounting the number of possible rotational states of a ...
- 647
2
votes
0
answers
1k
views
What is the precise meaning of "in-phase" (and "out-of-phase") in this context?
I am currently studying the textbook Infrared and Raman Spectroscopy, 2nd edition, by Peter Larkin. In a section entitled Symmetry: Infrared and Raman Active Vibrations, the author says the following:
...
- 1,083
2
votes
0
answers
51
views
Determining symmetry correction by looking at rotational quantum states
I'm trying to understand the relationship between symmetry correction and rotational quantum states, particularly in the case of dipoles with identical atoms.
For an angular momentum quantum number $...
- 647
2
votes
0
answers
250
views
Why is the transition (0,0,0) -> (1,0,1) observed in a gas phase IR spectrum of CO2?
Let ($v_1$,$v_2$,$v_3$) denote the vibrational state of $CO_2$.
Why is the transition $(0,0,0)\rightarrow (1,0,1)$ observed when the trasition $(0,0,0)\rightarrow(1,0,0)$ (asymmetric stretch) is not ...
- 21
0
votes
1
answer
116
views
On the meaning of distinguishability, and wavefunctions for 3 electron atoms
In a 2-electron atom at lowest energy, the $(1s)^2$ is occupied and the electronic wave-function must satisfy anti-symmetry requirements in the particle coordinates, as the spatial wave function is ...
- 133
1
vote
0
answers
57
views
Stabilizing donor-acceptor interaction between orthogonal orbitals in the SN2 transition state?
For the $\mathrm{S_N2}$ reaction between chloroacetone and iodide, my professor has drawn a donor-acceptor interaction between the iodine lone pair attacking the Cl-substituted carbon and the π ...
3
votes
1
answer
137
views
Spatial Wavefunction Symmetries and Identical Particles
I was reading this and it mentions in the 3-electron section, that for a spacial wave function to be symmetric under fermion swapping, it must be a function of even parity. Similarly for anti-symmetry ...
- 133
4
votes
0
answers
62
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Multiplicity letter codes for large amount of states
Well, let's say we have a large amount of states computed (e.g. over 50), all with the same multiplicity.
So, our ground state can be $X^2\Sigma^+_g$ and we can continue with $B^2, C^2$ etc. as ...
- 1,267
13
votes
2
answers
2k
views
Relationship between the symmetry number of a molecule as used in rotational spectroscopy and point group
While doing a problem set I noticed that the symmetry number of a molecule turns out (usually) to be half the number of symmetry elements that the point group the molecule belongs to.
When I say ...
- 1,443
5
votes
0
answers
226
views
How to derive a state symmetry in D2h point group from its wavefunction?
Let's have an atomic carbon with the following electron configuration:
$$
1s^2 2s^2 2p^2
$$
One of it's levels is ${}^1S_0$, which is corresponding with the following state:
$$
\begin{align}
\left| ...
- 1,267
4
votes
1
answer
349
views
Molecular orbitals symmetry - states notation
I'm reading some papers and I'm repeatedly seeing the following notation of system states:
Could you, please, explain to me the meaning of it?
E.g. the state $B^2 \Sigma_u^+$ - I'm aware, that $\...
- 1,267
4
votes
1
answer
217
views
Breaking degeneracy in phosphorus pentachloride
Recently, in a class discussion, the following point was brought up:
Although the axial and equatorial bond lengths in $\ce {PCl5}$ are inequivalent, when we consider the time-averaged $\ce {P-Cl}$...
- 10.7k
15
votes
2
answers
463
views
What constraints are imposed on a wavefunction by the symmetry of the system?
As a follow-up to my answer here, I'd like to ask what exactly does it mean for a wavefunction to "respect the symmetry" of the system.
The original context is: immediately after ionisation of $\ce{...
- 71.6k
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
5
votes
1
answer
914
views
Is there an example of a closed shell molecule with a permanent ground state magnetic dipole?
It seems that molecules of point group C$_{n}$ and C$_{nh}$ can in principle support a permanent magnetic dipole moment (Barron, 2004). However, I cannot think of any closed shell molecules that ...
- 2,120
21
votes
2
answers
6k
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Jahn-Teller Distortions in Square Planar Complexes?
A Jahn-Teller distortion is predicted whenever a non-linear symmetric molecule has degenerate orbitals and has unequal electron occupation in those degenerate orbitals. Of course, this most often is ...
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