All Questions
Tagged with quantum-chemistry group-theory
17
questions
8
votes
2
answers
612
views
Mulliken Labels: How do I tell apart E, doubly degenerate, symmetry apart from T, triply degenerate, symmetry for a molecular orbital?
With A and B, it's pretty simple. If you rotate the molecule about its principle axis to where the orbitals line up, and the signs change, it's Mulliken label has a B. otherwise, it's A.
I heard E ...
- 109
0
votes
0
answers
47
views
Reduction of direct product representation
When we do the reduction of the reducible representation generated from the total wavefunction expressed as product of MOs of appropriate symmetry, we can find the direct sum of more than one ...
- 101
0
votes
0
answers
54
views
Group theory and exact Eigenfunctions of Hamiltonian
I think I've understand why the real Eigenfunctions of Hamiltonian belong to a given irreducible representation and I've read that also MOs have to transform as irreducible representation due to the ...
- 101
7
votes
2
answers
101
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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
views
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
0
votes
0
answers
70
views
Electronic states of VO vanadium oxide in $C_{2v}$ point group
The electron configuration of $V^{2+}$: ... 3$d^{3}$ with 3 d electrons in 3 d orbitals. In $C_{\infty v}$, $d_{xz}$ and $d_{yz}$ have $\Pi$ IRREP; $d_{z}^{2}$ has $\Sigma^{+}$ IRREP; $d_{x^{2}-y^{2}}$...
- 309
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
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
9
votes
0
answers
430
views
Vanishing integral rule for two-electron integrals
I understand the vanishing integral rule for a one-electron integral to be:
$$\langle i | \hat{O} | j \rangle = 0 \hspace{1cm} \mathrm{if} \hspace{0.2cm} \Gamma_O \neq \Gamma_i \otimes \Gamma_j$$
...
- 1,271
7
votes
1
answer
944
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 ...
- 369
14
votes
2
answers
5k
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 ...
- 1,267
11
votes
2
answers
2k
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 ...
- 1,267
3
votes
2
answers
17k
views
How can the ground state electron configuration for a d3 complex correspond to an F term symbol?
The ground-state term symbol from a $\mathrm{d^3}$ Tanabe-Sugano diagram is $\mathrm{^4F}$. My question is how the total orbital quantum number $\Lambda=3$, or $\mathrm{F}$ term, arises.
For a $\...
- 1,648
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