All Questions
Tagged with symmetry group-theory
70
questions
2
votes
1
answer
73
views
Identifying Type of Symmetry Operations
From the given set of symmetry operations for a space group, say, P-3m1 or Cmma, how can one identify the type of all symmetry operations. For example, how to distinguish the axis of rotation symmetry ...
- 123
0
votes
0
answers
59
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How do we determine the local symmetry of anatase TiO2?
In this physical review B paper, the authors mentioned that the local symmetry of anatase TiO2 is D2d point group. Also, in this applied physics letters paper, the authors mentioned that the symmetry ...
- 273
1
vote
1
answer
88
views
Electronic configuration and symmetry labels of 3d$^7$ ions
In 3d$^7$ ions, e.g. Co$^{2+}$, the ground state is $^4$F, and it contains different levels due to the crystal field, such as $^4T_{1g}$, $^4T_{2g}$ and $^4A_{2g}$. Can anyone tell me what exactly ...
- 11
1
vote
0
answers
49
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How do I assign functions for cartesian coordinates and rotations to irreducible representations of a character table?
I do not really understand the intuition behind the functions assigned to irreducible representations.
For example, in H₂O, the A₂ representation is given by
...
- 128
2
votes
1
answer
208
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Is there a difference between $A_{1g}$ modes and $A_{g}$ modes?
I know that both are totally symmetric and that the '$1$', according to the Mulliken table, refers to symmetry around the $C_2$ axis but I was reading some papers and found that modes were sometimes ...
- 65
3
votes
1
answer
50
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Are A1g modes reduced at 180 degrees polarisation in Raman spectra?
I have read that A1g modes are identifiable in Raman spectra by looking at cross-polarised Raman spectra and seeing peaks that strongly reduce in intensity. So essentially, the intensity of A1g modes ...
- 65
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
2
votes
0
answers
77
views
Factor Group Analysis of Na2SO4 - Site Group Symmetry
I'm still trying to understand how to construct a factor group analysis for a given molecular point group and the resulting solid state group symmetry. For this I searched for some examples and found ...
- 4,322
3
votes
1
answer
305
views
Relation between symmetry of a reciprocal vector and lattice planes perpendicular to it
What is the relation the symmetry of a high-symmetry point in the first Brillouin zone and lattice planes perpendicular to it? Are the two symmetries equivalent?
I have this question because I want to ...
- 273
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
411
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
2
votes
1
answer
405
views
What is m.2m point group?
I'm using Bilbao Crystallographic Server to find 3D crystallographic point groups of the K points of anatase TiO2.
Since the space group of anatse TiO2 is $I4_1/amd$, on this page, I found the point ...
- 273
3
votes
1
answer
1k
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How do we find the SALCs?
I am trying to understand exactly what IRREPs are and, in order to know more about it, I started reading the chem.libretext course on molecular symmetry which up to this point seemed fairly ...
- 131
10
votes
0
answers
141
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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
0
answers
59
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Is there a better coordinate framework and symmetry operator for constructing molecular orbitals of molecules with higher-order geometry?
The following excerpt is taken from [1] (with a few rewording, emphasizes are mine).
In an attempt to construct molecular orbital (MO) of any molecule, one needs to determine the symmetries of ...
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