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Questions tagged [symmetry]

Questions relating to symmetries and symmetry groups encountered in materials modeling.

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20 votes
2 answers

How to deduce phase transitions from a phonon calculation?

I came across the concept of using phonons to establish a material's dynamical stability, based on whether or not imaginary frequencies are present in its phonon band structure. What I am struggling ...
koroma's user avatar
  • 303
17 votes
1 answer

How to understand the time-reversal symmetry in graphene?

A lot of references say that the Dirac cone in graphene is protected by inversion and time-reversal symmetries. How can one understand this statement? How can one show explicitly that the gapless ...
JensenPang's user avatar
  • 2,903
4 votes
1 answer

When orbitals are labeled based on their irreps in D2h, how are the orbitals ordered for an N atom?

I am performing calculations on a Nitrogen atom using CFOUR. A nitrogen atom has a point group of Dinfh, but ⁠CFOUR uses a lower symmetry of D2h instead. So, looking at the available Irreducible ...
Hemanth Haridas's user avatar
19 votes
4 answers

How is group theory used to deduce which of these integrals are equal to 0?

The number of all two-electron integrals: $$ \tag{1} \langle \phi_1 \phi_2|\phi_3\phi_4 \rangle = \int d^3\mathbf r' \int d^3\mathbf r'' \, \phi_1(\mathbf r'') \, \phi_2(\mathbf r') \frac{1}{|\mathbf ...
nougako's user avatar
  • 605
16 votes
2 answers

What are good tools for visualizing glide planes and screw axes?

While there are a few tools for visualizing crystal structures, I'm particularly curious to know tools for visualizing space group symmetry, including: screw axes glide planes I teach a class on ...
Geoff Hutchison's user avatar
12 votes
2 answers

Effect of ISYM tag on Partial Density of States (VASP version < 6)

This is from the entry for LORBIT in the VASP Wiki. For LORBIT >= 11 and ...
Hitanshu Sachania's user avatar
12 votes
1 answer

Dealing with symmetry of ordered primitive cell during DFT structure relaxation

I have a large disordered cubic structure that I would like to do AIMD on to look at cation diffusion. I found the primitive cell and then ordered it to create several configurations. I will then ...
DoubleKx's user avatar
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10 votes
1 answer

Proposing a 2D quasicrystal; what are the necessary and sufficient conditions? (If it looks like a duck and quacks like a duck, or...?)

Quasicrystals show repeating motifs or patterns but are not periodic. And yet their Fourier transforms invariably demonstrate a pattern of sharp peaks revealing that there is still an underlying... ...
uhoh's user avatar
  • 2,034
9 votes
1 answer

Partial density of states in random solid solutions

This question comes as a follow-up to; nonetheless, it is relevant on its own as well. To designate a particular crystal structure to a random ...
Hitanshu Sachania's user avatar
9 votes
1 answer

Why does mcsqs change the space group of generated SQS?

I made a binary special quasi-random structure (SQS) using mcsqs (distributed as part of the ...
Hitanshu Sachania's user avatar
6 votes
1 answer

For one atom, what is the correct point group?

I have a concern related to the follwoing question When orbitals are labeled based on their irreps in D2h, how are the orbitals ordered for an N atom? In which the following Answer clearly states that ...
Jaafar Mehrez's user avatar
5 votes
1 answer

Examples of anti-symmetric rank-3/4 tensors?

The anti-symmetric rank-3 and rank-4 tensors hold the following properties: \begin{align} \sigma_{mnk} &=-\sigma_{nmk} \\ \sigma_{mnkp} &=-\sigma_{nmkp} \end{align} Note I'm using ...
Jack's user avatar
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3 votes
1 answer

Why can this tensor have a T-odd and T-even part at the same time?

In this paper, the author discusses the following nonlinear response relation: $$\delta s_a=\alpha_{abc}E_bE_c \tag{1},$$ where $\delta s_a$ represents the spin polarization generated by the current ...
Jack's user avatar
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