22
votes
Is the number of possible Bravais lattices a mathematical fact?
Quasicrystals were known well before 2015. The recent developments is in showing that such crystals exist naturally, rather than just in synthesized samples. The first (nowadays generally accepted) ...
- 4,711
21
votes
Accepted
How to understand the time-reversal symmetry in graphene?
Two-band model for graphene. To simplify the discussion of Dirac points, it is sufficient to consider a nearest-neighbor tight-binding 2-band model for graphene. This is a spinless model because spin-...
- 10.9k
20
votes
Accepted
How to deduce phase transitions from a phonon calculation?
Background theory. In the harmonic approximation, the potential energy surface (PES) is expanded about an equilibrium point to second order, to obtain the Hamiltonian:
$$
\hat{H}=\sum_{p,\alpha}-\frac{...
- 10.9k
14
votes
Accepted
How is group theory used to deduce which of these integrals are equal to 0?
The question is too broad to be answered directly so I will provide a somewhat general scheme.
Basically in an integral like
$$
\int d\mu A B C
$$
one would seek to expand each part in irreducible ...
- 256
11
votes
Accepted
Topological order in Weyl Semimetal
A Weyl point is a crossing of two bands. A two-band crossing can be described using the general Hamiltonian:
$$
\hat{H}(\mathbf{k})=d_0(\mathbf{k})+d_1(\mathbf{k})\sigma_1+d_2(\mathbf{k})\sigma_2+d_3(\...
- 10.9k
11
votes
Accepted
conceptual problem about the energy band along the High symmetry point in the Brillouin zone
I will try to outline this in simple terms. There are certainly more rigorous explanations.
The high-symmetry points in the Brillouin zone are those that remain physically identical when certain ...
- 876
11
votes
What are good tools for visualizing glide planes and screw axes?
Jmol/JSmol
Did you consider Jmol/JSmol? It is freely available for Windows / Mac / Linux, scriptable, may export what is being displayed in formats relevant to chemistry (e.g., .pdb, .sdf), as image (...
- 1,579
10
votes
Accepted
Get fractional coordinates from special Wyckoff positions
From that reference, what we got is the bond length from the atomic positions.
One easy way is to look for a CIF file with the crystal information.
From the CIF49801 bellow, we get the following info:
...
- 22.3k
10
votes
Accepted
Does the spin polarised DFT calculation mean broken time reversal symmetry?
Yes, broken symmetry solutions do break time-reversal symmetry, and that's one of the reasons why they are unphysical when the total magnetic moment of the system is 0 (although they are physical when ...
- 9,076
10
votes
Accepted
How to extract the crystal symmetry from VASPs POSCAR/CONTCAR file?
There are multiple programs that can do this. As far as I know, all the open source codes use the excellent spglib package by Atsushi Togo "under the hood" for space group perception, ...
- 9,045
9
votes
How is group theory used to deduce which of these integrals are equal to 0?
First, you have to transform all the basis functions into the irreducible representations (irreps) of the point group of the molecule. You can do this with standard projection formulas.
Once, you know ...
- 1,431
9
votes
How to build a nanocluster?
A possible tool is the ASE python package (open-source):
https://wiki.fysik.dtu.dk/ase/ase/cluster/cluster.html
Another tool is materials studio software. Unfortunately, it is not free.
- 14.9k
9
votes
Nematicity in superconductors
Yes, nematic order is an alignment of rotational degrees of freedom without spatial structure.
One good example of a nematic phase occurs in a liquid crystal composed of elongated molecules. The ...
- 6,579
9
votes
Accepted
Symmetry group of p-benzoquinone
tldr: For a UV/Vis spectra, it shouldn't matter much.
I've found that Gaussian's AM1 / PM3 implementation often breaks symmetry during optimization. So I'm not surprised at your finding.
Moreover, in ...
- 9,045
9
votes
Inconsistencies in a famous point group table
After hours of conversation with three participants including me, I can make the following conclusions.
Answer to the question
It's likely an unintentional "error" in the publication. In ...
- 33.6k
8
votes
How to build a nanocluster?
Nanocut
From its site:
Nanocut is a program designed to cut out various objects from three
dimensional crystal structures. It is aimed to be helpful when
creating geometry input for atomistic ...
- 22.3k
8
votes
Rotation of crystal structure to match another structure of the same compound/polymorph
If you know which atoms correspond to each other in the two structures,
you can use a structural superposition method.
Least-squares superposition methods find the rotation matrix and translation that ...
- 1,780
8
votes
What will break the time-reversal symmetry?
Another way to explicitly break time-reversal symmetry is by applying circularly polarized light. Under time reversal, left circularly polarized light transforms to right circularly polarized light, ...
- 4,711
8
votes
What will break the time-reversal symmetry?
I will first take a generic view-point and then quote some examples in condensed matter & materials modeling. Time-reversal symmetry is one of two discrete symmetries usually discussed in the ...
- 2,342
8
votes
What is the difference between U(1) and O(2) symmetry?
The 1-dimensional unitary group U(1) simply corresponds to all complex numbers with a modulus of 1. This is isomorphic to the special orthogonal group SO(2), which corresponds to all real 2x2 rotation ...
- 1,431
8
votes
Effect of ISYM tag on Partial Density of States (VASP version < 6)
The typical calculation flow for the density of states is:
Geometric relaxation to obtain the lowest-energy structure (CONTCAR) [1relax] (For your system, you should do the spin-polarized calculation ...
- 14.9k
8
votes
Accepted
Inversion symmetry in 2D materials
Let's give it another go: In the monolayer you would place the inversion centre on the green atom. But this would reverse the direction of the trigonal prism formed by the yellow atoms. Hence, there ...
- 1,431
7
votes
What does it mean to assign group operations to distinct sets for space groups?
When your lattice is primitive you have only the (0,0,0)+ set; when your lattice has some kind of centering (body- or face-centering) other sets are present, such as (1/2, 1/2, 1/2)+ or (1/2, 1/2, 0)+
...
- 651
7
votes
Accepted
Effect of ISYM tag on Partial Density of States (VASP version < 6)
Based on the comments I shared above, it seems that the quality of the charge density is fine. It is just the projection onto atoms that may not be done correctly. If this is indeed the case, then you ...
- 7,281
7
votes
Accepted
Should one consider the spatial degeneracies of the electronic state while calculating the Gibbs free energy?
First, let's look from the most fundamental point of view. For this part of the answer I'll be referencing McQuarrie's Statistical Mechanics [1].
As the Gibbs free energy, $G$, can be calculated from ...
7
votes
About LaCrO3 space group stability
First of all make sure both phases are stable or not, to check stability of any phase, find mechanical stability and dynamical stability. From mechanical stability, I am referring to stiffness matrix ...
- 3,921
6
votes
Accepted
How to analyze the band symmetry with Quantum ESPRESSO?
This is standard output of bands.x which is a post-processing code to plot band structures used in QE under the PP folder.
- 2,048
6
votes
Is there a difference in performance when the symmetry is specified via ibrav in Quantum ESPRESSO?
There is no guaranteed increase in performance if you specify a non-zero value for ibrav. There is an additional layer to this - Whether the atomic positions are specified in cartesian or crystal ...
- 2,342
6
votes
Rotation of crystal structure to match another structure of the same compound/polymorph
If you're familiar with Python, this can be done using pymatgen fairly easily.
To illustrate, let's first define our problem:
...
- 1,501
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