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) ...
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  • 3,938
18 votes
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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-...
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  • 10k
17 votes
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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{...
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  • 10k
14 votes
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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 ...
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13 votes

How to deduce phase transitions from a phonon calculation?

The answer of @ProfM is already very complete, but I wanted to tackle your question from a more practical point of view. The presence of imaginary frequencies indicate that there are atomic positions ...
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  • 391
11 votes
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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 ...
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  • 856
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 (...
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  • 1,457
10 votes
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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(\...
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  • 10k
10 votes
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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: ...
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10 votes
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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 ...
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  • 6,408
10 votes
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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, ...
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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 ...
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  • 1,411
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.
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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 ...
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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 ...
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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 ...
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  • 1,485
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, ...
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  • 3,938
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 ...
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  • 2,172
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 ...
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  • 1,411
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 ...
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8 votes
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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 ...
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  • 1,411
8 votes
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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 ...
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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)+ ...
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  • 601
7 votes
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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 ...
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  • 6,852
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 ...
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  • 3,054
6 votes
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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.
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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 ...
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  • 2,172
6 votes
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How do I extract the wave function from a VASP calculation?

It seems you are looking for a package to compute the irreducible representation of electronic states computed by VASP. This has been recently developed: J. Gao J, Wu Q, Persson C, Z. Wang. Irvsp: to ...
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6 votes

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

Independent of facing a 3D sample, or one of 2D/2.5D, IUCr's definition applies to both of them when stating «There are two definitions of the notion of quasicrystal. A quasicrystal is an aperiodic ...
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  • 1,457
6 votes
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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 ...
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