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Here I will take Mg3Sb2 from Materials Project as an example to demonstrate the bandstructure calculation flow with the MBJ method.
(I) structure relaxation
(II) PBE band calculation based on the relaxed structure
(a) self-consistent (SCF) calculation [10_scf_cal].
(b) band calculation based on converged charge density at (II-a) [11_band_cal].
(c) read ...
12
A little background on why I asked this question:
I have a desktop PC with an AMD Ryzen 5 processor, 4 cores 8 logical threads and 32GB DDR4 RAM. I'm trying to do DFT-GGA calculations on a 2D Xene with hydrogen atoms adsorbed at the surface. I'm using a 4x4 supercell as a model for a total of 32 atoms (16 for X and 16 for H). Without spin-orbit coupling (...
12
For the "why" you should use the tetrahedron method when computing the density of states, check out this paper on exactly that topic! In short, other approaches (e.g. Gaussian smearing) will occasionally obscure (and artificially introduce) some features of the density of states.
As for how the method works, quoting from the paper directly about ...
11
The usual strategy to perform a band structure calculation in DFT has two steps:
Perform a self-consistent calculation using a uniform $\mathbf{k}$-point grid to determine the self-consistent potential.
Perform a non-self-consistent calculation using the potential determined in step 1 for some $\mathbf{k}$-point path along the Brillouin zone.
In VASP, the ...
11
Short answer: Yes, doubling the volume of the simulation cell you will be able to effectively sample a finer $\mathbf{k}$-point grid to calculate the dielectric function. However, the calculation will be more expensive than simply increasing the number of $\mathbf{k}$-points directly in the primitive cell calculation.
Longer answer: In reciprocal space, the ...
11
It is not necessary to care about the total energy versus the number of k points in irreducible reciprocal space, which is closely related to the symmetry of the investigated structure. Of course, you can always read it from IBZKPT with a self-consistent run or any other run using VASP. Also, the printed number in IBZKPT is related to the ISYM tag.
I assume ...
11
If the crystal unit cell is in a format readable by ASE, then you can use code that looks approximately like so:
from ase.io import read
atoms = read("myfilename.xyz")
bandpath = atoms.cell.bandpath()
This bandpath object will have the relevant attributes to play with (kpoint coordinates, special point labels, special point coordinates, etc). ...
10
In brief, it will influence the electronic energy and thereby all properties derived from that. Too small a smearing width and you might have trouble converging the self-consistent field. Too large and the extrapolation back to 0 K from the fictitious finite temperature will be less accurate. Depending on the smearing method (e.g. Gaussian smearing), you can ...
10
How to make a k-point convergence test for a bulk structure with a lower k-point in the z-direction?
If you have already obtained satisfactory convergence with a (relatively) sparse k-point grid, there is no motivation to go for a denser grid. So if you have already achieved convergence with 12x12x4, there's no need to go to 12x12x12.
If you are talking about graphene, which is 2-D, there is no need to sample points along the out-of-plane direction.
There ...
10
When using a method like density functional theory we have to consider the accuracy of (i) the numerical solution of the problem and (ii) the physical model we use.
The convergence you are refering to is numerical (i.e. how many $\mathbf{k}$-points to include in the numerical approximation of replacing an integral over the Brillouin zone with a discrete sum)....
10
As already specified in the previous answers, the choice of K-Grid mesh should be taken upon verifying the convergence of the desired quantity. We usually start with the convergence of the total energy, but for other properties like optical spectra, for example, the converged grid with respect to the energy should not be enough, and a denser grid is usually ...
9
Like many other parameters in QE one of the best methods is to simply test yourself and weight your options.
You may start with 1x1x1 and go to 3x3x3 for example and check the following.
Do you get convergence?
What is final energy?
What is dE in the final step?
(plot the above parameters to see the diminishing returns)
Then determine computation time ...
9
Very good question.
I think that when you select one of the many different disordered structures as been a representative one, that structure is not disordered anymore, it is an structure as any other. Following this, I think that the convergence test can be done in a similar way that for any other primitive cell.
The problem of course, is when you decide ...
9
It will obviously affect the calculation time, which would be the only reason I would discourage you based on my knowledge. It should not harm anything to continue with a higher symmetry k-mesh, but I believe there are problems with a lower symmetry k-mesh.
Lattice of (2, 2, 4) can use a k-mesh of (9, 9, 5)
Lattice of (4, 4, 4) should probably not use a ...
9
If you give the explicit points in the KPOINTS file in VASP for a band structure calculation, for example as required for hybrid functionals, the bands will only be calculated at the explicit $\mathbf{k}$-points you list. For example, if you have a cubic cell and want the path between $\Gamma$ at $(0,0,0)$ and X at $(0.5,0,0)$, then simply writing:
$$
0.0 \,\...
9
Calculating densities of states is a tricky problem, as you correctly recognized. The density of states is:
$$
\tag{1}
g(E)=\sum_{n}\int\frac{d\mathbf{k}}{(2\pi)^3}\delta(E-E_{n\mathbf{k}}),
$$
where $E_{n\mathbf{k}}$ are the electronic energies and the integral is over the Brillouin zone. There are various strategies that one can follow, including:
...
8
In order to generate the k-path for any material, the first thing to know is the crystal system (a,b) of it. This information can be obtained experimentally via X-ray diffraction analysis, form the crystallographic information file (CIF) or from material databases.
Knowing the crystal system, then you have to look for the corresponding Brillouin zone. The ...
8
If you are really interested in learning how to generate the path, I strongly advice you to avoid using any automatic tool like suggested in previous answers.
In the Wiki page entitle Brillouin zone you can find the first Brillouin zone for each one of the Bravais lattice. This Wiki is based on the following paper:
Setyawan, Wahyu; Curtarolo, Stefano (2010)....
7
To add to ProfM's answer, you can generate lists of k-points along high-symmetry paths in the Brillouin zone using XCrySDen. Open your structure (you can format it as a XYZ file) and go to the Tools menu, and open k-path selection. Now you will be shown your Brillouin zone, and you can click the points you want to include in your path. After you're satisfied ...
7
How to make a k-point convergence test for a bulk structure with a lower k-point in the z-direction?
I agree with the answer provided by Xivi76. I just wanted to add that some codes have a very nice functionality that facilitates convergence: rather than explicitly writing out a $\mathbf{k}$-point grid $n_1\times n_2\times n_3$, in which in principle you have to converge three values; you can instead specify a $\mathbf{k}$-point spacing or density, in which ...
7
You can upload your structure [many formats are supported] into the following website to generate the input file for your Quantum Espresso calculation.
Materials Cloud Website
There are three choices for the k sampling in terms of the distance between two k points.
Very fine [0.15 1/A]
Fine [0.2 1/A]
Normal [0.3 1/A]
Very often, you can just take the ...
7
Gamma Only:
A k-point mesh (grid) only includes (samples) the gamma point of the Brillouin zone.
Gamma Centred:
A k-point mesh (grid) that is centred around the gamma point of the Brillouin zone, and includes other points (often equally spaced, though not always). A gamma centred k-point grid often reduces computation cost, and contains important information ...
6
The reason why even number k-point grids are prefered in the case of some symmetries like FCC lattices is mainly due to the concept of the Irreducible Brillouin Zone (IBZ).
Here is an example for FCC:
Here the number of points in the k-point grid in the IBZ is the same for even as well as odd k-points (M value). Here the points in the IBZ determine the ...
6
In sisl one can create a Monkhorst-Pack grid with zooming capabilities.
Here is a small Python snippet which creates the k-points for the zoomed in region.
import numpy as np
import sisl
# time-reversal-symmetry
trs = True
# first argument is the lattice vectors (in case you want them in 1/Ang)
# in this case it is just a square box of side-lengths 1 Ang
...
6
How to make a k-point convergence test for a bulk structure with a lower k-point in the z-direction?
As far as my knowledge this a relationship between k-points and lattice constants values. I'll give you an example of a layered hexagonal material WS2:
Lattice constants : a=3.17 b=3.17 c=12.41 ; so c/a = 12.41/3.17=3.91
K-points : If I chose kx=12, ky will be equal to 12 but kz should be equal to an integer close to the kx divided by c/a. I mean kz=12/3.91=...
6
The best strategy when performing convergence tests is to directly converge the quantity you are interested in. This "quantity" can be a straight-forward physical property, like the band gap of a material, or a composite (for lack of a better word) property. In your case, you are interested in comparing the electronic density of states (DOS) ...
6
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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The computational content of the cited paper includes two parts:
DFT calculations (such as band structures) with QE;
Transport calculations (such as Seebeck coefficients) with BoltzTraP based on DFT calculations.
The $8 \times 8 \times 8$ and $9 \times 9 \times 9$ are chosen for DFT calculations. However, the dense k-mesh with $40000$ points in the first ...
6
The k-point discretization has the same meaning in plane wave codes as LCAO based codes. In fact, it has the same meaning in all DFT related codes. It defines the integration of the Brillouin zone. You want the integration to be good enough to capture the relevant physics (e.g. graphene with k-point sampling touching the Dirac point vs Gamma-only) but also ...
6
You can start with this bash script for Aluminum to begin
Note: Make sure to fix two quantities while changing third one among INCAR,KPOINTS,POSCAR
Lattice optimization
for i in `seq -w 4.01 0.01 4.05` # change the range needed
do
cat <<EOF >POSCAR
Al bulk FCC
$i
0 0.5 0.5
0.5 0 0.5
0.5 0.5 0
1
direct
0.0 0.0 0.0
EOF
mkdir $i
cp INCAR $i/
cp ...
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