Danny Rehn

        

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Band Structure via VASP

Contents

Prerequisites

Before starting, you will want the following software:

  1. VASP 5.3 or greater (this requires a license)
  2. pymatgen python libraries. See here for instructions on installing - I recommend installing with conda.
  3. Access to materialsproject.com
  4. VESTA (not entirely necessary, but useful visualizations of crystal structures)

Overview

Here we will compute the band structure of MoS\(_2\). The main steps are:

  1. Relax the atomic positions and/or cell
  2. Check atomic positions/lattice constants to ensure cell symmetries have not been broken
  3. Perform scf procedure with full \(\mathbf{k}\) mesh
  4. Calculate bands with selected \(\mathbf{k}\) points

It is useful to set up different directories corresponding to steps 1, 3, and 4.

$ ls
1-relax/  2-scf/  3-bands/

The initial structures for MoS\(_2\) come from the Materials Project (mp-2815).

1. Cell & atom relaxation

Files for this section: github link

In order to get accurate phonon modes, it is necessary to first relax the atomic positions and/or lattice constants. VASP provides several different methods for relaxation, provided by specifying the ISIF tag (see here for details).

Generally, there are two different cases:

  1. The desired symmetry of the cell is known, but the atomic positions and/or lattice constants are not known. In this case, you want to enforce symmetry of the starting structure in the POSCAR file. You should use: IBRION = 2, ISYM = 2. The choice of ISIF also needs to be specified. To relax atom positions only (lattice constants fixed), choose ISIF = 2. For relaxation of the lattice constants, choose either ISIF = 3 (cell volume can vary) or ISIF = 4 (cell volume remains fixed).
  2. The symmetry of the initial structure is not known to be correct. In this case, use IBRION = 2, ISYM = 0 (i.e., turn off symmetry). Usually you want ISIF = 3 for this case.

After this calculation, you will want to look at the CONTCAR file that is output. Depending on the choice of parameters in the INCAR file, you may notice that the symmetry of the cell has changed. For example, see the result of the second option above here. This file will need to be modified further (see part 2 below) before use in DFPT calculations.

2. Enforcing symmetries

Files for this section: github link

After performing the relaxation, it is possible that the resulting atomic positions and lattice constants in CONTCAR will not be symmetrized. For example, if using IBRION = 2, ISYM = 0, ISIF = 3, you will almost certainly not have the exact same lattice constants as you started with.

For band structure calculations, the wrong symmetry can cause the choice of \(\mathbf{k}\) path to be wrong if using automated scripts to generate the path for you. For example, the structure in CONTCAR could be very close to a hexagonal or tetragonal unit cell, but there could be just enough difference in the lattice constants for the cell to be classified as triclinic. This will result in the wrong choice of path for the band structure calculation.

To fix this problem, you may want to edit the CONTCAR file and enforce the symmetry you desire. For example, you could see values like -0.00001248932473 in the x,y, or z components of the lattice constants. This should most likely be 0, so you can modify and round to 0.00000000000000. After doing this for the lattice constants and atomic positions, it isn’t a terrible idea to run another relaxation, but this time with fixed lattice constants (ISIF =2) and possibly enforcing symmetry this time (ISYM = 2). This will leave you with a structure that has the symmetry properties that you most likely want for phonon calculations.

3. Self-consistent electron relaxation

Files for this section: github link

After relaxing the cell, you can use the final CONTCAR as input to the scf calculation (i.e., mv 1-relax/CONTCAR 2-scf/POSCAR).

SYSTEM  = MoS2
NCORE   = 8
#KPAR   = 8

ENCUT   = 600
ALGO    = Fast
IBRION  = -1
NSW     = 0
EDIFF   = 1.0e-06
ISYM    = 0
LREAL   = .FALSE.
ISMEAR  = 0
SIGMA   = 0.05
PREC    = Accurate
ADDGRID = .TRUE.

NWRITE  = 1
LCHARG  = .TRUE.
LWAVE   = .FALSE.

After running this, you can plot the electronic density of states using output from the DOSCAR file. The file vasp-dos.py in the 2-scf/ directory will do this automatically. The density of states is shown at right.

4. Calculate electron bands

Files for this section: github link

After performing the scf calculation, we need to choose an appropriate high symmetry path through the Brillouin zone and create a new KPOINTS. We then run a non-self-consistent electron calculation using VASP using the CHGCAR file from the 2-scf/folder. Before running VASP, do the following:

$ cp 2-scf/CHGCAR 3-bands

The easiest way to find the appropriate high symmetry path is by using the AFLOW website. Go to http://aflow.org/aflow_online.html. This website allows you to copy and paste a POSCAR file from VASP and will automatically figure out the appropriate \(\mathbf{k}\)-space path. Paste the POSCAR file to the input window and select ‘Kpath in the reciprocal space for band structure calculations’, then hit the Submit button on the top right of the window. This will generate a file for use in electron band structure calculations. The \(\mathbf{k}\)-path for the hexagonal lattice we are using is shown at right.

The output from AFLOW can now be used to generate band.conf. Our path is \(\Gamma\)-\(M\)-\(K\)-\(\Gamma\)-\(A\)-\(L\)-\(H\)-\(A\)-\(L\)-\(M\)-\(K\)-\(H\).

The bands are plotted using the electron-bands.py script shown in the 3-bands/ folder. This script uses pymatgen directly to get the bands from the vasprun.xml file.

AFLOW citation: S. Curtarolo, W. Setyawan, G. L. W. Hart, M. Jahnatek, R. V. Chepulskii, R. H. Taylor, S. Wang, J. Xue, K. Yang, O. Levy, M. Mehl, H. T. Stokes, D. O. Demchenko, and D. Morgan, AFLOW: an automatic framework for high-throughput materials discovery, Comp. Mat. Sci. 58, 218-226 (2012). [doi=10.1016/j.commatsci.2012.02.005]