My first VASP (fcc Si)

I start to use VASP. Now I start VASP with workshop example for fcc Si.

cms.mpi.univie.ac.at
 
VASP example calculations - Vaspwiki
http://cms.mpi.univie.ac.at/wiki/index.php/VASP_example_calculations

This is the sample to calculate the energy for various lattice constant. We can get the optimized lattice parameter with the lowest energy.

INCAR

System = fcc Si    # names of System
ISTART = 0         # startjob: 0-new 1-cont 2-samecut
ICHARG = 2         # charge: 1-file 2-atom 10-const
ENCUT = 240        # energy cutoff in eV
ISMEAR = 0         # part. occupancies: -5-Blochl -4-tet -1-fermi 0-gaus 0 MP
SIGMA = 0.1        # broadening in eV -4-tet -1-fermi 0-gaus
ISTARTISTART determines whether or not to read the WAVECAR file. 0 for initial orbitals. 1 for reading WAVECAR file. If you don’t set this parameter, if WAVECAR exists, 1 is set. if no WAVECAR, 0 is set. I don’t know WAVECAR yet, I think it include the information of orbitals of wave function.
ICHARGICHARG determines how VASP constructs the initial charge density. (I don’t know the initial charge density. that of an isolated atom?) 0: initial charge density, 1: read CHGCAR, 2: superposition?, 4: read potential from file POT (?). VASP5.1 or later, 10: non-selfconsistent calculations.Default value is 2 for ISTART=0, 0 for others.
ENCUTCutoff energy. Default value is largest ENMAX on the POTCAR file. 
ISMEARI don’t understand but it’s setting for ion smearing which determines how the partial occupancies. -1: Fermi model, 0: Gaussian smearing, 1…N: Methfessel-Paxton (MP) order N, -2: read WAVECAR, -3: smearing-parameters supplied in the INCAR file, -4: tetrahedron method without Blochl corrections。-5: tetrahedron method with Blochl corrections。Default value is 1. -5 is recommended for total energy and DOS calculation. The calculated forces and the stress tensor can be wrong by up to 5 to 10% for metals. For the calculation of phonon frequencies based on forces, ISMEAR>0 is recommend. The method of Methfessel-Paxton (ISMEAR>0) also results in a very accurate description of the total energy, nevertheless the width of the smearing (SIGMA) must be chosen carefully. Too large smearing-parameters (SIGMA?) might result in a wrong total energy, smearing-parameter. Small smearing parameters require a dense mesh of k-points. SIGMA should be as large as possible keeping the difference between the free energy and the total energy (i.e. the term entropy T*S). The Gaussian smearing method also leads to reasonable results in most cases.
SIGMAThe width of smearing. Default value is 0.2. It’s used when ISMEAR is -4, -1, or 0?

KPOINTS

k-points
 0
Monkhorst Pack
 11 11 11
 0 0 0

line 1: comments
line 2: number of k-points. Automatically generated if 0.
line 3: Start “G” or “g” for Gamma centered grid, start “M” or “m” for MonkHorst-Pack scheme. Others are not recommended.
Line 4: subdivisions
line 5: optional shift of the mesh. Generally 0.

POSCAR

fcc Si:
 3.9
 0.5 0.5 0.0
 0.0 0.5 0.5
 0.5 0.0 0.5
   1
cartesian
0 0 0

line 1: comments
line 2: lattice constant
line 3-5: lattice vector
line 6: number of each element. Order is required to set the same as the order in POTCAR.
line 7: How to set atoms coordinate
line 8-: coordinate of atoms

POTCAR

Copy the potential from potential directory. PAW_PBE is used here.

loop.sh

Batch file for the iterate calculation. Lattice constant is changed from 3.5 to 4.3. We need to change output file to remain and path for VASP. 

Results

Total energy from OSZICAR is summarized in SUMMARY.fcc. We can get the following plot using gnuplot (or excel).

 We find the lattice constant of about 3.9 is the most stable. 

Relaxation

If we make INCAR as follows, we can find the most stable structure and energy by relaxation.

System = fcc Si    # names of System
ISTART = 0         # startjob: 0-new 1-cont 2-samecut
ICHARG = 2         # charge: 1-file 2-atom 10-const
ENCUT = 240        # energy cutoff in eV
ISMEAR = 0         # part. occupancies: -5-Blochl -4-tet -1-fermi 0-gaus 0 MP
SIGMA = 0.1        # broadening in eV -4-tet -1-fermi 0-gaus
IBRION = 1         # relaxation method
NSW = 100          # maximum steps of ion
NELMIN = 4         # minimum of self consistent loop
ISIF = 3           # calculation mode for force etc.

IBRION: way to relaxation. -1 is the default value.
NSW: maximum step for relaxation. 0 is default. Calculation is finished when the difference of energy reaches less than EDIFF (default: 10-4).
NELMIN: minimum step for self consistent loop. For IBRION=1 (a quasi-Newton algorithm), 4~8 is good.
ISIF: determines whether the stress tensor is calculated and which principal degrees-of-freedom are allowed to change in relaxation and molecular dynamics runs.

The results (OUTCAR) showed Etot=-4.878 eV for lattice constant of 3.86 A is the most stable.

k-points mesh

I try to check the convergence of calculation for various k-points. loop.sh is modified as follows.

#! /bin/bash
BIN=vasp_std
rm WAVECAR SUMMARY.fcc
for i in  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ; do
cat KPOINTS !
K-Points
 0
Monkhorst Pack
 $i $i $i
 0  0  0
!
echo "a= $i" ; $BIN
E=`awk '/F=/ {print $0}' OSZICAR` ; echo $i $E  SUMMARY.kpoints
done
cat SUMMARY.kpoints

The following plot is shown energy vs k-points.

Energy is converged more than k-points of 4.

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