Band gap renormalization in diamond using one-shot method

From VASP Wiki

Task

Calculating the zero-point renormalization of the band gap in cubic diamond carbon.

Input

POSCAR

  • Primitive cell (POSCAR.prim):
C_2_fcc
   1.00000000000000
     0.0000000000000000   1.783493 1.783493
     1.783493   0.0000000000000000   1.783493
     1.783493 1.783493    0.0000000000000000
   C
     2
Direct
  0.0000000000000000  0.0000000000000000  0.0000000000000000
  0.7500000000000000  0.7500000000000000  0.7500000000000000 
  • 4x4x4 super cell used in this calculation (POSCAR.4x4x4):
C_128_fcc
   1.00000000000000
    0.00000000   7.13397200   7.13397200
    7.13397200   0.00000000   7.13397200
    7.13397200   7.13397200   0.00000000
   C
  128
Direct
   0.00000000   0.00000000   0.00000000
   0.25000000   0.00000000   0.00000000
   0.50000000   0.00000000   0.00000000
   0.75000000   0.00000000   0.00000000
   0.00000000   0.25000000   0.00000000
   0.25000000   0.25000000   0.00000000
   0.50000000   0.25000000   0.00000000
   0.75000000   0.25000000   0.00000000
   0.00000000   0.50000000   0.00000000
   0.25000000   0.50000000   0.00000000
   0.50000000   0.50000000   0.00000000
   0.75000000   0.50000000   0.00000000
   0.00000000   0.75000000   0.00000000
   0.25000000   0.75000000   0.00000000
   0.50000000   0.75000000   0.00000000
   0.75000000   0.75000000   0.00000000
   0.00000000   0.00000000   0.25000000
   0.25000000   0.00000000   0.25000000
   0.50000000   0.00000000   0.25000000
   0.75000000   0.00000000   0.25000000
   0.00000000   0.25000000   0.25000000
   0.25000000   0.25000000   0.25000000
   0.50000000   0.25000000   0.25000000
   0.75000000   0.25000000   0.25000000
   0.00000000   0.50000000   0.25000000
   0.25000000   0.50000000   0.25000000
   0.50000000   0.50000000   0.25000000
   0.75000000   0.50000000   0.25000000
   0.00000000   0.75000000   0.25000000
   0.25000000   0.75000000   0.25000000
   0.50000000   0.75000000   0.25000000
   0.75000000   0.75000000   0.25000000
   0.00000000   0.00000000   0.50000000
   0.25000000   0.00000000   0.50000000
   0.50000000   0.00000000   0.50000000
   0.75000000   0.00000000   0.50000000
   0.00000000   0.25000000   0.50000000
   0.25000000   0.25000000   0.50000000
   0.50000000   0.25000000   0.50000000
   0.75000000   0.25000000   0.50000000
   0.00000000   0.50000000   0.50000000
   0.25000000   0.50000000   0.50000000
   0.50000000   0.50000000   0.50000000
   0.75000000   0.50000000   0.50000000
   0.00000000   0.75000000   0.50000000
   0.25000000   0.75000000   0.50000000
   0.50000000   0.75000000   0.50000000
   0.75000000   0.75000000   0.50000000
   0.00000000   0.00000000   0.75000000
   0.25000000   0.00000000   0.75000000
   0.50000000   0.00000000   0.75000000
   0.75000000   0.00000000   0.75000000
   0.00000000   0.25000000   0.75000000
   0.25000000   0.25000000   0.75000000
   0.50000000   0.25000000   0.75000000
   0.75000000   0.25000000   0.75000000
   0.00000000   0.50000000   0.75000000
   0.25000000   0.50000000   0.75000000
   0.50000000   0.50000000   0.75000000
   0.75000000   0.50000000   0.75000000
   0.00000000   0.75000000   0.75000000
   0.25000000   0.75000000   0.75000000
   0.50000000   0.75000000   0.75000000
   0.75000000   0.75000000   0.75000000
   0.18750000   0.18750000   0.18750000
   0.43750000   0.18750000   0.18750000
   0.68750000   0.18750000   0.18750000
   0.93750000   0.18750000   0.18750000
   0.18750000   0.43750000   0.18750000
   0.43750000   0.43750000   0.18750000
   0.68750000   0.43750000   0.18750000
   0.93750000   0.43750000   0.18750000
   0.18750000   0.68750000   0.18750000
   0.43750000   0.68750000   0.18750000
   0.68750000   0.68750000   0.18750000
   0.93750000   0.68750000   0.18750000
   0.18750000   0.93750000   0.18750000
   0.43750000   0.93750000   0.18750000
   0.68750000   0.93750000   0.18750000
   0.93750000   0.93750000   0.18750000
   0.18750000   0.18750000   0.43750000
   0.43750000   0.18750000   0.43750000
   0.68750000   0.18750000   0.43750000
   0.93750000   0.18750000   0.43750000
   0.18750000   0.43750000   0.43750000
   0.43750000   0.43750000   0.43750000
   0.68750000   0.43750000   0.43750000
   0.93750000   0.43750000   0.43750000
   0.18750000   0.68750000   0.43750000
   0.43750000   0.68750000   0.43750000
   0.68750000   0.68750000   0.43750000
   0.93750000   0.68750000   0.43750000
   0.18750000   0.93750000   0.43750000
   0.43750000   0.93750000   0.43750000
   0.68750000   0.93750000   0.43750000
   0.93750000   0.93750000   0.43750000
   0.18750000   0.18750000   0.68750000
   0.43750000   0.18750000   0.68750000
   0.68750000   0.18750000   0.68750000
   0.93750000   0.18750000   0.68750000
   0.18750000   0.43750000   0.68750000
   0.43750000   0.43750000   0.68750000
   0.68750000   0.43750000   0.68750000
   0.93750000   0.43750000   0.68750000
   0.18750000   0.68750000   0.68750000
   0.43750000   0.68750000   0.68750000
   0.68750000   0.68750000   0.68750000
   0.93750000   0.68750000   0.68750000
   0.18750000   0.93750000   0.68750000
   0.43750000   0.93750000   0.68750000
   0.68750000   0.93750000   0.68750000
   0.93750000   0.93750000   0.68750000
   0.18750000   0.18750000   0.93750000
   0.43750000   0.18750000   0.93750000
   0.68750000   0.18750000   0.93750000
   0.93750000   0.18750000   0.93750000
   0.18750000   0.43750000   0.93750000
   0.43750000   0.43750000   0.93750000
   0.68750000   0.43750000   0.93750000
   0.93750000   0.43750000   0.93750000
   0.18750000   0.68750000   0.93750000
   0.43750000   0.68750000   0.93750000
   0.68750000   0.68750000   0.93750000
   0.93750000   0.68750000   0.93750000
   0.18750000   0.93750000   0.93750000
   0.43750000   0.93750000   0.93750000
   0.68750000   0.93750000   0.93750000
   0.93750000   0.93750000   0.93750000

KPOINTS

K-Points
 0
Gamma
 1  1  1
 0  0  0

INCAR

general:
 System = cd-C
 PREC = Accurate
 ALGO = FAST
 ISMEAR = 0 
 SIGMA = 0.1;
 IBRION = 6
 PHON_LMC = .TRUE.
 PHON_NSTRUCT = 0
 PHON_NTLIST = 1
 PHON_TLIST = 0.0
  • The tags with "PHON_" control the electron-phonon couplings (EPC). PHON_LMC enables electron-phonon coupling in the calculations using Monte Carlo sampling. By selecting PHON_NSTRUCT=0 a one-shot configuration (ZG configuration) is obtained. The tag PHON_NTLIST selects the number of temperatures for which the structure with the one shot calculation is obtained. This requires also the list of temperatures given by PHON_TLIST which have exact PHON_NTLIST number of elements.
  • IBRION=6 is selected to obtain the eigenvectors and eigenvalues of the dynamical matrix at the Gamma point.

Calculation

This example will use a one-shot method, where only a single structure comprising the EPC is required for a given temperature.

The calculation consists of two steps:

  1. Obtain new "distorted" POSCAR file which contains the EPC. This calculation also contains the band gap of the original structure.
  2. Execute simple DFT calculation for the EPC structure to obtain the band gap.
  3. Extract ZPR as the difference between the band gaps from the two calculations.


Step 1 obtain structure containing EPC

To run the calculation POSCAR.4x4x4 needs to be copied to POSCAR and INCAR.init to INCAR.

Execute VASP.

Copy the OUTCAR file to OUTCAR.init. It will be later used for the band gap of the "undistorted" structure.

The new POSCAR file containing the configurations according to the electron-phonon couplings is given as POSCAR.T=0..

Step 2 calculate electronic levels of structure containing EPC

Copy the file POSCAR.T=0. to POSCAR.

Delete (or comment out with #) all the lines in the INCAR file related to EPC so that it looks like the following:

System = cd-C
PREC = Accurate
ALGO = FAST
ISMEAR = 0 
SIGMA = 0.1;

Execute VASP.

Copy OUTCAR to OUTCAR.T=0..

Step 3 extract ZPR

We extract the band gap renormalization as

where and are the band gaps with and without EPC, respectively.

The band gaps are extracted from the previously saved files OUTCAR.init and OUTCAR.T=0. using the following script:

Click to show/extract_zpr_cd_carbon.sh
  1. REDIRECT Extract zpr

To use the script please type:

bash extract_zpr_cd_carbon.sh

The output of the script should look like the following:

The band gap (in eV) without zero-point vibrations is:
4.4049
The band gap (in eV) including zero-point vibrations is:
4.05102
The zero-point renormalization of the band gap (in eV) is:
-0.353883

Step 4 better accuracy

The accuracy of the band gap renormalization depends dominantly on the size of the super cell, so this is the quantity that has to be usually converged in this type of calculation.

This example contains a POSCAR file for a 5x5x5 cell (POSCAR.5x5x5) in the directory SUPERCELL5x5x5. After repeating all above steps with this POSCAR file the following results should be obtained:

Download