Electron-phonon interactions from Monte-Carlo sampling

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For the theory on electron-interactions from Monte-Carlo sampling please click here.

First of all this method needs a sufficiently large super cell. It also involves phonon calculations for the point (see Phonons from finite differences). So many tags in the INCAR will be used from the phonon calculations.

The first implementation of electron-phonon interactions from MC sampling in VASP is found in Ref. [1].

The original publication of the ZG configuration (one-shot method) is found in Ref. [2].

Step-by-step instructions

Step 1: Run a single calculation to create the POSCAR file(s) with special positions either belonging to the ZG configuration method or Monte Carlo sampling. To enable electron-phonon interactions from MC methods PHON_LMC=.TRUE. has to be set in the INCAR file. Also IBRION=6 has to be selected (the Monte-Carlo (MC) method is currently only implemented for IBRION=6). The description of the remaining required INCAR tags for each method is given below. Both methods produce POSCAR files with different distorted Wycoff positions but unchanged Brillouin matrixThe. The ZG configuration method produces one structure for each temperature defined in PHON_TLIST. The files are labeled as 

POSCAR.T=TEMP.

The MC sampling code produces many POSCAR files at a given temperature defined by TEBEG. The files are labeled as 

POSCAR.T=TEBEG.NUMBER

where NUMBER runs from 1 to PHON_NSTRUCT.

Step 2: Run calculation for the previously created POSCAR files on the desired observable. These calculations can be anything that is suitable for a Monte Carlo sum , for example band gap calculations, absorption spectra calculations, etc.

Step 3 (optional): Calculate the desired observable for the original "pristine" supercell. This step can be necessary when changes of an observable due to electron-phonon interactions is required. An example for such a calculation is the calculation of the band-gap renormalization due to electron-phonon interactions.

Step 4 (optional): If Monte Carlo sampling was used average the results over the number of structures created in step 1 (PHON_NSTRUCT).

ZG configuration (one-shot sampling)

M. Zacharias and F. Giustino[2] introduced a one-shot method (named ZG configuration after the authors). This method is an approximation to full Monte Carlo sampling. It only uses a single distorted structure and hence it is orders of magnitude faster than the full MC sampling. It retains an accuracy very close to the full MC sampling for converged super cell sizes. For example we showed that for the zero-point renormalization of the band gap the accuracy is within 5 meV between the ZG configurations and the full MC sampling[1]. Hence we suggest to use this method preferably, where convergence of the super cell size is hard to achieve or the 5 meV accuracy is enough.

To select the ZG configuration PHON_NSTRUCT=0 has to be set in the INCAR file.

The number of different temperatures and the list of temperatures (in K) have to be provided using the tags PHON_NTLIST and PHON_TLIST, respectively, in the INCAR file. An example would look like: 

PHON_NTLIST = 4
PHON_TLIST = 0.0 100.0 200.0 350.0

This makes the simultaneous calculation of the ZG configuration at several temperatures possible.

An example INCAR file for a temperature range from 0-700 K (with step size of 100 K) is given as: 

System = DEFAULT
PREC = Accurate
ISMEAR = 0; SIGMA = 0.1;
IBRION = 6
PHON_NTLIST = 8
PHON_TLIST = 0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0
PHON_NSTRUCT = 0
PHON_LMC = .TRUE.

Full MC sampling

The tag PHON_NSTRUCT sets the number of structures generated due to the MC sampling. Convergence of the observable with respect to this number should be monitored.

The tag TEBEG=0 is also needed to choose the temperature at which the sampling is run.

Additionally the PHON_LBOSE can be set .TRUE. or .FALSE. (default PHON_LBOSE=.TRUE.), which selects Bose-Einstein or Maxwell-Boltzmann statistics, respectively.

A sample INCAR file for 0 K looks like the following: 

System = DEFAULT
PREC = Accurate
ISMEAR = 0; SIGMA = 0.1;
IBRION = 6

PHON_LMC = .TRUE.
PHON_NSTRUCT = 100
TEBEG = 0.0

Related tags and articles

References

  1. ↑ a b F. Karsai, M. Engel, E. Flage-Larssen, and G. Kresse, New J. of Phys. 20, 123008 (2018).
  2. ↑ a b M. Zacharias and F. Giustino, Phys. Rev. B 94, 075125 (2016).
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