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# Electron-phonon interactions from Monte-Carlo sampling

Important: This feature will be only available from VASP6.0 or higher.

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

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 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].

## Full MC sampling

### Input

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
```

### Output

The MC sampling code produces many POSCAR files with different distorted Wycoff positions but unchanged Brillouin matrix. The files are labeled as

```POSCAR.TEBEG.NUMBER
```

where the NUMBER runs from 1 to PHON_NSTRUCT.

## ZG configuration (one-shot sampling)

Alternatively to the full MC sampling, a one shot method, introduced by M. Zacharias and F. Giustino[2] (named ZG configuration after the authors), is available. This method only uses a single distorted structure and hence it is orders of magnitude faster than the full MC sampling, while 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.

### Input

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.
```

### Output

Similar to the MC sampling the ZG configuration method produces several POSCAR files with different distorted Wycoff positions but unchanged Brillouin matrix. The files are labeled as

```POSCAR.TEMP
```

where TEMP runs over all temperatures defined by PHON_TLIST.