5. Running FOCEX

5.1. Preliminaries

The input to FOCEX is a set of foce-displacement files, outputs of DFT calculation of supercells in which atoms have moved according to some scheme. There is a separate file for each supercell shape. Typically users use only one supercell, like 3x3x3, but you can generate more. The needed files by FOCEX are called POSCAR1 and FORCEDISP1 if there is only one supercell shape, otherwise you will also have POSCAR2 and FORCEDISP2, etc… These files are generated using the utility sc_snaps.x which has 3 input files. cell.inp contains the information on atoms in the primitive or conventional cell. supercell.inp contains the three translation vectors of the supercell in terms of those of the primitive cell as defined in cell.inp. Finally in snaps.inp the user specifies the temperature for canonical sampling, a typical frequency scale and the number of required snapshots (typically, depending on the size of the supercell, and the number of required force constants 10 to 50 should be enough). 1-Run sc_snaps.x to generate the needed POSCAR files corresponding to each snapshot. They have the standard VASP format. After running VASP on each of these files, you collect a bunch of OUTCAR files, which you can rename outcar1, outcar2, … outcarn. 2-Run xtract.sh script to generate the FORCEDISP1 file which will be used by FOCEX. The POSCAR1 file contains the equilibrium atomic coordinates (force=0) in the supercell.

Before running FOCEX you also need to prepare its other input files: default.params (you need it but don’t have to touch it), structure.params, dielectric.params containing the dielectric tensor and Born effective charges, kpbs.params containing the k-point paths for phonon band structure calculation, latdyn.params for density of states and thermodynamic properties calculations. Example are provided, and explanation of each line is in the file itself.

The workflow of the FOCEX code is shown below to give a general understanding of how the code is structured and executed

5.2. Workflow of FOCEX

The workflow of the FOCEX code is shown below to give a general understanding of how the code is structured and executed as a black box. Many of the intermediate steps in this process flow may even not be necessary to actually run the code. The one which are important are highlighted on the workflow diagram and are later explained in detail.

General steps for running FOCEX to get the force constants are given below:

5.3. Description of input and output files

Preparing FOCEX data files

FOCEX code accepts DFT force displacement files prepared by any software like VASP, or Quantum Espresso. We provide utility tools to extract forces and displacements in a supercell from VASP OUTCAR or Quantum Espresso output files. All the generated displacement-force data for each atomic snapshot are concatenated into a single file called FORCEDISP1. The equilibrium atomic positions in the supercell should be in a file called POSCAR1 which has the exact format of the VASP POSCAR file except atom type name. For example if the POSCAR file for Ge is this

Ge8
0
6748542148543777    0.0000000000000000    0.0000000000000003
0000000000000009    5.6748542148543777    0.0000000000000003
0000000000000000    0.0000000000000000    5.6748542148543777
Ge
8
direct
0000000000000000    0.0000000000000000    0.5000000000000000
2500000000000000    0.2500000000000000    0.7500000000000000
0000000000000000    0.5000000000000000    0.0000000000000000
2500000000000000    0.7500000000000000    0.2500000000000000
5000000000000000    0.0000000000000000    0.0000000000000000
7500000000000000    0.2500000000000000    0.2500000000000000
5000000000000000    0.5000000000000000    0.5000000000000000
7500000000000000    0.7500000000000000    0.7500000000000000

Then POSCAR1 file is this:

Ge8
0
6748542148543777    0.0000000000000000    0.0000000000000003
0000000000000009    5.6748542148543777    0.0000000000000003
0000000000000000    0.0000000000000000    5.6748542148543777
8
direct
0000000000000000    0.0000000000000000    0.5000000000000000
2500000000000000    0.2500000000000000    0.7500000000000000
0000000000000000    0.5000000000000000    0.0000000000000000
2500000000000000    0.7500000000000000    0.2500000000000000
5000000000000000    0.0000000000000000    0.0000000000000000
7500000000000000    0.2500000000000000    0.2500000000000000
5000000000000000    0.5000000000000000    0.5000000000000000
7500000000000000    0.7500000000000000    0.7500000000000000

If there are other supercells, the equilibrium positions and displacement-force data should be stored in POSCAR2 and FORCEDISP2 … etc. The detailed description of the FORCEDISP1 file is given in the example section Ge

utility tool

To prepare the FORCEDISPi file there is a shell script inside utility folder. The shell script process_dft.sh executes the read_outcar.x and read_qe.x binary to generate force-displacement file for VASP and QE respectively.

Preparing input files

The input file(s) required to run FOCEX are structure.params, dielectric.params, kpbs.params, latdyn.params, defaults.params, POSCAR1 and FORCEDISP1.

structure.params

something about structure.params file

dielectric.params

something about dielectric.params file

kpbs.params

something about kpbs.params file

defaults.params

something about defaults.params file

latdyn.params

something about latdyn.params file

POSCAR1

something about POSCAR1

FORCEDISP1

The format of this file is : First line is a comment and should contain ” # POSITION …”, second line should contain an integer followed by the total energy of the supercell snapshot in eV. Units for positions or displacements should be in Angstrom, and forces in eV/Ang.

kpbs.params

The first line contains a flag. If 0, the kpoints are given in reduced units of the primitive vectors of the reciprocal space, else they should be in reduced coordinates of the conventional lattice vectors of the reciprocal space. The second line contains the number of kpoints along each direction, The third line contains the number of direction paths. The following lines contain the name of the special point followed by the 3 reduced components of the special kpoint in units of primitive (if flag=0) or conventional (if flag is non-zero) vectors of the reciprocal lattice.

kpbs.params

30 # number of kpoints along each direction
4  # number of directions
G 0 0 0
K 0.75 0.75 0
X 1 1 0
G 0 0 0
L 0.5 0.5 0.5

output files
- fc1.dat and fc2_irr.dat
- fc2.dat and fc2_irr.dat
- fc3.dat and fc3_irr.dat
- lat_fc.xyz
- log***.dat

5.4. Example of Running FOCEX

Ge

FOrce Constant Extraction (FOCEX) is a code to extract force constants from force-displacements data, the output of which can be used as input to the following codes. The installation of FOCEX has to be done before using it and is given in section FOCEX. This code, FOCEX (FOrce Constant EXtraction) included in ALATDYN (Anharmonic LATtice DYNamics) employs the force constant calculation, 2nd, 3rd and 4th order to be latter used for other thermodynamical properties. The installation of FOCEX is simple and just require the fortran compiler.

An example of Ge is provided inside FOCEX/example which contains the needed input files described above, and the FOCEX output. In this calculation a single Ge atom in the 2x2x2 Ge supercell (64 atoms) is displaced by 4% to evaluate the forces. The force-displacement data is stored in FORCEDISP1 file. The equilibrium coordinates are in POSCAR1 in the older VASP POSCAR format as below.

Ge8 # this is a comment
0  # scale factor
5257244110         0.0000000000         0.0000000000  # supercell
0000000000        11.5257244110         0.0000000000
0000000000         0.0000000000        11.5257244110
# number of atoms in the supercell
Cartesian
881431103         0.000000000         2.881431103
881431103         0.000000000         8.644293308
881431103         5.762862206         2.881431103
881431103         5.762862206         8.644293308
644293308         0.000000000         2.881431103
644293308         0.000000000         8.644293308
644293308         5.762862206         2.881431103
644293308         5.762862206         8.644293308
440715551         1.440715551         1.440715551
440715551         1.440715551         7.203577757
440715551         7.203577757         1.440715551
440715551         7.203577757         7.203577757
203577757         1.440715551         1.440715551
203577757         1.440715551         7.203577757
203577757         7.203577757         1.440715551
203577757         7.203577757         7.203577757
881431103         2.881431103         0.000000000
881431103         2.881431103         5.762862206
881431103         8.644293308         0.000000000
881431103         8.644293308         5.762862206
644293308         2.881431103         0.000000000
644293308         2.881431103         5.762862206
644293308         8.644293308         0.000000000
644293308         8.644293308         5.762862206
440715551         4.322146654         4.322146654
440715551         4.322146654        10.085008860
440715551        10.085008860         4.322146654
440715551        10.085008860        10.085008860
203577757         4.322146654         4.322146654
203577757         4.322146654        10.085008860
203577757        10.085008860         4.322146654
203577757        10.085008860        10.085008860
000000000         0.000000000         0.000000000
000000000         0.000000000         5.762862206
000000000         5.762862206         0.000000000
000000000         5.762862206         5.762862206
762862206         0.000000000         0.000000000
762862206         0.000000000         5.762862206
762862206         5.762862206         0.000000000
762862206         5.762862206         5.762862206
322146654         1.440715551         4.322146654
322146654         1.440715551        10.085008860
322146654         7.203577757         4.322146654
322146654         7.203577757        10.085008860
085008860         1.440715551         4.322146654
085008860         1.440715551        10.085008860
085008860         7.203577757         4.322146654
085008860         7.203577757        10.085008860
000000000         2.881431103         2.881431103
000000000         2.881431103         8.644293308
000000000         8.644293308         2.881431103
000000000         8.644293308         8.644293308
762862206         2.881431103         2.881431103
762862206         2.881431103         8.644293308
762862206         8.644293308         2.881431103
762862206         8.644293308         8.644293308
322146654         4.322146654         1.440715551
322146654         4.322146654         7.203577757
322146654        10.085008860         1.440715551
322146654        10.085008860         7.203577757
085008860         4.322146654         1.440715551
085008860         4.322146654         7.203577757
085008860        10.085008860         1.440715551
085008860        10.085008860         7.203577757

Here, only the type of atom is not present in POSCAR1 as compared to the new format of VASP POSCAR file. Similarly, FORCEDISP1 is a force-displacement data format accepted by FOCEX code and its format for example in the case of Ge is given below.

# POSITION (ang)     TOTAL FORCE (eV/Ang)
     -289.18629538 =t, Etot(eV)     # snapshot #1
8929600000000000        0.0000000000000000        2.8814299999999999      -0.11758299999999999       -0.0000000000000000       -0.0000000000000000
8814299999999999        0.0000000000000000        8.6442899999999998        4.9600000000000002E-004  -0.0000000000000000       -0.0000000000000000
8814299999999999        5.7628599999999999        2.8814299999999999        4.9600000000000002E-004  -0.0000000000000000       -0.0000000000000000
8814299999999999        5.7628599999999999        8.6442899999999998       -4.5640000000000003E-003  -0.0000000000000000       -0.0000000000000000
6442899999999998        0.0000000000000000        2.8814299999999999        3.2899999999999997E-004  -0.0000000000000000       -0.0000000000000000
6442899999999998        0.0000000000000000        8.6442899999999998       -1.5699999999999999E-004  -0.0000000000000000       -0.0000000000000000
6442899999999998        5.7628599999999999        2.8814299999999999       -1.5699999999999999E-004  -0.0000000000000000       -0.0000000000000000
6442899999999998        5.7628599999999999        8.6442899999999998        2.6699999999999998E-004  -0.0000000000000000       -0.0000000000000000
4407200000000000        1.4407200000000000        1.4407200000000000        2.8677000000000001E-002  -1.9474999999999999E-002   1.9474999999999999E-002
4407200000000000        1.4407200000000000        7.2035799999999997       -4.8099999999999998E-004  -7.1400000000000001E-004   3.2800000000000000E-004
4407200000000000        7.2035799999999997        1.4407200000000000       -4.8099999999999998E-004  -3.2800000000000000E-004   7.1400000000000001E-004
4407200000000000        7.2035799999999997        7.2035799999999997        2.4350000000000001E-003  -4.0000000000000003E-005   4.0000000000000003E-005
2035799999999997        1.4407200000000000        1.4407200000000000       -1.8400000000000000E-004  -3.3000000000000000E-004   3.3000000000000000E-004
2035799999999997        1.4407200000000000        7.2035799999999997        8.3999999999999995E-005  -4.3999999999999999E-005   3.4000000000000000E-005
2035799999999997        7.2035799999999997        1.4407200000000000        8.3999999999999995E-005  -3.4000000000000000E-005   4.3999999999999999E-005
2035799999999997        7.2035799999999997        7.2035799999999997       -2.1599999999999999E-004  -3.4400000000000001E-004   3.4400000000000001E-004
8814299999999999        2.8814299999999999        0.0000000000000000       -4.0619999999999996E-003   7.2599999999999997E-004  -7.2599999999999997E-004
8814299999999999        2.8814299999999999        5.7628599999999999       -4.0780000000000000E-003  -7.3099999999999999E-004  -7.3099999999999999E-004
8814299999999999        8.6442899999999998        0.0000000000000000       -4.0780000000000000E-003   7.3099999999999999E-004   7.3099999999999999E-004
8814299999999999        8.6442899999999998        5.7628599999999999       -4.0619999999999996E-003  -7.2599999999999997E-004   7.2599999999999997E-004
6442899999999998        2.8814299999999999        0.0000000000000000        1.0700000000000000E-004   6.0000000000000002E-005  -6.0000000000000002E-005
6442899999999998        2.8814299999999999        5.7628599999999999        1.0300000000000000E-004  -5.7000000000000003E-005  -5.7000000000000003E-005
6442899999999998        8.6442899999999998        0.0000000000000000        1.0300000000000000E-004   5.7000000000000003E-005   5.7000000000000003E-005
6442899999999998        8.6442899999999998        5.7628599999999999        1.0700000000000000E-004  -6.0000000000000002E-005   6.0000000000000002E-005
4407200000000000        4.3221499999999997        4.3221499999999997       -4.8099999999999998E-004   3.2800000000000000E-004  -7.1400000000000001E-004
4407200000000000        4.3221499999999997        10.085010000000000        2.4350000000000001E-003   4.0000000000000003E-005  -4.0000000000000003E-005
4407200000000000        10.085010000000000        4.3221499999999997        2.8677000000000001E-002   1.9474999999999999E-002  -1.9474999999999999E-002
4407200000000000        10.085010000000000        10.085010000000000       -4.8099999999999998E-004   7.1400000000000001E-004  -3.2800000000000000E-004
2035799999999997        4.3221499999999997        4.3221499999999997        8.3999999999999995E-005   3.4000000000000000E-005  -4.3999999999999999E-005
2035799999999997        4.3221499999999997        10.085010000000000       -2.1599999999999999E-004   3.4400000000000001E-004  -3.4400000000000001E-004
2035799999999997        10.085010000000000        4.3221499999999997       -1.8400000000000000E-004   3.3000000000000000E-004  -3.3000000000000000E-004
2035799999999997        10.085010000000000        10.085010000000000        8.3999999999999995E-005   4.3999999999999999E-005  -3.4000000000000000E-005
0000000000000000        0.0000000000000000        0.0000000000000000        1.6290000000000000E-003  -7.2499999999999995E-004   1.4820000000000000E-003
0000000000000000        0.0000000000000000        5.7628599999999999        1.6290000000000000E-003   7.2499999999999995E-004  -1.4820000000000000E-003
0000000000000000        5.7628599999999999        0.0000000000000000        4.2000000000000002E-004  -5.8000000000000000E-005  -8.8500000000000004E-004
0000000000000000        5.7628599999999999        5.7628599999999999        4.2000000000000002E-004   5.8000000000000000E-005   8.8500000000000004E-004
7628599999999999        0.0000000000000000        0.0000000000000000        1.6550000000000000E-003  -7.3399999999999995E-004  -1.5030000000000000E-003
7628599999999999        0.0000000000000000        5.7628599999999999        1.6550000000000000E-003   7.3399999999999995E-004   1.5030000000000000E-003
7628599999999999        5.7628599999999999        0.0000000000000000        4.2000000000000002E-004  -5.7000000000000003E-005   8.8000000000000003E-004
7628599999999999        5.7628599999999999        5.7628599999999999        4.2000000000000002E-004   5.7000000000000003E-005  -8.8000000000000003E-004
3221499999999997        1.4407200000000000        4.3221499999999997        2.8958999999999999E-002   2.0014000000000001E-002   2.0014000000000001E-002
3221499999999997        1.4407200000000000        10.085010000000000       -4.8400000000000000E-004   7.0799999999999997E-004   3.3000000000000000E-004
3221499999999997        7.2035799999999997        4.3221499999999997       -4.8400000000000000E-004   3.3000000000000000E-004   7.0799999999999997E-004
3221499999999997        7.2035799999999997        10.085010000000000        2.4480000000000001E-003   4.0000000000000003E-005   4.0000000000000003E-005
085010000000000        1.4407200000000000        4.3221499999999997       -1.8000000000000001E-004   3.2899999999999997E-004   3.2899999999999997E-004
085010000000000        1.4407200000000000        10.085010000000000        7.7999999999999999E-005   3.4999999999999997E-005   2.8000000000000000E-005
085010000000000        7.2035799999999997        4.3221499999999997        7.7999999999999999E-005   2.8000000000000000E-005   3.4999999999999997E-005
085010000000000        7.2035799999999997        10.085010000000000       -2.1200000000000000E-004   3.4699999999999998E-004   3.4699999999999998E-004
0000000000000000        2.8814299999999999        2.8814299999999999        1.6290000000000000E-003  -1.4820000000000000E-003   7.2499999999999995E-004
0000000000000000        2.8814299999999999        8.6442899999999998        4.2000000000000002E-004   8.8500000000000004E-004   5.8000000000000000E-005
0000000000000000        8.6442899999999998        2.8814299999999999        1.6290000000000000E-003   1.4820000000000000E-003  -7.2499999999999995E-004
0000000000000000        8.6442899999999998        8.6442899999999998        4.2000000000000002E-004  -8.8500000000000004E-004  -5.8000000000000000E-005
7628599999999999        2.8814299999999999        2.8814299999999999        1.6550000000000000E-003   1.5030000000000000E-003   7.3399999999999995E-004
7628599999999999        2.8814299999999999        8.6442899999999998        4.2000000000000002E-004  -8.8000000000000003E-004   5.7000000000000003E-005
7628599999999999        8.6442899999999998        2.8814299999999999        1.6550000000000000E-003  -1.5030000000000000E-003  -7.3399999999999995E-004
7628599999999999        8.6442899999999998        8.6442899999999998        4.2000000000000002E-004   8.8000000000000003E-004  -5.7000000000000003E-005
3221499999999997        4.3221499999999997        1.4407200000000000       -4.8400000000000000E-004  -3.3000000000000000E-004  -7.0799999999999997E-004
3221499999999997        4.3221499999999997        7.2035799999999997        2.4480000000000001E-003  -4.0000000000000003E-005  -4.0000000000000003E-005
3221499999999997        10.085010000000000        1.4407200000000000        2.8958999999999999E-002  -2.0014000000000001E-002  -2.0014000000000001E-002
3221499999999997        10.085010000000000        7.2035799999999997       -4.8400000000000000E-004  -7.0799999999999997E-004  -3.3000000000000000E-004
085010000000000        4.3221499999999997        1.4407200000000000        7.7999999999999999E-005  -2.8000000000000000E-005  -3.4999999999999997E-005
085010000000000        4.3221499999999997        7.2035799999999997       -2.1200000000000000E-004  -3.4699999999999998E-004  -3.4699999999999998E-004
085010000000000        10.085010000000000        1.4407200000000000       -1.8000000000000001E-004  -3.2899999999999997E-004  -3.2899999999999997E-004
085010000000000        10.085010000000000        7.2035799999999997        7.7999999999999999E-005  -3.4999999999999997E-005  -2.8000000000000000E-005
# POSITION (ang)     TOTAL FORCE (eV/Ang)
     -289.18629538 =t, Etot(eV)     # snapshot #2
8929600000000000        0.0000000000000000        2.8814299999999999      -0.11758299999999999       -0.0000000000000000       -0.0000000000000000
8814299999999999        0.0000000000000000        8.6442899999999998        4.9600000000000002E-004  -0.0000000000000000       -0.0000000000000000
 ...

The first line in FORCEDISP1 is the header and should contain the word POSITION. The second line consists of the energy of structure in electron volt and the lines after second are positions (first three columns, \(x\), \(y\) and \(z\)) and forces (the last three columns \(F_x\), \(F_y\) and \(F_z\) are in \(eV/{\\A}\)) respectively. If there are many force-displacement snapshots of the structure, then the other snapshots follow these lines in the same format. There is a tool and a shell script for converting the VASP outcar or QE outputfile into the FORCEDISP1 format for the FOCEX code. It is available in utility folder inside FOCEX. To convert the VASP outcar into FORCEDISP1 user need to execute ./process_dft.sh name_of_vasp_directory(s) or ./process_dft.sh name_of_vasp_file shell script within utility folder. Here, name_of_vasp_directory(s) is the multiple directory containing VASP runs or QE runs or name_of_vasp_file is the OUTCAR file(s) for VASP or the outputfile for QE runs. This shell script will call the readoutcar.x or readpfpwscf.x taking as input the DFT output from VASP or QE. The shell script can be tailored as per your needs. As for the other inputs file of FOCEX, they are given below

structure.params

1 1 90 90 90          # a, b, c, alpha, beta, gamma of the conventional cell
.5 .5   .5 0 .5   .5 .5 0 # reduced coordinates of primitive lattice (in this case FCC) in terms of conventional lattice (in this case cubic)
7628622055            # scale factor for lattice size
1 1 1                 # include FC1234, 1st, 2nd, third and fourth order harmonic force constant(s) in the fitting process. 1 is to include and 0 is to not include
1 0 0                 # invariances to impose, (translational, rotational, Huang) last is enforce inv using elimination
300                   # temperature and whether or not implement it (do not implement if 0,2, or ..)
.true.                # number  of FORCEDISPi files, verbosity
                     # type of atoms
64                   # masses of each type of atoms
Ge                      # names of atoms
                     # number of atoms of each type in the primitive cell
                     # flag for setting the range of FC2s (if 0 take default; else use below)
5                     # number of shells for rank 2 (harmonic) for each atom if not default
1                     # number of shells for rank 3 (cubic) for each atom (there is no default value)
1                     # number of shells for rank 4 (quartic) for each atom (there is no default value)
1 0 0 0               # atom index, type of atom, position x, position y, position z in units of a,b,c of the conventional lattice
1 0.25 0.25 0.25      # atom index, type of atom, position x, position y, position z in units of a,b,c

The fitting is done using singular value decomposition based on the requested symmetry constraints and POSCAR1 and FORCEDISP1 i.e. by creating the force displacement matrix.

The next input file is dielectric.params. It is required to get the phonon dispersion (and eventually thermal conductivity using THERMACOND). It consists of a flag which is zero if the Born charges are to be excluded. The second, third and fourth lines contain the dielectric constant tensor values which is written as follows in the example folder inside FOCEX

dielectric.params

             # do not include Born charges in the fitting
5078 0.0  0.0 # for example, dielectric constant (necessary but not used if flag is zero)
0 2.5078 0.0
0 0.0 2.5078
0 0           # Born charge tensor of atom 1 in order it appears in the ``structure.params``
0 0
0 0
0 0           # Born charge tensor of atom 2 in order it appears in the ``structure.params``
0 0
0 0

Now, put the POSCAR1, FORCEDISP1 , structure.params, dielectric.params and kpbs.params in same directory, simply run focex.x. After successful run fc2.dat, fc2_irr.dat, fc3.dat, fc3_irr.dat, fc4.dat and fc4_irr.dat along with other output files and log file should be available. fc2.dat, fc2_irr.dat are the fitted second order force constants in eV/Ang^2. The former contains all the pairs regardless of symmetry, and the latter contains the irreducible ones from which all the rest is contructed using crystal symmetry. Likewise fc3.dat, fc3_irr.dat and fc4.dat, fc4_irr.dat contain the third order and fourth order full and irreducible force constants in eV/Ang^3 and eV/Ang^4 respectively. Users are advised to look for more information in the log file log***.dat to know more details about the run.