Interface with BoltzTraP

OpenMX is interfaced with BoltzTraP [99] which calculates electron transport coefficients based on the Boltzmann theory from the wave number dependence of the energy eigenvalues in the Kohn-Sham equation. The interface [100] with BoltzTraP enables us to calculate physical properties such as the Seebeck coefficient, electrical conductivity, electronic thermal conductivity, and the Hall coefficient. The functionality is compatible with not only the collinear calculations, but also the non-collinear calculations. When you publish a paper using the functionality, we would like to appreciate your citation of Ref. [100]. The interface with BoltzTraP2 will be released in the next version. The interface, which bridges between OpenMX and BoltzTraP, can be used by copying MX_TRAP.sh which is stored in the directory 'source' to the directory 'work' and executing it. As an example, let us introduce a calculation of non-doped Si bulk. One can perform the SCF calculation using an input file 'Si_BoltzTraP.dat' which is available in the directory 'work' as follows:

    % mpirun -np 28 ./openmx Si_BoltzTraP

After the SCF calculation finishes normally, you obtain the out file 'Si_BoltzTraP.out'. Then, you need to copy MX_TRAP.sh which is stored in the directory 'source' to the directory 'work'. After that, you can perform MX_TRAP.sh as follows:

    % sh MX_TRAP.sh

Then, the name of the 'out' files in the directory is listed as may be shown below.

    =========================Outputfile List==========================    
    Si_BoltzTraP.out
    ==================================================================

    Please enter the outputfile name ; Outputfile name =

Then, please enter the file name of the 'out' file after "Outputfile name =" and execute it by typing enter. Here we take Si_BoltzTraP.out as an example, and you may enter as

    Please enter the output file name: Outputfile name = Si_BoltzTraP.out

When you press the enter key, the following message will be displayed:

    ..
    ....
    Nospin::kloop kx ky kz:1681/1686
    Nospin::kloop kx ky kz:1682/1686
    Nospin::kloop kx ky kz:1683/1686
    Nospin::kloop kx ky kz:1684/1686
    Nospin::kloop kx ky kz:1685/1686
    Nospin::kloop kx ky kz:1686/1686
    .energy file for BoltzTraP has been generated.

    .struct file for BoltzTraP has been generated.

    .intrans file for BoltzTraP has been generated.

    Conversion has been finished.

    Directory is Si_BoltzTraP

Figure 85: Computational protocol of the electron transport caculation by OpenMX and BoltzTraP.

After the above message is displayed, a directory named 'Si_BoltzTraP' is created, and four files such as 'Si_BoltzTraP.energy','Si_BoltzTraP.intrans', and 'Si_BoltzTraP.struct' will be stored in the directory as shown below:

  % cd Si_BoltzTraP
  % ls 
  Si_BoltzTraP.out Si_BoltzTraP.energy Si_BoltzTraP.struct Si_BoltzTraP.intrans

The '.out' file is a copy of the out file which was analyzed by the conversion. The '.energy' file is a file of energy eigenvalues. If the keyword 'scf.SpinPolarization' in the '.out' file is 'ON', then the '.energyup' and ".energydn" files are output, while '.energyso' file is output if the keyword 'scf. SpinPolarization' in the '.out' file is 'NC'. The '.struct' file is a file of unit lattice vectors. The unit is converted automatically into atomic units. The '.intrans' file describes input parameters necessary for electronic transport calculation. For details, please refer to the pdf manual enclosed with BoltzTraP package. The numerical value of the first item in the third line is the chemical potential $\mu$ calculated by OpenMX (unit is Ryd). The value of 10 in the fifth line is the Fourier interpolation factor of the band, which is set to 10 by default. The numerical value in the eighth row is the electron temperature of the Fermi distribution. The first item is the maximum temperature. The second item is the temperature step size when calculating the temperature dependence. If the temperature dependence is not to be calculated, then enter the same value as the first item. By default, the temperature specified by 'scf.ElectronicTemperature' in the '.out' file is entered. If 'scf.ElectronicTemperature' is not specified, $T = 300 K$ will be assigned.

Figure 86: (a) Seebeck coefficient $S$, and (b) the electric conductivity $\sigma\tau_{\rm el}^{-1}$ of non-doped Si in the diamond structure as a function of the chemical potential at 300 K obtained by OpenMX and BoltzTraP. The Fourier interpolation factor was set to 25. The input file 'Si_BoltzTraP.dat' used for the calculation is available in the directory 'work'.

Next, please move to the directory 'Si_BoltzTraP' and type BoltzTraP as shown below. The procedure from this point is the same as the normal BoltzTraP calculation. Therefore, please refer to the PDF manual enclosed in the BoltzTraP package for details.

    % cd Si_BoltzTraP
    % 'path to BoltzTrap'/boltztrap-1.2.5/sr/x_trans BoltzTraP

If the stored energy eigenvalue file is '.energyup', '.energydn' or '.energyso', please add '-up', '-dn', or '-so' as an option after x_trans BoltzTraP, and execute it. Then, electron transport calculations are performed for the energy eigenvalue file specified by the option. When the calculation is completed normally, the following message will be displayed:

    ========================== BoltzTraP vs 1.2.5 =============
    99.786 u 0.076 s 1: 40.04 99.8\% 0 + 0 k 0 + 1612 0 io 0 pf + 0 w

The average values of the electron transport properties over the $x$-, $y$-, and $z$-axes are stored in 'Si_BoltzTraP.trace.', while the electron transport properties of the $x$-, $y$-, and $z$-axes are stored in 'Si_BoltzTraP.condtens'. Figure 85 summarizes the computational protocol of the electron transport calculation by OpenMX and BoltzTraP. In Fig. 86 we show the Seebeck coefficient $S$ and chemicafnl potential $\mu$ dependence of electrical conductivity $\sigma \tau _{\rm el}^{-1}$ of non-doped Si bulk. The input file 'Si_BoltzTraP.dat' used for the calculation is available in the directory 'work'.

Extensitve benchmark calculations using the functionality are found in the supplementary material: '11664_2017_6020_MOESM1_ESM.pdf' of Ref. [100]. Among the benchmark calculations we show in Fig. 87 a computational result for GaCuS$_2$ bulk in which the non-collinear calculation with spin-orbit coupling was performed. The input file 'GaCuS2_mp-5238_symmetrized_SOC.dat' used for the calculation is available in the directory 'work'.

Figure 87: (a) Seebeck coefficient $S$, and (b) electric conductivity $\sigma\tau_{\rm el}^{-1}$ of GaCuS$_2$ bulk as a function of the chemical potential at 300 K obtained by OpenMX and BoltzTraP. The Fourier interpolation factor was set to 10. The input file 'GaCuS2_mp-5238_symmetrized_SOC.dat' used for the calculation is available in the directory 'work'.