Input Keywords for Exercises

We here summarize input keywords that appear in Exercise. A thorough list of the input keywords can be found in the downloaded file in List of all input keywords.

&calculation

Mandatory: theory

&calculation
  theory = 'dft'
/

The value of the theory should be one of 'dft', 'dft_md', 'tddft_response', 'tddft_pulse', 'single_scale_maxwell_tddft', 'multi_scale_maxwell_tddft', 'maxwell', and 'dft_k_expand'.

dft : ground state calculation based on DFT

dft_md : adiabatic ab initio MD simulations based on DFT

tddft_response : simulations based on TDDFT to obtain linear-response

tddft_pulse : simulations based on TDDFT using pulsed light

single_scale_maxwell_tddft : coupled Maxwell and TDDFT single-scale simulation

multi_scale_maxwell_tddft : coupled Maxwell and TDDFT multi-scale simulation

maxwell : electromagnetic simulations based on the Maxwell's equations

dft_k_expand : convert checkpoint data of dft with k-points calculation to that of larger supercell system with gamma-point

&units

Mandatory: none

&units
  unit_system = 'A_eV_fs'
/

This namelist specifies the unit system to be used in the input file. Options are 'A_eV_fs' for Angstrom, eV, and fs, and 'a.u.' or 'au' for atomic units. If you do not specify it, atomic unit will be used as default.

For isolated systems (specified by yn_periodic = 'n' in &system), the unit of 1/eV is used for the output files of DOS and PDOS if unit_system = 'A_eV_fs' is specified, while atomic unit is used if not. For other output files, the Angstrom/eV/fs units are used irrespective of the input keyword.

For periodic systems (specified by yn_periodic = 'y' in &system), the unit system specified by this input keyword is used for most output files. See the first few lines of output files to confirm the unit system adopted in the file.

&control

Mandatory: none

&control
  sysname = 'C2H2'
/

'C2H2' defined by sysname = 'C2H2' will be used in the filenames of output files. If you do not specify it, the file name will start with 'default'.

&system

Mandatory: yn_periodic, al, nelem, natom, nelec, nstate

For an isolated molecule (Exercises-1, 2, 3, 8, 9):

&system
  yn_periodic = 'n'
  al(1:3) = 16.0d0, 16.0d0, 16.0d0
  nelem = 2
  natom = 4
  nelec = 10
  nstate = 6
/

yn_periodic = 'n' indicates that the isolated boundary condition will be used in the calculation. al(1:3) = 16.0d0, 16.0d0, 16.0d0 specifies the lengths of three sides of the rectangular parallelepiped where the grid points are prepared. nelem = 2 and natom = 4 indicate the number of elements and the number of atoms in the system, respectively. nelec = 10 indicate the number of valence electrons in the system.

nstate = 6 indicates the number of Kohn-Sham orbitals to be solved.

nstate should be equal to or larger than nelec/2.

For a periodic system (Exercises-4, 5, 6, 7):

&system
  yn_periodic = 'y'
  al(1:3) = 10.26d0, 10.26d0, 10.26d0
  nelem = 1
  natom = 8
  nelec = 32
  nstate = 32
/

yn_periodic = 'y' indicates that three dimensional periodic boundary condition (bulk crystal) is assumed. al(1:3) = 10.26d0, 10.26d0, 10.26d0 specifies the lattice constans of the unit cell. nelem = 1 and natom = 8 indicate the number of elements and the number of atoms in the system, respectively. nelec = 32 indicate the number of valence electrons in the system. nstate = 32 indicates the number of Kohn-Sham orbitals to be solved.

&pseudo

Mandatory: pseudo_file, izatom

For C2H2 molecule:

&pseudo
  file_pseudo(1) = './C_rps.dat'
  file_pseudo(2) = './H_rps.dat'
  izatom(1) = 6
  izatom(2) = 1
  lloc_ps(1) = 1
  lloc_ps(2) = 0
/

Parameters related to atomic species and pseudopotentials. pseudo_file(1) = './C_rps.dat' indicates the filename of the pseudopotential of element. izatom(1) = 6 specifies the atomic number of the element.

For crystalline Si:

&pseudo
  file_pseudo(1) = './Si_rps.dat'
  izatom(1) = 14
  lloc_ps(1) = 2
/

file_pseudo(1) = './Si_rps.dat' indicates the pseudopotential filename of element. izatom(1) = 14 indicates the atomic number of the element.

&functional

&functional
  xc ='PZ'
/

xc ='PZ' indicates that (adiabatic) local density approximation is adopted (Perdew-Zunger: Phys. Rev. B23, 5048 (1981)). This is the default choice.

For isolated systems (specified by yn_periodic = 'n' in &system), only the default choice of 'PZ' is available at present.

For periodic systems (specified by ``yn_periodic = 'y' in &system), the following functionals may be available in addition to 'PZ', xc = 'PZM'

Perdew-Zunger LDA with modification to improve sooth connection between high density form and low density one, xc = 'TBmBJ' cval = 1.0 :J. P. Perdew and Alex Zunger, Phys. Rev. B 23, 5048 (1981).

Tran-Blaha meta-GGA exchange with Perdew-Wang correlation. :Fabien Tran and Peter Blaha, Phys. Rev. Lett. 102, 226401 (2009). John P. Perdew and Yue Wang, Phys. Rev. B 45, 13244 (1992). This potential is known to provide a reasonable description for the bandage of various insulators. For this choice, the additional mixing parameter 'cval' may be specified. If cval is set to a minus value, the mixing-parameter will be computed following the formula in the original paper [Phys. Rev. Lett. 102, 226401 (2009)]. The default value for this parameter is 1.0.

Since version 1.1.0, exchange-correlation functionals in Libxc library (http://www.tddft.org/programs/libxc/) have been usable in SALMON. At present, usable functionals are limited to LDA and GGA. For periodic systems, meta-GGA functionals are usable as well. To specify the exchange-correlation potentials of Libxc library, there are two ways. If the exchange and correlation potentials are given separately, you need to specify both alibx and alibc separately. If the exchange and correlation potentials are given as a combined set, you need to specify alibxc. We show below an example:

&functional
  alibx = 'LDA_X'
  alibc = 'LDA_C_PZ'
/

Available sets of the functionals are listed at the website http://www.tddft.org/programs/libxc/functionals/ .

Note that, the hybrid functionals (hybrid gga/mgga) are not supported in the current (version 2.0.0) of SALMON.

&rgrid

Mandatory: dl or num_rgrid

dl(1:3) = 0.25d0, 0.25d0, 0.25d0 specify the grid spacing in three Cartesian coordinates. This is adopted for C2H2 calculation (Excercises-1, 2, 3, 8, 9).

&rgrid
  dl(1:3) = 0.25d0, 0.25d0, 0.25d0
/

num_rgrid(1:3) = 12, 12, 12 specify the number of grid points in each Cartesian direction. This is adopted for crystalline Is calculation (Excercises-4, 5, 6, 7).

&rgrid
  num_rgrid(1:3) = 12, 12, 12
/

&kgrid

Mandatory: none

This group provides grid spacing of k-space for periodic systems.

&kgrid
  num_kgrid(1:3) = 4, 4, 4
/

&scf

Mandatory: nscf

This group specifies parameters related to the self-consistent field calculation.

&scf
  nscf = 200
  threshold = 1.0d-9
/

nscf = 200 is the number of scf iterations in the ground state calculation. the scf loop in the ground state calculation ends before the number of the scf iterations reaches nscf, if a convergence criterion is satisfied.

&analysis

Mandatory: none

The following input keywords specify whether the output files are created or not after the calculation. In the ground state calculation of isolated systems (Excercise-1):

&analysis
  yn_out_psi  = 'y'
  yn_out_dns  = 'y'
  yn_out_dos  = 'y'
  yn_out_pdos = 'y'
  yn_out_elf  = 'y'
/

In the following input keywords, variables related to time-frequency Fourier analysis are specified.

&analysis
  de = 1.0d-2
  nenergy = 3000
/

de = 1.0d-2 specifies the energy spacing, and nenergy = 3000 specifies the number of energy steps in the time-frequency Fourier transformation.

&tgrid

Mandatory: dt, nt

&tgrid
  dt = 1.25d-3
  nt = 5000
/

dt = 1.25d-3 specifies the time step of the time evolution calculation. nt = 5000 specifies the number of time steps in the calculation.

&emfield

This group specifies the pulse shape of an electric filed applied to the system in time evolution calculations. We explain below separating two cases, Linear response calculations and Pulsed electric field calculations.

Linear response calculations

A weak impulsive field is applied at t = 0. For this case, ae_shape1 = 'impulse' should be described.

Mandatory: ae_shape1

&emfield
  ae_shape1 = 'impulse'
  epdir_re1(1:3) = 0.0d0, 0.0d0, 1.0d0
/

epdir_re1(1:3) = 0.0d0, 0.0d0, 1.0d0 specifies a unit vector that indicates the direction of the impulse.

For a periodic system specified by yn_periodic = 'y', one may add trans_longi. It has the value, 'tr'(transverse) or 'lo'(longitudinal), that specifies the treatment of the polarization in the time evolution calculation. The default is 'tr'.

The magnitude of the impulse of the pulse may be explicitly specified by, for example, e_impulse = 1.00d-2. The default is '1.00d-2' in atomic unit.

Pulsed electric field calculations

A Pulsed electric field of finite time duration is applied. For this case, as_shape1 should be specified. It indicates the shape of the envelope of the pulse. The options include 'Acos2' and 'Ecos2' (See below for other options).

Mandatory: ae_shape1, {I_wcm2_1 or E_amplitude1}, tw1, omega1, epdir_re1, phi_cep1

&emfield
  ae_shape1 = 'Ecos2'
  I_wcm2_1 = 1.00d8
  tw1 = 6.00d0
  omega1 = 9.28d0
  epdir_re1(1:3) = 0.00d0, 0.00d0, 1.00d0
  phi_cep1 = 0.75d0
/

ae_shape1 = 'Ecos2' specifies the envelope of the pulsed electric field, 'Ecos2' for the cos^2 envelope for the electric field. If 'Acos2' is specified, this gives cos^2 envelope for the vector potential. Note that 'phi_cep1' must be 0.75 (or 0.25) if one employs 'Ecos2' pulse shape, since otherwise the time integral of the electric field does not vanish. There is no such restriction for the 'Acos2' pulse shape.

I_wcm2_1 = 1.00d8 specifies the maximum intensity of the applied electric field in unit of W/cm^2. It is also possible to specify the maximum intensity of the pulse by E_amplitude1.

tw1 = 6.00d0 specifies the pulse duration. Note that it is not the FWHM but a full duration of the cos^2 envelope.

omega1 = 9.28d0 specifies the average photon energy (frequency multiplied with hbar).

epdir_re1(1:3) = 0.00d0, 0.00d0, 1.00d0 specifies the real part of the unit polarization vector of the pulsed electric field. If only the real part is specified, it describes a linearly polarized pulse. Using both real ('epdir_re1') and imaginary ('epdir_im1') parts of the polarization vector, circularly (and general ellipsoidary) polarized pulses may be described.

phi_cep1 = 0.75d0 specifies the carrier envelope phase of the pulse. As noted above, 'phi_cep1' must be 0.75 (or 0.25) if one employs 'Ecos2' pulse shape, since otherwise the time integral of the electric field does not vanish. There is no such restriction for the 'Acos2' pulse shape.

It is possible to use two pulses simultaneously to simulate pump-probe experiments, adding information for two pulses. To specify the second pulse, change from 1 to 2 in the input keywords, like ae_shape2. The time delay between two pulses is specified by the input keyword 't1_t2'.

For a periodic system specified by yn_periodic = 'y', one may add trans_longi. It has the value, 'tr'(transverse) or 'lo'(longitudinal), that specifies the treatment of the polarization in the time evolution calculation. The default is 'tr'. For a periodic system, it is also specify 'Acos3', 'Acos4', 'Acos6', 'Acos8' for ae_shape1.

&multiscale

This group specifies information necessary for Maxwell-TDDFT multiscale calculations.

&multiscale
  nx_m = 8
  ny_m = 1
  nz_m = 1
  hx_m = 100.0d0
  hy_m = 100.0d0
  hz_m = 100.0d0
  nxvacl_m = 1000
  nxvacr_m = 1000
/

nx_m = 8 specifies the number of the macroscopic grid points for x-direction in the spatial region where the material exists. ny_m = 1 and nz_m = 1 are those for y- and z-directions.

hx_m = 100.0d0 specifies the grid spacing of the macroscopic grid for x-direction. hy_m = 100.0d0 and hz_m = 100.0d0 are those for y- and z-directions.

nxvacl_m = 1000 and nxvacr_m = 1000 indicate the number of grid points in the vacuum region, nxvacl_m for the left and nxvacr_m for the right from the surface of the material.

&atomic_coor

Mandatory: atomic_coor or atomic_red_coor

For C2H2 molecule:

&atomic_coor
  'C'    0.000000    0.000000    0.599672  1
  'H'    0.000000    0.000000    1.662257  2
  'C'    0.000000    0.000000   -0.599672  1
  'H'    0.000000    0.000000   -1.662257  2
/

Cartesian coordinates of atoms. The first column indicates the element. Next three columns specify Cartesian coordinates of the atoms. The number in the last column labels the element.

&atomic_red_coor

Mandatory: atomic_coor or atomic_red_coor

For a crystalline silicon:

&atomic_red_coor
  'Si'       .0      .0      .0      1
  'Si'       .25     .25     .25     1
  'Si'       .5      .0      .5      1
  'Si'       .0      .5      .5      1
  'Si'       .5      .5      .0      1
  'Si'       .75     .25     .75     1
  'Si'       .25     .75     .75     1
  'Si'       .75     .75     .25     1
/

Cartesian coordinates of atoms are specified in a reduced coordinate system. First column indicates the element, next three columns specify reduced Cartesian coordinates of the atoms, and the last column labels the element.