Exercises

Getting started

Welcome to SALMON Exercises!

In these exercises, we explain the use of SALMON from the very beginning, taking a few samples that cover applications of SALMON in several directions. We assume that you are in the computational environment of UNIX/Linux OS. First you need to download and install SALMON in your computational environment. If you have not yet done it, do it following the instruction, download and Install and Run.

As described in Install and Run, you are required to prepare at least an input file and pseudopotential files to run SALMON. In the following, we present input files for several sample calculations and provide a brief explanation of the input keywords that appear in the input files. You may modify the input files to execute for your own calculations. Pseudopotential files of elements that appear in the samples are also attached. We also present explanations of main output files.

We present 10 exercises.

First 3 exercises (Exercise-1 ~ 3) are for an isolated molecule, acetylene C2H2. If you are interested in learning electron dynamics calculations in isolated systems, please look into these exercises. In SALMON, we usually calculate the ground state solution first using a static density functional theory (DFT). This is illustrated in Exercise-1. After finishing the ground state calculation, two exercises of electron dynamics calculations based on time-dependent density functional theory (TDDFT) are prepared. Exercise-2 illustrates the calculation of linear optical responses in real time, obtaining polarizability and photoabsorption of the molecule. Exercise-3 illustrates the calculation of electron dynamics in the molecule under a pulsed electric field.

Next 3 exercises (Exercise-4 ~ 6) are for a crystalline solid, silicon. If you are interested in learning electron dynamics calculations in extended periodic systems, please look into these exercises. Exercise-4 illustrates the ground state calculation of the crystalline silicon based on DFT. Exercise-5 illustrates the calculation of linear response properties of the crystalline silicon based on TDDFT to obtain the dielectric function. Exercise-6 illustrates the calculation of electron dynamics in the crystalline silicon induced by a pulsed electric field.

Exercise-7 is for a simultaneous calculation of the propagation of a pulsed light and electronic motion in a bulk silicon, coupling Maxwell equations for the electromagnetic fields of the pulsed light and the electron dynamics in the unit cells based on TDDFT. This calculation is quite time-consuming and is recommended to execute using massively parallel supercomputers. Exercise-7 illustrates the calculation of a linearly polarized pulsed light irradiating normally on a surface of a bulk silicon.

Next 2 exercises (Exercise-8 ~ 9) are for geometry optimization based on DFT and Ehrenfest molecular dynamics based on TDDFT for an isolated molecule, acetylene C2H2. Exercise-8 illustrates the geometry optimization in the ground state. Exercise-9 illustrates the Ehrenfest molecular dynamics induced by a pulsed electric field.

Exercise-10 is for a macroscopic light propagation through a metallic nanosphere solving Maxwell equations. The optical response of the nanosphere is described by a dielectric function. Finite-Difference Time-Domain (FDTD) method is used to calculated the three-dimensional light propagation.

Input files of exercises are included in SALMON, in the directory SALMON/samples/exercise_##_<description>/.

C2H2 (isolated molecules)

Exercise-1: Ground state of C2H2 molecule

In this exercise, we learn the calculation of the ground state of acetylene (C2H2) molecule, solving the static Kohn-Sham equation. This exercise will be useful to learn how to set up calculations in SALMON for any isolated systems such as molecules and nanoparticles.

Acetylene molecule is a linear chain molecule composed of two Carbon atoms and two Hydrogen atoms.

_images/acetylene.png

In SALMON, we use a three-dimensional (3D) uniform grid system to express physical quantities such as electron orbitals.

_images/acetylene_grid.png

Input files

To run the code, following files in the directory SALMON/samples/exercise_01_C2H2_gs/ are used:

file name

description

C2H2_gs.inp

input file that contains input keywords and their values

C_rps.dat

pseodupotential file for carbon atom

H_rps.dat

pseudopotential file for hydrogen atom

Pseudopotential files are needed for two elements, Carbon (C) and Hydrogen (H). The pseudopoential depends on the angular momentum, and looks as follows (for Carbon).

_images/C_rps_pot.png

In the input file C2H2_gs.inp, input keywords are specified. Most of them are mandatory to execute the ground state calculation. This will help you to prepare an input file for other systems that you want to calculate. A complete list of the input keywords that can be used in the input file can be found in List of input keywords.

!########################################################################################!
! Excercise 01: Ground state of C2H2 molecule                                            !
!----------------------------------------------------------------------------------------!
! * The detail of this excercise is expained in our manual(see chapter: 'Exercises').    !
!   The manual can be obtained from: https://salmon-tddft.jp/documents.html              !
! * Input format consists of group of keywords like:                                     !
!     &group                                                                             !
!       input keyword = xxx                                                              !
!     /                                                                                  !
!   (see chapter: 'List of all input keywords' in the manual)                            !
!----------------------------------------------------------------------------------------!
! * Conversion from unit_system = 'a.u.' to 'A_eV_fs':                                   !
!   Length: 1 [a.u.] = 0.52917721067    [Angstrom]                                       !
!   Energy: 1 [a.u.] = 27.21138505      [eV]                                             !
!   Time  : 1 [a.u.] = 0.02418884326505 [fs]                                             !
!########################################################################################!

&calculation
  !type of theory
  theory = 'dft'
/
theory specifies which theoretical method is used in the calculation.
&control
  !common name of output files
  sysname = 'C2H2'
/
sysname is a prefix for filenames of output files.
&units
  !units used in input and output files
  unit_system = 'A_eV_fs'
/
unit_system specifies which unit system is used in the input and output files.
&system
  !periodic boundary condition
  yn_periodic = 'n'

  !grid box size(x,y,z)
  al(1:3) = 16.0d0, 16.0d0, 16.0d0

  !number of elements, atoms, electrons and states(orbitals)
  nelem  = 2
  natom  = 4
  nelec  = 10
  nstate = 6
/
yn_periodic specifies whether or not periodic boundary condition is applied.
al(i) specifies the spatial box size of the cubiod cell.
nelem is the number of elements in the system.
natom is the number of atoms in the system.
nelec is the number of electrons in the system.
nstate is the number of orbitals that are used in the calculation.
&pseudo
  !name of input pseudo potential file
  file_pseudo(1) = './C_rps.dat'
  file_pseudo(2) = './H_rps.dat'

  !atomic number of element
  izatom(1) = 6
  izatom(2) = 1

  !angular momentum of pseudopotential that will be treated as local
  lloc_ps(1) = 1
  lloc_ps(2) = 0
  !--- Caution ---------------------------------------!
  ! Indices must correspond to those in &atomic_coor. !
  !---------------------------------------------------!
/
file_pseudo(n) specifies the filename of the pseudopotential file of the n-th element.
izatom(n) is the atomic number of the n-th element.
lloc_ps(n) specifies which angular momentum component is chosen as the local potential for the n-th element.
&functional
  !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).)
  xc = 'PZ'
/
xc specifies the exchange-correlation potential to be used in the calculation.
&rgrid
  !spatial grid spacing(x,y,z)
  dl(1:3) = 0.25d0, 0.25d0, 0.25d0
/
dl(i) specifies the spatial grid spacing in i-th direction.
&scf
  !maximum number of scf iteration and threshold of convergence
  nscf      = 300
  threshold = 1.0d-9
/
nscf specifies the maximum number of SCF iterations.
threshold specifies the threshold to judge the convergence.
&analysis
  !output of all orbitals, density,
  !density of states, projected density of states,
  !and electron localization function
  yn_out_psi  = 'y'
  yn_out_dns  = 'y'
  yn_out_dos  = 'y'
  yn_out_pdos = 'y'
  yn_out_elf  = 'y'
/
yn_out_psi, yn_out_dns, yn_out_dos, yn_out_pdos, yn_out_elf specify output files that are generated after the calculation.
&atomic_coor
  !cartesian atomic coodinates
  '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
  !--- Format ---------------------------------------------------!
  ! 'symbol' x y z index(correspond to that of pseudo potential) !
  !--------------------------------------------------------------!
/
&atomic_coor specifies spatial coordinates of atoms.

Execusion

In a multiprocess environment, calculation will be executed as

$ mpiexec -n NPROC salmon < C2H2_gs.inp > C2H2_gs.out

where NPROC is the number of MPI processes. A standard output will be stored in the file C2H2_gs.out.

Output files

After the calculation, following output files and a directory are created in the directory that you run the code in addition to the standard output file,

You may download the above files (zipped file, except for the directory data_for_restart) from:

We first explain the standard output file. In the beginning of the file, input variables used in the calculation are shown.

##############################################################################
# SALMON: Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
#
#                             Version 2.0.1
##############################################################################
  Libxc: [disabled]
   theory= dft
---------------------------------------- init_sym_sub(start)
 symmetry-operation file ( sym.dat  ) can not be found.
------------------------------------------ init_sym_sub(end)
   use of real value orbitals =  T
 ======
 MPI distribution:
   nproc_k     :           1
   nproc_ob    :           1
   nproc_rgrid :           4           4           4
 OpenMP parallelization:
   number of threads :           1
.........

After that, the SCF loop starts. At each iteration step, the total energy as well as orbital energies and some other quantities are displayed.

 -----------------------------------------------
 iter=     1     Total Energy=       -23.25680398     Gap=   -20.23579640     Vh iter= 211
     1       -23.8823      2        -3.9239      3        13.6149      4       -15.2285
     5        -1.7855      6        -6.6209
iter and int_x|rho_i(x)-rho_i-1(x)|dx/nelec        =      1 0.20779375E+00
 Ne=   10.0000000000000
 -----------------------------------------------
 iter=     2     Total Energy=      -163.16222784     Gap=   -22.02054947     Vh iter= 235
     1       -44.5138      2        -3.8925      3         6.1788      4       -28.1284
     5        -3.4269      6       -15.8417
iter and int_x|rho_i(x)-rho_i-1(x)|dx/nelec        =      2 0.43197789E+00
 Ne=  10.00000000000000
 -----------------------------------------------
 iter=     3     Total Energy=      -188.25766814     Gap=   -20.90219256     Vh iter= 217
     1       -41.7361      2        -5.0101      3         5.4169      4       -27.5078
     5        -3.3350      6       -15.4853
iter and int_x|rho_i(x)-rho_i-1(x)|dx/nelec        =      3 0.14362457E+00
 Ne=   10.0000000000000

When the convergence criterion is satisfied, the SCF calculation ends.

 -----------------------------------------------
 iter=   126     Total Energy=      -339.69524618     Gap=     6.78879114     Vh iter=   1
     1       -18.4106      2       -13.9966      3       -12.4163      4        -7.3385
     5        -7.3385      6        -0.5498
iter and int_x|rho_i(x)-rho_i-1(x)|dx/nelec        =    126 0.46706835E-08
 Ne=   10.0000000000000
 -----------------------------------------------
 iter=   127     Total Energy=      -339.69524615     Gap=     6.78879057     Vh iter=   1
     1       -18.4106      2       -13.9966      3       -12.4163      4        -7.3385
     5        -7.3385      6        -0.5498
iter and int_x|rho_i(x)-rho_i-1(x)|dx/nelec        =    127 0.29853988E-09
 Ne=   10.0000000000000
  #GS converged at   128  : 0.29853988E-09

Next, the force acting on ions and some other information related to orbital energies are shown.

      ===== force =====
          1 -0.11747820E-04  0.22186082E-04 -0.59497394E+00
          2 -0.20094975E-05  0.41046764E-05  0.57651242E+00
          3 -0.11356190E-04  0.23640028E-04  0.59492966E+00
          4 -0.16079702E-05  0.45416509E-05 -0.57651956E+00
  band information-----------------------------------------
  Bottom of VB -0.676576557928278
  Top of VB -0.269686692329130
  Bottom of CB -2.020322940577464E-002
  Top of CB -2.020322940577464E-002
  Fundamental gap  0.249483462923356
  BG between same k-point  0.249483462923356
  Physicaly upper bound of CB for DOS -2.020322940577464E-002
  Physicaly upper bound of CB for eps(omega)  0.656373328522503
  ---------------------------------------------------------
  Bottom of VB[eV]  -18.4105852335900
  Top of VB[eV]  -7.33854842782885
  Bottom of CB[eV] -0.549757854614016
  Top of CB[eV] -0.549757854614016
  Fundamental gap[eV]   6.78879057321483
  BG between same k-point[eV]   6.78879057321483
---------------------------------------------------------

In the directory data_for_restart, files that will be used in the next-step time evolution calculations are stored.

Other output files include following information.

C2H2_info.data

Calculated orbital and total energies as well as parameters specified in the input file are shown.

C2H2_eigen.data

Orbital energies.

#esp: single-particle energies (eigen energies)
#occ: occupation numbers, io: orbital index
# 1:io, 2:esp[eV], 3:occ

C2H2_k.data

k-point distribution(for isolated systems, only gamma point is described).

# ik: k-point index
# kx,ky,kz: Reduced coordinate of k-points
# wk: Weight of k-point
# 1:ik[none] 2:kx[none] 3:ky[none] 4:kz[none] 5:wk[none]
# coefficients (2*pi/a [a.u.]) in kx, ky, kz

psi_ob1.cube, psi_ob2.cube, ...

Cube files for electron orbitals. The number in the filename indicates the index of the orbital. Atomic unit is adopted in all cube files.

dns.cube

A cube file for electron density.

dos.data

A file for density of states. The units used in this file are affected by the input parameter, unit_system in &unit.

elf.cube

A cube file for electron localization function (ELF).

We show several image that are created from the output files.

  • Highest occupied molecular orbital (HOMO)

    The output files psi_ob1.cube, psi_ob2.cube, ... are used to create the image.

    _images/HOMO.png
  • Electron density

    The output files dns.cube, ... are used to create the image.

    _images/Dns.png
  • Electron localization function

    The output files elf.cube, ... are used to create the image.

    _images/Elf.png

Exercise-2: Polarizability and photoabsorption of C2H2 molecule

In this exercise, we learn the linear response calculation in the acetylene (C2H2) molecule, solving the time-dependent Kohn-Sham equation. The linear response calculation provides the polarizability and the oscillator strength distribution of the molecule. This exercise should be carried out after finishing the ground state calculation that was explained in Exercise-1. In the calculation, an impulsive perturbation is applied to all electrons in the C2H2 molecule along the molecular axis which we take z axis. Then a time evolution calculation is carried out without any external fields. During the calculation, the electric dipole moment is monitored. After the time evolution calculation, a time-frequency Fourier transformation is carried out for the electric dipole moment to obtain the frequency-dependent polarizability. The imaginary part of the frequency-dependent polarizability is proportional to the oscillator strength distribution and the photoabsorption cross section.

Input files

To run the code, the input file C2H2_rt_response.inp that contains input keywords and their values for the linear response calculation is required. The directory restart that is created in the ground state calculation as data_for_restart and pseudopotential files are also required. The pseudopotential files should be the same as those used in the ground state calculation. The input files are in samples.

name

description

C2H2_rt_response.inp

input file that contains input keywords and their values

C_rps.dat

pseodupotential file for carbon

H_rps.dat

pseudopotential file for hydrogen

restart

directory created in the ground state calculation (rename the directory from data_for_restart to restart)

In the input file C2H2_rt_response.inp, input keywords are specified. Most of them are mandatory to execute the linear response calculation. This will help you to prepare the input file for other systems that you want to calculate. A complete list of the input keywords that can be used in the input file can be found in List of input keywords.

!########################################################################################!
! Excercise 02: Polarizability and photoabsorption of C2H2 molecule                      !
!----------------------------------------------------------------------------------------!
! * The detail of this excercise is expained in our manual(see chapter: 'Exercises').    !
!   The manual can be obtained from: https://salmon-tddft.jp/documents.html              !
! * Input format consists of group of keywords like:                                     !
!     &group                                                                             !
!       input keyword = xxx                                                              !
!     /                                                                                  !
!   (see chapter: 'List of all input keywords' in the manual)                            !
!----------------------------------------------------------------------------------------!
! * Conversion from unit_system = 'a.u.' to 'A_eV_fs':                                   !
!   Length: 1 [a.u.] = 0.52917721067    [Angstrom]                                       !
!   Energy: 1 [a.u.] = 27.21138505      [eV]                                             !
!   Time  : 1 [a.u.] = 0.02418884326505 [fs]                                             !
!----------------------------------------------------------------------------------------!
! * Copy the ground state data directory('data_for_restart') (or make symbolic link)     !
!   calculated in 'samples/exercise_01_C2H2_gs/' and rename the directory to 'restart/'  !
!   in the current directory.                                                            !
!########################################################################################!

&calculation
  !type of theory
  theory = 'tddft_response'
/
theory specifies which theoretical method is used in the calculation.
&control
  !common name of output files
  sysname = 'C2H2'
/
sysname is a prefix for filenames of output files.
&units
  !units used in input and output files
  unit_system = 'A_eV_fs'
/
unit_system specifies which unit system is used in the input and output files.
&system
  !periodic boundary condition
  yn_periodic = 'n'

  !grid box size(x,y,z)
  al(1:3) = 16.0d0, 16.0d0, 16.0d0

  !number of elements, atoms, electrons and states(orbitals)
  nelem  = 2
  natom  = 4
  nelec  = 10
  nstate = 6
/
yn_periodic specifies whether or not periodic boundary condition is applied.
al(i) specifies the spatial box size of the cubiod cell.
nelem is the number of elements in the system.
natom is the number of atoms in the system.
nelec is the number of electrons in the system.
nstate is the number of orbitals that are used in the calculation.
&pseudo
  !name of input pseudo potential file
  file_pseudo(1) = './C_rps.dat'
  file_pseudo(2) = './H_rps.dat'

  !atomic number of element
  izatom(1) = 6
  izatom(2) = 1

  !angular momentum of pseudopotential that will be treated as local
  lloc_ps(1) = 1
  lloc_ps(2) = 0
  !--- Caution ---------------------------------------!
  ! Indices must correspond to those in &atomic_coor. !
  !---------------------------------------------------!
/
file_pseudo(n) specifies the filename of the pseudopotential file of the n-th element.
izatom(n) is the atomic number of the n-th element.
lloc_ps(n) specifies which angular momentum component is chosen as the local potential for the n-th element.
&functional
  !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).)
  xc = 'PZ'
/
xc specifies the exchange-correlation potential to be used in the calculation.
&rgrid
  !spatial grid spacing(x,y,z)
  dl(1:3) = 0.25d0, 0.25d0, 0.25d0
/
dl(i) specifies the spatial grid spacing in i-th direction.
&tgrid
  !time step size and number of time grids(steps)
  dt = 1.25d-3
  nt = 5000
/
dt specifies the time step.
nt is the number of time steps for the time propagation.
&emfield
  !envelope shape of the incident pulse('impulse': impulsive field)
  ae_shape1 = 'impulse'

  !polarization unit vector(real part) for the incident pulse(x,y,z)
  epdir_re1(1:3) = 0.0d0, 0.0d0, 1.0d0
  !--- Caution ---------------------------------------------------------!
  ! Defenition of the incident pulse is wrriten in:                     !
  ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 !
  !---------------------------------------------------------------------!
/
ae_shape1 specifies the envelope of the field. For a linear response calculation, as_shape1='impulse' is used. It indicates that a weak impulsive perturbation is applied at t=0.
epdir_re1(i) specifies the i-th component of the real part of the polarization unit vector.
&analysis
  !energy grid size and number of energy grids for output files
  de      = 1.0d-2
  nenergy = 3000
/
de specifies the energy grid size for frequency-domain analysis.
nenergy specifies the number of energy grid points for frequency-domain analysis.
&atomic_coor
  !cartesian atomic coodinates
  '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
  !--- Format ---------------------------------------------------!
  ! 'symbol' x y z index(correspond to that of pseudo potential) !
  !--------------------------------------------------------------!
/
&atomic_coor specifies spatial coordinates of atoms.

Output files

After the calculation, following output files are created in the directory that you run the code,

file name

description

C2H2_response.data

polarizability and oscillator strength distribution as functions of energy

C2H2_rt.data

components of change of dipole moment (electrons/plus definition) and total dipole moment (electrons/minus + ions/plus) as functions of time

C2H2_rt_energy.data

components of total energy and difference of total energy as functions of time

PS_C_KY_n.dat

information on pseodupotential file for carbon atom

PS_H_KY_n.dat

information on pseodupotential file for hydrogen atom

You may download the above files (zipped file) from:

Explanations of the output files are below:

C2H2_response.data

Time-frequency Fourier transformation of the dipole moment gives the polarizability of the system. Then the strength function is calculated.

# Fourier-transform spectra:
# alpha: Polarizability
# df/dE: Strength function
# 1:Energy[eV] 2:Re(alpha_x)[Augstrom^2/V] 3:Re(alpha_y)[Augstrom^2/V] 4:Re(alpha_z)[Augstrom^2/V] 5:Im(alpha_x)[Augstrom^2/V] 6:Im(alpha_y)[Augstrom^2/V] 7:Im(alpha_z)[Augstrom^2/V] 8:df_x/dE[none] 9:df_y/dE[none] 10:df_z/dE[none]

C2H2_rt.data

Results of time evolution calculation for vector potential, electric field, and dipole moment.

# Real time calculation:
# Ac_ext: External vector potential field
# E_ext: External electric field
# Ac_tot: Total vector potential field
# E_tot: Total electric field
# ddm_e: Change of dipole moment (electrons/plus definition)
# dm: Total dipole moment (electrons/minus + ions/plus)
# 1:Time[fs] 2:Ac_ext_x[fs*V/Angstrom] 3:Ac_ext_y[fs*V/Angstrom] 4:Ac_ext_z[fs*V/Angstrom] 5:E_ext_x[V/Angstrom] 6:E_ext_y[V/Angstrom] 7:E_ext_z[V/Angstrom] 8:Ac_tot_x[fs*V/Angstrom] 9:Ac_tot_y[fs*V/Angstrom] 10:Ac_tot_z[fs*V/Angstrom] 11:E_tot_x[V/Angstrom] 12:E_tot_y[V/Angstrom] 13:E_tot_z[V/Angstrom] 14:ddm_e_x[Angstrom] 15:ddm_e_y[Angstrom] 16:ddm_e_z[Angstrom] 17:dm_x[Angstrom] 18:dm_y[Angstrom] 19:dm_z[Angstrom]

C2H2_rt_energy.data

Eall and Eall-Eall0 are total energy and electronic excitation energy, respectively.

# Real time calculation:
# Eall: Total energy
# Eall0: Initial energy
# 1:Time[fs] 2:Eall[eV] 3:Eall-Eall0[eV]

Exercise-3: Electron dynamics in C2H2 molecule under a pulsed electric field

In this exercise, we learn the calculation of the electron dynamics in the acetylene (C2H2) molecule under a pulsed electric field, solving the time-dependent Kohn-Sham equation. As outputs of the calculation, such quantities as the total energy and the electric dipole moment of the system as functions of time are calculated. This tutorial should be carried out after finishing the ground state calculation that was explained in Exercise-1. In the calculation, a pulsed electric field that has cos^2 envelope shape is applied. The parameters that characterize the pulsed field such as magnitude, frequency, polarization direction, and carrier envelope phase are specified in the input file.

Input files

To run the code, following files in samples are used. The directory restart is created in the ground state calculation as data_for_restart. Pseudopotential files are already used in the ground state calculation. Therefore, C2H2_rt_pulse.inp that specifies input keywords and their values for the pulsed electric field calculation is the only file that the users need to prepare.

file name

description

C2H2_rt_pulse.inp

input file that contain input keywords and their values.

C_rps.dat

pseodupotential file for carbon

H_rps.dat

pseudopotential file for hydrogen

restart

directory created in the ground state calculation (rename the directory from data_for_restart to restart)

In the input file C2H2_rt_pulse.inp, input keywords are specified. Most of them are mandatory to execute the calculation of electron dynamics induced by a pulsed electric field. This will help you to prepare the input file for other systems and other pulsed electric fields that you want to calculate. A complete list of the input keywords that can be used in the input file can be found in List of input keywords.

!########################################################################################!
! Excercise 03:  Electron dynamics in C2H2 molecule under a pulsed electric field        !
!----------------------------------------------------------------------------------------!
! * The detail of this excercise is expained in our manual(see chapter: 'Exercises').    !
!   The manual can be obtained from: https://salmon-tddft.jp/documents.html              !
! * Input format consists of group of keywords like:                                     !
!     &group                                                                             !
!       input keyword = xxx                                                              !
!     /                                                                                  !
!   (see chapter: 'List of all input keywords' in the manual)                            !
!----------------------------------------------------------------------------------------!
! * Conversion from unit_system = 'a.u.' to 'A_eV_fs':                                   !
!   Length: 1 [a.u.] = 0.52917721067    [Angstrom]                                       !
!   Energy: 1 [a.u.] = 27.21138505      [eV]                                             !
!   Time  : 1 [a.u.] = 0.02418884326505 [fs]                                             !
!----------------------------------------------------------------------------------------!
! * Copy the ground state data directory('data_for_restart') (or make symbolic link)     !
!   calculated in 'samples/exercise_01_C2H2_gs/' and rename the directory to 'restart/'  !
!   in the current directory.                                                            !
!########################################################################################!

&calculation
  !type of theory
  theory = 'tddft_pulse'
/
theory specifies which theoretical method is used in the calculation.
&control
  !common name of output files
  sysname = 'C2H2'
/
sysname is a prefix for filenames of output files.
&units
  !units used in input and output files
  unit_system = 'A_eV_fs'
/
unit_system specifies which unit system is used in the input and output files.
&system
  !periodic boundary condition
  yn_periodic = 'n'

  !grid box size(x,y,z)
  al(1:3) = 16.0d0, 16.0d0, 16.0d0

  !number of elements, atoms, electrons and states(orbitals)
  nelem  = 2
  natom  = 4
  nelec  = 10
  nstate = 6
/
yn_periodic specifies whether or not periodic boundary condition is applied.
al(i) specifies the spatial box size of the cubiod cell.
nelem is the number of elements in the system.
natom is the number of atoms in the system.
nelec is the number of electrons in the system.
nstate is the number of orbitals that are used in the calculation.
&pseudo
  !name of input pseudo potential file
  file_pseudo(1) = './C_rps.dat'
  file_pseudo(2) = './H_rps.dat'

  !atomic number of element
  izatom(1) = 6
  izatom(2) = 1

  !angular momentum of pseudopotential that will be treated as local
  lloc_ps(1) = 1
  lloc_ps(2) = 0
  !--- Caution ---------------------------------------!
  ! Indices must correspond to those in &atomic_coor. !
  !---------------------------------------------------!
/
file_pseudo(n) specifies the filename of the pseudopotential file of the n-th element.
izatom(n) is the atomic number of the n-th element.
lloc_ps(n) specifies which angular momentum component is chosen as the local potential for the n-th element.
&functional
  !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).)
  xc = 'PZ'
/
xc specifies the exchange-correlation potential to be used in the calculation.
&rgrid
  !spatial grid spacing(x,y,z)
  dl(1:3) = 0.25d0, 0.25d0, 0.25d0
/
dl(i) specifies the spatial grid spacing in i-th direction.
&tgrid
  !time step size and number of time grids(steps)
  dt = 1.25d-3
  nt = 5000
/
dt specifies the time step.
nt is the number of time steps for the time propagation.
&emfield
  !envelope shape of the incident pulse('Ecos2': cos^2 type envelope for scalar potential)
  ae_shape1 = 'Ecos2'

  !peak intensity(W/cm^2) of the incident pulse
  I_wcm2_1 = 1.00d8

  !duration of the incident pulse
  tw1 = 6.00d0

  !mean photon energy(average frequency multiplied by the Planck constant) of the incident pulse
  omega1 = 9.28d0

  !polarization unit vector(real part) for the incident pulse(x,y,z)
  epdir_re1(1:3) = 0.00d0, 0.00d0, 1.00d0

  !carrier emvelope phase of the incident pulse
  !(phi_cep1 must be 0.25 + 0.5 * n(integer) when ae_shape1 = 'Ecos2')
  phi_cep1 = 0.75d0
  !--- Caution ---------------------------------------------------------!
  ! Defenition of the incident pulse is wrriten in:                     !
  ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 !
  !---------------------------------------------------------------------!
/
ae_shape1 specifies the envelope of the field.
I_wcm2_1 specify the intensity of the pulse in unit of W/cm2.
tw1 specifies the duration of the pulse.
omega1 specifies the mean photon energy of the pulse.
epdir_re1(i) specifies the i-th component of the real part of the polarization unit vector.
phi_cep1 specifies the carrier-envelope phase of the pulse.
&atomic_coor
  !cartesian atomic coodinates
  '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
  !--- Format ---------------------------------------------------!
  ! 'symbol' x y z index(correspond to that of pseudo potential) !
  !--------------------------------------------------------------!
/
&atomic_coor specifies spatial coordinates of atoms.

Output files

After the calculation, following output files are created in the directory that you run the code,

file name

description

C2H2_pulse.data

dipole moment as functions of energy

C2H2_rt.data

components of change of dipole moment (electrons/plus definition) and total dipole moment (electrons/minus + ions/plus) as functions of time

C2H2_rt_energy.data

components of total energy and difference of total energy as functions of time

PS_C_KY_n.dat

information on pseodupotential file for carbon atom

PS_H_KY_n.dat

information on pseodupotential file for hydrogen atom

You may download the above files (zipped file) from:

Explanations of the files are described below:

C2H2_pulse.data

Time-frequency Fourier transformation of the dipole moment.

# Fourier-transform spectra:
# energy: Frequency
# dm: Dopile moment
# 1:energy[eV] 2:Re(dm_x)[fs*Angstrom] 3:Re(dm_y)[fs*Angstrom] 4:Re(dm_z)[fs*Angstrom] 5:Im(dm_x)[fs*Angstrom] 6:Im(dm_y)[fs*Angstrom] 7:Im(dm_z)[fs*Angstrom] 8:|dm_x|^2[fs^2*Angstrom^2] 9:|dm_y|^2[fs^2*Angstrom^2] 10:|dm_z|^2[fs^2*Angstrom^2]

C2H2_rt.data

Results of time evolution calculation for vector potential, electric field, and dipole moment.

# Real time calculation:
# Ac_ext: External vector potential field
# E_ext: External electric field
# Ac_tot: Total vector potential field
# E_tot: Total electric field
# ddm_e: Change of dipole moment (electrons/plus definition)
# dm: Total dipole moment (electrons/minus + ions/plus)
# 1:Time[fs] 2:Ac_ext_x[fs*V/Angstrom] 3:Ac_ext_y[fs*V/Angstrom] 4:Ac_ext_z[fs*V/Angstrom] 5:E_ext_x[V/Angstrom] 6:E_ext_y[V/Angstrom] 7:E_ext_z[V/Angstrom] 8:Ac_tot_x[fs*V/Angstrom] 9:Ac_tot_y[fs*V/Angstrom] 10:Ac_tot_z[fs*V/Angstrom] 11:E_tot_x[V/Angstrom] 12:E_tot_y[V/Angstrom] 13:E_tot_z[V/Angstrom] 14:ddm_e_x[Angstrom] 15:ddm_e_y[Angstrom] 16:ddm_e_z[Angstrom] 17:dm_x[Angstrom] 18:dm_y[Angstrom] 19:dm_z[Angstrom]

C2H2_rt_energy.data

Eall and Eall-Eall0 are total energy and electronic excitation energy, respectively.

# Real time calculation:
# Eall: Total energy
# Eall0: Initial energy
# 1:Time[fs] 2:Eall[eV] 3:Eall-Eall0[eV]

Crystalline silicon (periodic solids)

Exercise-4: Ground state of crystalline silicon

In this exercise, we learn the the ground state calculation of the crystalline silicon of a diamond structure. Calculation is done in a cubic unit cell that contains eight silicon atoms. This exercise will be useful to learn how to set up calculations in SALMON for any periodic systems such as crystalline solid.

Input files

To run the code, following files in samples are used:

file name

description

Si_gs.inp

input file that contains input keywords and their values

Si_rps.dat

pseodupotential file for silicon atom

In the input file Si_gs.inp, input keywords are specified. Most of them are mandatory to execute the ground state calculation. This will help you to prepare an input file for other systems that you want to calculate. A complete list of the input keywords that can be used in the input file can be found in List of input keywords.

!########################################################################################!
! Excercise 04: Ground state of crystalline silicon(periodic solids)                     !
!----------------------------------------------------------------------------------------!
! * The detail of this excercise is expained in our manual(see chapter: 'Exercises').    !
!   The manual can be obtained from: https://salmon-tddft.jp/documents.html              !
! * Input format consists of group of keywords like:                                     !
!     &group                                                                             !
!       input keyword = xxx                                                              !
!     /                                                                                  !
!   (see chapter: 'List of all input keywords' in the manual)                            !
!----------------------------------------------------------------------------------------!
! * Conversion from unit_system = 'a.u.' to 'A_eV_fs':                                   !
!   Length: 1 [a.u.] = 0.52917721067    [Angstrom]                                       !
!   Energy: 1 [a.u.] = 27.21138505      [eV]                                             !
!   Time  : 1 [a.u.] = 0.02418884326505 [fs]                                             !
!########################################################################################!

&calculation
  !type of theory
  theory = 'dft'
/
theory specifies which theoretical method is used in the calculation.
&control
  !common name of output files
  sysname = 'Si'
/
sysname is a prefix for filenames of output files.
&units
  !units used in input and output files
  unit_system = 'a.u.'
/
unit_system specifies which unit system is used in the input and output files.
&system
  !periodic boundary condition
  yn_periodic = 'y'

  !grid box size(x,y,z)
  al(1:3) = 10.26d0, 10.26d0, 10.26d0

  !number of elements, atoms, electrons and states(bands)
  nelem  = 1
  natom  = 8
  nelec  = 32
  nstate = 32
/
yn_periodic specifies whether or not periodic boundary condition is applied.
al(i) specifies the side length of the unit cell.
nelem is the number of elements in the system.
natom is the number of atoms in the system.
nelec is the number of electrons in the system.
nstate is the number of orbitals that are used in the calculation.
&pseudo
  !name of input pseudo potential file
  file_pseudo(1) = './Si_rps.dat'

  !atomic number of element
  izatom(1) = 14

  !angular momentum of pseudopotential that will be treated as local
  lloc_ps(1) = 2
  !--- Caution -------------------------------------------!
  ! Index must correspond to those in &atomic_red_coor.   !
  !-------------------------------------------------------!
/
file_pseudo(n) specifies the filename of the pseudopotential file of the n-th element.
izatom(n) is the atomic number of the n-th element.
lloc_ps(n) specifies which angular momentum component is chosen as the local potential for the n-th element.
&functional
  !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).)
  xc = 'PZ'
/
xc specifies the exchange-correlation potential to be used in the calculation.
&rgrid
  !number of spatial grids(x,y,z)
  num_rgrid(1:3) = 12, 12, 12
/
num_rgrid(i) specifies the number of real-space grid point in i-th direction.
&kgrid
  !number of k-points(x,y,z)
  num_kgrid(1:3) = 4, 4, 4
/
num_kgrid(i) specifies the number of k-points for i-th direction discretizing the Brillouin zone.
&scf
  !maximum number of scf iteration and threshold of convergence
  nscf      = 300
  threshold = 1.0d-9
/
nscf specifies the maximum number of SCF iterations.
threshold specifies the threshold to judge the convergence.
&atomic_red_coor
  !cartesian atomic reduced coodinates
  '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
  !--- Format ---------------------------------------------------!
  ! 'symbol' x y z index(correspond to that of pseudo potential) !
  !--------------------------------------------------------------!
/
&atomic_red_coor specifies spatial coordinates of atoms in reduced coordinate system.

Output files

After the calculation, following output files and a directory are created in the directory that you run the code,

name

description

Si_info.data

information on ground state solution

Si_eigen.data

energy eigenvalues of orbitals

Si_k.data

k-point distribution

PS_Si_KY_n.dat

information on pseodupotential file for silicon atom

data_for_restart

directory where files used in the real-time calculation are contained

You may download the above files (zipped file, except for the directory data_for_restart) from:

Main results of the calculation such as orbital energies are included in Si_info.data. Explanations of the Si_info.data and other output files are below:

Si_info.data

Calculated orbital and total energies as well as parameters specified in the input file are shown in this file.

Si_eigen.data

1 particle energies.

#esp: single-particle energies (eigen energies)
#occ: occupation numbers, io: orbital index
# 1:io, 2:esp[a.u.], 3:occ

Si_k.data

k-point distribution.

# ik: k-point index
# kx,ky,kz: Reduced coordinate of k-points
# wk: Weight of k-point
# 1:ik[none] 2:kx[none] 3:ky[none] 4:kz[none] 5:wk[none]
# coefficients (2*pi/a [a.u.]) in kx, ky, kz

Exercise-5: Dielectric function of crystalline silicon

In this exercise, we learn the linear response calculation of the crystalline silicon of a diamond structure. Calculation is done in a cubic unit cell that contains eight silicon atoms. This exercise should be carried out after finishing the ground state calculation that was explained in Exercise-4. An impulsive perturbation is applied to all electrons in the unit cell along z direction. Since the dielectric function is isotropic in the diamond structure, calculated dielectric function should not depend on the direction of the perturbation. During the time evolution, electric current averaged over the unit cell volume is calculated. A time-frequency Fourier transformation of the electric current gives us a frequency-dependent conductivity. The dielectric function may be obtained from the conductivity using a standard relation.

Input files

To run the code, following files in samples are used:

file name

description

Si_rt_response.inp

input file that contain input keywords and their values.

Si_rps.dat

pseodupotential file of silicon

restart

directory created in the ground state calculation (rename the directory from data_for_restart to restart)

In the input file Si_rt_response.inp, input keywords are specified. Most of them are mandatory to execute the calculation. This will help you to prepare the input file for other systems that you want to calculate. A complete list of the input keywords can be found in List of input keywords.

!########################################################################################!
! Excercise 05: Dielectric function of crystalline silicon                               !
!----------------------------------------------------------------------------------------!
! * The detail of this excercise is expained in our manual(see chapter: 'Exercises').    !
!   The manual can be obtained from: https://salmon-tddft.jp/documents.html              !
! * Input format consists of group of keywords like:                                     !
!     &group                                                                             !
!       input keyword = xxx                                                              !
!     /                                                                                  !
!   (see chapter: 'List of all input keywords' in the manual)                            !
!----------------------------------------------------------------------------------------!
! * Conversion from unit_system = 'a.u.' to 'A_eV_fs':                                   !
!   Length: 1 [a.u.] = 0.52917721067    [Angstrom]                                       !
!   Energy: 1 [a.u.] = 27.21138505      [eV]                                             !
!   Time  : 1 [a.u.] = 0.02418884326505 [fs]                                             !
!----------------------------------------------------------------------------------------!
! * Copy the ground state data directory('data_for_restart') (or make symbolic link)     !
!   calculated in 'samples/exercise_04_bulkSi_gs/' and rename the directory to 'restart/'!
!   in the current directory.                                                            !
!########################################################################################!

&calculation
  !type of theory
  theory = 'tddft_response'
/
theory specifies which theoretical method is used in the calculation.
&control
  !common name of output files
  sysname = 'Si'
/
sysname is a prefix for filenames of output files.
&units
  !units used in input and output files
  unit_system = 'a.u.'
/
unit_system specifies which unit system is used in the input and output files.
&system
  !periodic boundary condition
  yn_periodic = 'y'

  !grid box size(x,y,z)
  al(1:3) = 10.26d0, 10.26d0, 10.26d0

  !number of elements, atoms, electrons and states(bands)
  nelem  = 1
  natom  = 8
  nelec  = 32
  nstate = 32
/
yn_periodic specifies whether or not periodic boundary condition is applied.
al(i) specifies the side length of the unit cell.
nelem is the number of elements in the system.
natom is the number of atoms in the system.
nelec is the number of electrons in the system.
nstate is the number of orbitals that are used in the calculation.
&pseudo
  !name of input pseudo potential file
  file_pseudo(1) = './Si_rps.dat'

  !atomic number of element
  izatom(1) = 14

  !angular momentum of pseudopotential that will be treated as local
  lloc_ps(1) = 2
  !--- Caution -------------------------------------------!
  ! Index must correspond to those in &atomic_red_coor.   !
  !-------------------------------------------------------!
/
file_pseudo(n) specifies the filename of the pseudopotential file of the n-th element.
izatom(n) is the atomic number of the n-th element.
lloc_ps(n) specifies which angular momentum component is chosen as the local potential for the n-th element.
&functional
  !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).)
  xc = 'PZ'
/
xc specifies the exchange-correlation potential to be used in the calculation.
&rgrid
  !number of spatial grids(x,y,z)
  num_rgrid(1:3) = 12, 12, 12
/
num_rgrid(i) specifies the number of real-space grid point in i-th direction.
&kgrid
  !number of k-points(x,y,z)
  num_kgrid(1:3) = 4, 4, 4
/
num_kgrid(i) specifies the number of k-points for i-th direction discretizing the Brillouin zone.
&tgrid
  !time step size and number of time grids(steps)
  dt = 0.08d0
  nt = 6000
/
dt specifies the time step.
nt is the number of time steps for the time propagation.
&emfield
  !envelope shape of the incident pulse('impulse': impulsive field)
  ae_shape1 = 'impulse'

  !polarization unit vector(real part) for the incident pulse(x,y,z)
  epdir_re1(1:3) = 0.00d0, 0.00d0, 1.00d0
  !--- Caution ---------------------------------------------------------!
  ! Defenition of the incident pulse is wrriten in:                     !
  ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 !
  !---------------------------------------------------------------------!
/
ae_shape1 specifies the envelope of the field. For a linear response calculation, as_shape1='impulse' is used. It indicates that a weak impulsive perturbation is applied at t=0.
epdir_re1(i) specifies the i-th component of the real part of the polarization unit vector.
&analysis
  !energy grid size and number of energy grids for output files
  de      = 4.0d-4
  nenergy = 5000
/
de specifies the energy grid size for frequency-domain analysis.
nenergy specifies the number of energy grid points for frequency-domain analysis.
&atomic_red_coor
  !cartesian atomic reduced coodinates
  '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
  !--- Format ---------------------------------------------------!
  ! 'symbol' x y z index(correspond to that of pseudo potential) !
  !--------------------------------------------------------------!
/
&atomic_red_coor specifies spatial coordinates of atoms in reduced coordinate system.

Output files

After the calculation, following output files are created in the directory that you run the code,

file name

description

Si_response.data

Fourier spectra of the conductivity and dielectric functions

Si_rt.data

vector potential, electric field, and matter current as functions of time

Si_rt_energy

components of total energy and difference of total energy as functions of time

PS_Si_KY_n.dat

information on pseodupotential file for silicon atom

You may download the above files (zipped file) from:

Explanations of the output files are described below:

Si_response.data

Time-frequency Fourier transformation of the macroscopic current gives the conductivity of the system. Then the dielectric function is calculated.

# Fourier-transform spectra:
# sigma: Conductivity
# eps: Dielectric constant
# 1:Energy[a.u.] 2:Re(sigma_x)[a.u.] 3:Re(sigma_y)[a.u.] 4:Re(sigma_z)[a.u.] 5:Im(sigma_x)[a.u.] 6:Im(sigma_y)[a.u.] 7:Im(sigma_z)[a.u.] 8:Re(eps_x)[none] 9:Re(eps_y)[none] 10:Re(eps_z)[none] 11:Im(eps_x)[none] 12:Im(eps_y)[none] 13:Im(eps_z)[none]

Si_rt.data

Results of time evolution calculation for vector potential, electric field, and matter current density.

# Real time calculation:
# Ac_ext: External vector potential field
# E_ext: External electric field
# Ac_tot: Total vector potential field
# E_tot: Total electric field
# Jm: Matter current density (electrons)
# 1:Time[a.u.] 2:Ac_ext_x[a.u.] 3:Ac_ext_y[a.u.] 4:Ac_ext_z[a.u.] 5:E_ext_x[a.u.] 6:E_ext_y[a.u.] 7:E_ext_z[a.u.] 8:Ac_tot_x[a.u.] 9:Ac_tot_y[a.u.] 10:Ac_tot_z[a.u.] 11:E_tot_x[a.u.] 12:E_tot_y[a.u.] 13:E_tot_z[a.u.]  14:Jm_x[a.u.] 15:Jm_y[a.u.] 16:Jm_z[a.u.]

Si_rt_energy

Eall and Eall-Eall0 are total energy and electronic excitation energy, respectively.

# Real time calculation:
# Eall: Total energy
# Eall0: Initial energy
# 1:Time[a.u.] 2:Eall[a.u.] 3:Eall-Eall0[a.u.]

Exercise-6: Electron dynamics in crystalline silicon under a pulsed electric field

In this exercise, we learn the calculation of electron dynamics in a unit cell of crystalline silicon of a diamond structure. Calculation is done in a cubic unit cell that contains eight silicon atoms. This exercise should be carried out after finishing the ground state calculation that was explained in Exercise-4. A pulsed electric field that has cos^2 envelope shape is applied. The parameters that characterize the pulsed field such as magnitude, frequency, polarization, and carrier envelope phase are specified in the input file.

Input files

To run the code, following files in samples are used:

file name

description

Si_rt_pulse.inp

input file that contain input keywords and their values.

Si_rps.dat

pseodupotential file for Carbon

restart

directory created in the ground state calculation (rename the directory from data_for_restart to restart)

In the input file Si_rt_pulse.inp, input keywords are specified. Most of them are mandatory to execute the calculation. This will help you to prepare the input file for other systems that you want to calculate. A complete list of the input keywords can be found in List of input keywords.

!########################################################################################!
! Excercise 06: Electron dynamics in crystalline silicon under a pulsed electric field   !
!----------------------------------------------------------------------------------------!
! * The detail of this excercise is expained in our manual(see chapter: 'Exercises').    !
!   The manual can be obtained from: https://salmon-tddft.jp/documents.html              !
! * Input format consists of group of keywords like:                                     !
!     &group                                                                             !
!       input keyword = xxx                                                              !
!     /                                                                                  !
!   (see chapter: 'List of all input keywords' in the manual)                            !
!----------------------------------------------------------------------------------------!
! * Conversion from unit_system = 'a.u.' to 'A_eV_fs':                                   !
!   Length: 1 [a.u.] = 0.52917721067    [Angstrom]                                       !
!   Energy: 1 [a.u.] = 27.21138505      [eV]                                             !
!   Time  : 1 [a.u.] = 0.02418884326505 [fs]                                             !
!----------------------------------------------------------------------------------------!
! * Copy the ground state data directory('data_for_restart') (or make symbolic link)     !
!   calculated in 'samples/exercise_04_bulkSi_gs/' and rename the directory to 'restart/'!
!   in the current directory.                                                            !
!########################################################################################!

&calculation
  !type of theory
  theory = 'tddft_pulse'
/
theory specifies which theoretical method is used in the calculation.
&control
  !common name of output files
  sysname = 'Si'
/
sysname is a prefix for filenames of output files.
&units
  !units used in input and output files
  unit_system = 'a.u.'
/
unit_system specifies which unit system is used in the input and output files.
&system
  !periodic boundary condition
  yn_periodic = 'y'

  !grid box size(x,y,z)
  al(1:3) = 10.26d0, 10.26d0, 10.26d0

  !number of elements, atoms, electrons and states(bands)
  nelem  = 1
  natom  = 8
  nelec  = 32
  nstate = 32
/
yn_periodic specifies whether or not periodic boundary condition is applied.
al(i) specifies the side length of the unit cell.
nelem is the number of elements in the system.
natom is the number of atoms in the system.
nelec is the number of electrons in the system.
nstate is the number of orbitals that are used in the calculation.
&pseudo
  !name of input pseudo potential file
  file_pseudo(1) = './Si_rps.dat'

  !atomic number of element
  izatom(1) = 14

  !angular momentum of pseudopotential that will be treated as local
  lloc_ps(1) = 2
  !--- Caution -------------------------------------------!
  ! Index must correspond to those in &atomic_red_coor.   !
  !-------------------------------------------------------!
/
file_pseudo(n) specifies the filename of the pseudopotential file of the n-th element.
izatom(n) is the atomic number of the n-th element.
lloc_ps(n) specifies which angular momentum component is chosen as the local potential for the n-th element.
&functional
  !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).)
  xc = 'PZ'
/
xc specifies the exchange-correlation potential to be used in the calculation.
&rgrid
  !number of spatial grids(x,y,z)
  num_rgrid(1:3) = 12, 12, 12
/
num_rgrid(i) specifies the number of real-space grid point in i-th direction.
&kgrid
  !number of k-points(x,y,z)
  num_kgrid(1:3) = 4, 4, 4
/
num_kgrid(i) specifies the number of k-points for i-th direction discretizing the Brillouin zone.
&tgrid
  !time step size and number of time grids(steps)
  dt = 0.08d0
  nt = 6000
/
dt specifies the time step.
nt is the number of time steps for the time propagation.
&emfield
  !envelope shape of the incident pulse('Acos2': cos^2 type envelope for vector potential)
  ae_shape1 = 'Acos2'

  !peak intensity(W/cm^2) of the incident pulse
  I_wcm2_1 = 5.0d11

  !duration of the incident pulse
  tw1 = 441.195136248d0

  !mean photon energy(average frequency multiplied by the Planck constant) of the incident pulse
  omega1 = 0.05696145187d0

  !polarization unit vector(real part) for the incident pulse(x,y,z)
  epdir_re1(1:3) = 0.0d0, 0.0d0, 1.0d0
  !--- Caution ---------------------------------------------------------!
  ! Defenition of the incident pulse is wrriten in:                     !
  ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 !
  !---------------------------------------------------------------------!
/
ae_shape1 specifies the envelope of the field.
I_wcm2_1 specify the intensity of the pulse in unit of W/cm2.
tw1 specifies the duration of the pulse.
omega1 specifies the mean photon energy of the pulse.
epdir_re1(i) specifies the i-th component of the real part of the polarization unit vector.
&atomic_red_coor
  !cartesian atomic reduced coodinates
  '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
  !--- Format ---------------------------------------------------!
  ! 'symbol' x y z index(correspond to that of pseudo potential) !
  !--------------------------------------------------------------!
/
&atomic_red_coor specifies spatial coordinates of atoms in reduced coordinate system.

Output files

After the calculation, following output files are created in the directory that you run the code,

file name

description

Si_pulse.data

matter current and electric field as functions of energy

Si_rt.data

vector potential, electric field, and matter current as functions of time

Si_rt_energy

components of total energy and difference of total energy as functions of time

PS_Si_KY_n.dat

information on pseodupotential file for silicon atom

You may download the above files (zipped file) from:

Explanations of the output files are described below:

Si_pulse.data

Time-frequency Fourier transformation of the matter current and electric field.

# Fourier-transform spectra:
# energy: Frequency
# Jm: Matter current
# E_ext: External electric field
# E_tot: Total electric field
# 1:energy[a.u.] 2:Re(Jm_x)[a.u.] 3:Re(Jm_y)[a.u.] 4:Re(Jm_z)[a.u.] 5:Im(Jm_x)[a.u.] 6:Im(Jm_y)[a.u.] 7:Im(Jm_z)[a.u.] 8:|Jm_x|^2[a.u.] 9:|Jm_y|^2[a.u.] 10:|Jm_z|^2[a.u.] 11:Re(E_ext_x)[a.u.] 12:Re(E_ext_y)[a.u.] 13:Re(E_ext_z)[a.u.] 14:Im(E_ext_x)[a.u.] 15:Im(E_ext_y)[a.u.] 16:Im(E_ext_z)[a.u.] 17:|E_ext_x|^2[a.u.] 18:|E_ext_y|^2[a.u.] 19:|E_ext_z|^2[a.u.] 20:Re(E_ext_x)[a.u.] 21:Re(E_ext_y)[a.u.] 22:Re(E_ext_z)[a.u.] 23:Im(E_ext_x)[a.u.] 24:Im(E_ext_y)[a.u.] 25:Im(E_ext_z)[a.u.] 26:|E_ext_x|^2[a.u.] 27:|E_ext_y|^2[a.u.] 28:|E_ext_z|^2[a.u.]

Si_rt.data

Results of time evolution calculation for vector potential, electric field, and matter current density.

# Real time calculation:
# Ac_ext: External vector potential field
# E_ext: External electric field
# Ac_tot: Total vector potential field
# E_tot: Total electric field
# Jm: Matter current density (electrons)
# 1:Time[a.u.] 2:Ac_ext_x[a.u.] 3:Ac_ext_y[a.u.] 4:Ac_ext_z[a.u.] 5:E_ext_x[a.u.] 6:E_ext_y[a.u.] 7:E_ext_z[a.u.] 8:Ac_tot_x[a.u.] 9:Ac_tot_y[a.u.] 10:Ac_tot_z[a.u.] 11:E_tot_x[a.u.] 12:E_tot_y[a.u.] 13:E_tot_z[a.u.]  14:Jm_x[a.u.] 15:Jm_y[a.u.] 16:Jm_z[a.u.]

Si_rt_energy

Eall and Eall-Eall0 are total energy and electronic excitation energy, respectively.

# Real time calculation:
# Eall: Total energy
# Eall0: Initial energy
# 1:Time[a.u.] 2:Eall[a.u.] 3:Eall-Eall0[a.u.]

Maxwell + TDDFT multiscale simulation

Exercise-7: Pulsed-light propagation through a silicon thin film

In this exercise, we learn the calculation of the propagation of a pulsed light through a thin film of crystalline silicon. We consider a silicon thin film of 42 nm thickness, and an irradiation of a few-cycle, linearly polarized pulsed light normally on the thin film. This exercise should be carried out after finishing the ground state calculation that was explained in Exercise-4. The pulsed light locates in the vacuum region in front of the thin film. The parameters that characterize the pulsed light such as magnitude and frequency are specified in the input file.

Input files

To run the code, following files in samples are used:

file name

description

Si_rt_multiscale.inp

input file that contain input keywords and their values.

Si_rps.dat

pseodupotential file for silicon

restart

directory created in the ground state calculation (rename the directory from data_for_restart to restart)

In the input file Si_rt_multiscale.inp, input keywords are specified. Most of them are mandatory to execute the calculation. This will help you to prepare the input file for other systems that you want to calculate. A complete list of the input keywords can be found in List of input keywords.

!########################################################################################!
! Excercise 07: Maxwell+TDDFT multiscale simulation                                      !
!               (Pulsed-light propagation through a silicon thin film)                   !
!----------------------------------------------------------------------------------------!
! * The detail of this excercise is expained in our manual(see chapter: 'Exercises').    !
!   The manual can be obtained from: https://salmon-tddft.jp/documents.html              !
! * Input format consists of group of keywords like:                                     !
!     &group                                                                             !
!       input keyword = xxx                                                              !
!     /                                                                                  !
!   (see chapter: 'List of all input keywords' in the manual)                            !
!----------------------------------------------------------------------------------------!
! * Conversion from unit_system = 'a.u.' to 'A_eV_fs':                                   !
!   Length: 1 [a.u.] = 0.52917721067    [Angstrom]                                       !
!   Energy: 1 [a.u.] = 27.21138505      [eV]                                             !
!   Time  : 1 [a.u.] = 0.02418884326505 [fs]                                             !
!----------------------------------------------------------------------------------------!
! * Copy the ground state data directory('data_for_restart') (or make symbolic link)     !
!   calculated in 'samples/exercise_04_bulkSi_gs/' and rename the directory to 'restart/'!
!   in the current directory.                                                            !
!########################################################################################!

&calculation
  !type of theory
  theory = 'multi_scale_maxwell_tddft'
/
theory specifies which theoretical method is used in the calculation.
&control
  !common name of output files
  sysname = 'Si'
/
sysname is a prefix for filenames of output files.
&units
  !units used in input and output files
  unit_system = 'a.u.'
/
unit_system specifies which unit system is used in the input and output files.
&system
  !periodic boundary condition
  yn_periodic = 'y'

  !grid box size(x,y,z)
  al(1:3) = 10.26d0, 10.26d0, 10.26d0

  !number of elements, atoms, electrons and states(bands)
  nelem  = 1
  natom  = 8
  nelec  = 32
  nstate = 32
/
yn_periodic specifies whether or not periodic boundary condition is applied.
al(i) specifies the side length of the unit cell.
nelem is the number of elements in the system.
natom is the number of atoms in the system.
nelec is the number of electrons in the system.
nstate is the number of orbitals that are used in the calculation.
&pseudo
  !name of input pseudo potential file
  file_pseudo(1) = './Si_rps.dat'

  !atomic number of element
  izatom(1) = 14

  !angular momentum of pseudopotential that will be treated as local
  lloc_ps(1) = 2
  !--- Caution -------------------------------------------!
  ! Index must correspond to those in &atomic_red_coor.   !
  !-------------------------------------------------------!
/
file_pseudo(n) specifies the filename of the pseudopotential file of the n-th element.
izatom(n) is the atomic number of the n-th element.
lloc_ps(n) specifies which angular momentum component is chosen as the local potential for the n-th element.
&functional
  !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).)
  xc = 'PZ'
/
xc specifies the exchange-correlation potential to be used in the calculation.
&rgrid
  !number of spatial grids(x,y,z)
  num_rgrid(1:3) = 12, 12, 12
/
num_rgrid(i) specifies the number of real-space grid point in i-th direction.
&kgrid
  !number of k-points(x,y,z)
  num_kgrid(1:3) = 4, 4, 4
/
num_kgrid(i) specifies the number of k-points for i-th direction discretizing the Brillouin zone.
&tgrid
  !time step size and number of time grids(steps)
  dt = 0.08d0
  nt = 6000
/
dt specifies the time step.
nt is the number of time steps for the time propagation.
&emfield
  !envelope shape of the incident pulse('Acos2': cos^2 type envelope for vector potential)
  ae_shape1 = 'Acos2'

  !peak intensity(W/cm^2) of the incident pulse
  I_wcm2_1 = 1.0d12

  !duration of the incident pulse
  tw1 = 441.195136248d0

  !mean photon energy(average frequency multiplied by the Planck constant) of the incident pulse
  omega1 = 0.05696145187d0

  !polarization unit vector(real part) for the incident pulse(x,y,z)
  epdir_re1(1:3) = 0.0d0, 0.0d0, 1.0d0
  !--- Caution ---------------------------------------------------------!
  ! Defenition of the incident pulse is wrriten in:                     !
  ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 !
  !---------------------------------------------------------------------!
/
ae_shape1 specifies the envelope of the field.
I_wcm2_1 specify the intensity of the pulse in unit of W/cm2.
tw1 specifies the duration of the pulse.
omega1 specifies the mean photon energy of the pulse.
epdir_re1(i) specifies the i-th component of the real part of the polarization unit vector.
&multiscale
  !number of macro grids in electromagnetic analysis for x, y, and z directions
  nx_m = 8
  ny_m = 1
  nz_m = 1

  !macro grid spacing for x, y, and z directions
  hx_m = 100.0d0
  hy_m = 100.0d0
  hz_m = 100.0d0

  !number of macroscopic grids for vacumm region
  !(nxvacl_m is for negative x-direction in front of material)
  !(nxvacr_m is for positive x-direction behind material)
  nxvacl_m = 1000
  nxvacr_m = 1000
/
nx_m, ny_m, nz_m specify the number of macroscopic grid points inside the material.
hx_m, hy_m, hz_m specify the grid spacing of macroscopic coordinates.
nxvacl_m / nxvacr_m specifies the number of grid points in the vacuum region in the left / right side of the material.
&maxwell
  !boundary condition of electromagnetic analysis
  !first index(1-3 rows) corresponds to x, y, and z directions
  !second index(1-2 columns) corresponds to bottom and top of the directions
  !('abc' is absorbing boundary condition)
  boundary_em(1,1) = 'abc'
  boundary_em(1,2) = 'abc'
/
boundary_em(i,n) specifies the boundary condition for the electromagnetic analysis. The first index i corresponds to the x,y, and z direction. The second index n specifies left or right side of the material.
&atomic_red_coor
  !cartesian atomic reduced coodinates
  '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
  !--- Format ---------------------------------------------------!
  ! 'symbol' x y z index(correspond to that of pseudo potential) !
  !--------------------------------------------------------------!
/
&atomic_red_coor specifies spatial coordinates of atoms in reduced coordinate system.

Output files

After the calculation, new directory multiscale/ is created, then, following output files are created in the directory,

file name

description

Si_m/mxxxxxx/Si_rt.data

vector potential, electric field, and matter current at macroscopic position xxxxxx as functions of time

Si_m/mxxxxxx/Si_rt_energy.data

components of total energy and difference of total energy at macroscopic position xxxxxx as functions of time

Si_m/mxxxxxx/PS_Si_KY_n.dat

information on pseodupotential file for silicon atom at macroscopic position xxxxxx

Si_RT_Ac/Si_Ac_yyyyyy.data

vector potential, electric field, magnetic field, electromagnetic current density at time step yyyyyy as function of space

Si_wave.data

amplitudes of incident, reflected, and transmitted wave

You may download the above files (zipped file) from:

Explanations of the output files are described below:

Si_m/mxxxxxx/Si_rt.data

The number in the file name specifies the macroscopic position. Results of time evolution calculation for vector potential, electric field, and matter current density.

# Real time calculation:
# Ac_ext: External vector potential field
# E_ext: External electric field
# Ac_tot: Total vector potential field
# E_tot: Total electric field
# Jm: Matter current density (electrons)
# 1:Time[a.u.] 2:Ac_ext_x[a.u.] 3:Ac_ext_y[a.u.] 4:Ac_ext_z[a.u.] 5:E_ext_x[a.u.] 6:E_ext_y[a.u.] 7:E_ext_z[a.u.] 8:Ac_tot_x[a.u.] 9:Ac_tot_y[a.u.] 10:Ac_tot_z[a.u.] 11:E_tot_x[a.u.] 12:E_tot_y[a.u.] 13:E_tot_z[a.u.]  14:Jm_x[a.u.] 15:Jm_y[a.u.] 16:Jm_z[a.u.]

Si_m/mxxxxxx/Si_rt_energy.data

The number in the file name specifies the macroscopic position. Eall and Eall-Eall0 are total energy and electronic excitation energy, respectively.

# Real time calculation:
# Eall: Total energy
# Eall0: Initial energy
# 1:Time[a.u.] 2:Eall[a.u.] 3:Eall-Eall0[a.u.]

Si_RT_Ac/Si_Ac_yyyyyy.data

The number in the file name specifies the iteration number. Various quantities at a time are shown as function of macroscopic position.

# Multiscale TDDFT calculation
# IX, IY, IZ: FDTD Grid index
# x, y, z: Coordinates
# Ac: Vector potential field
# E: Electric field
# J_em: Electromagnetic current density
# 1:IX[none] 2:IY[none] 3:IZ[none] 4:Ac_x[a.u.] 5:Ac_y[a.u.] 6:Ac_z[a.u.] 7:E_x[a.u.] 8:E_y[a.u.] 9:E_z[a.u.] 10:B_x[a.u.] 11:B_y[a.u.] 12:B_z[a.u.] 13:Jem_x[a.u.] 14:Jem_y[a.u.] 15:Jem_z[a.u.] 16:E_em[a.u./vol] 17:E_abs[a.u./vol]

Si_wave.data

Amplitudes of incident, reflected, and transmitted wave.

# 1D multiscale calculation:
# E_inc: E-field amplitude of incident wave
# E_ref: E-field amplitude of reflected wave
# E_tra: E-field amplitude of transmitted wave
# 1:Time[a.u.] 2:E_inc_x[a.u.] 3:E_inc_y[a.u.] 4:E_inc_z[a.u.] 5:E_ref_x[a.u.] 6:E_ref_y[a.u.] 7:E_ref_z[a.u.] 8:E_tra_x[a.u.] 9:E_tra_y[a.u.] 10:E_tra_z[a.u.]

Geometry optimization and Ehrenfest molecular dynamics

Exercise-8: Geometry optimization of C2H2 molecule

In this exercise, we learn the calculation of geometry optimization of acetylene (C2H2) molecule, solving the static Kohn-Sham equation. This exercise will be useful to learn how to set up calculations in SALMON for any isolated systems such as molecules and nanoparticles.

Input files

To run the code, following files in samples are used:

file name

description

C2H2_opt.inp

input file that contains input keywords and their values

C_rps.dat

pseodupotential file for carbon atom

H_rps.dat

pseudopotential file for hydrogen atom

In the input file C2H2_opt.inp, input keywords are specified. Most of them are mandatory to execute the geometry optimization. This will help you to prepare an input file for other systems that you want to calculate. A complete list of the input keywords that can be used in the input file can be found in List of input keywords.

!########################################################################################!
! Excercise 08: Geometry optimization of C2H2 molecule                                   !
!----------------------------------------------------------------------------------------!
! * The detail of this excercise is expained in our manual(see chapter: 'Exercises').    !
!   The manual can be obtained from: https://salmon-tddft.jp/documents.html              !
! * Input format consists of group of keywords like:                                     !
!     &group                                                                             !
!       input keyword = xxx                                                              !
!     /                                                                                  !
!   (see chapter: 'List of all input keywords' in the manual)                            !
!----------------------------------------------------------------------------------------!
! * Conversion from unit_system = 'a.u.' to 'A_eV_fs':                                   !
!   Length: 1 [a.u.] = 0.52917721067    [Angstrom]                                       !
!   Energy: 1 [a.u.] = 27.21138505      [eV]                                             !
!   Time  : 1 [a.u.] = 0.02418884326505 [fs]                                             !
!########################################################################################!

&calculation
  !type of theory
  theory = 'dft'

  !geometry optimization option
  yn_opt = 'y'
/
theory specifies which theoretical method is used in the calculation.
yn_opt is a switch to carry out the structure optimization.
&control
  !common name of output files
  sysname = 'C2H2'
/
sysname is a prefix for filenames of output files.
&units
  !units used in input and output files
  unit_system = 'A_eV_fs'
/
unit_system specifies which unit system is used in the input and output files.
&system
  !periodic boundary condition
  yn_periodic = 'n'

  !grid box size(x,y,z)
  al(1:3) = 12.0d0, 12.0d0, 16.0d0

  !number of elements, atoms, electrons and states(orbitals)
  nelem  = 2
  natom  = 4
  nelec  = 10
  nstate = 6
/
yn_periodic specifies whether or not periodic boundary condition is applied.
al(i) specifies the spatial box size of the cubiod cell.
nelem is the number of elements in the system.
natom is the number of atoms in the system.
nelec is the number of electrons in the system.
nstate is the number of orbitals that are used in the calculation.
&pseudo
  !name of input pseudo potential file
  file_pseudo(1) = './C_rps.dat'
  file_pseudo(2) = './H_rps.dat'

  !atomic number of element
  izatom(1) = 6
  izatom(2) = 1

  !angular momentum of pseudopotential that will be treated as local
  lloc_ps(1) = 1
  lloc_ps(2) = 0
  !--- Caution ---------------------------------------!
  ! Indices must correspond to those in &atomic_coor. !
  !---------------------------------------------------!
/
file_pseudo(n) specifies the filename of the pseudopotential file of the n-th element.
izatom(n) is the atomic number of the n-th element.
lloc_ps(n) specifies which angular momentum component is chosen as the local potential for the n-th element.
&functional
  !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).)
  xc = 'PZ'
/
xc specifies the exchange-correlation potential to be used in the calculation.
&rgrid
  !spatial grid spacing(x,y,z)
  dl(1:3) = 0.20d0, 0.20d, 0.20d0
/
dl(i) specifies the spatial grid spacing in i-th direction.
&scf
  !maximum number of scf iteration and threshold of convergence for ground state calculation
  nscf      = 300
  threshold = 1.0d-9
/
nscf specifies the maximum number of SCF iterations.
threshold specifies the threshold to judge the convergence.
&opt
  !threshold(maximum force on atom) of convergence for geometry optimization
  convrg_opt_fmax = 1.0d-3
/

&atomic_coor
  !cartesian atomic coodinates
  'C'    0.0    0.0    0.6  1  y
  'H'    0.0    0.0    1.7  2  y
  'C'    0.0    0.0   -0.6  1  y
  'H'    0.0    0.0   -1.7  2  y
  !--- Format -------------------------------------------------------!
  ! 'symbol' x y z index(correspond to that of pseudo potential) y/n !
  !--- Caution ------------------------------------------------------!
  ! final index(y/n) determines free/fix for the atom coordinate.    !
  !------------------------------------------------------------------!
/
&atomic_coor specifies spatial coordinates of atoms.

Output files

After the calculation, following output files and a directory are created in the directory that you run the code,

name

description

C2H2_info.data

information on ground state solution

C2H2_eigen.data

1 particle energies

C2H2_trj.xyz

atomic coordinates during the geometry optimization

C2H2_k.data

k-point distribution (for isolated systems, only gamma point is described)

data_for_restart

directory where files used in the real-time calculation are contained

PS_C_KY_n.dat

information on pseodupotential file for carbon atom

PS_H_KY_n.dat

information on pseodupotential file for hydrogen atom

You may download the above files (zipped file, except for the directory data_for_restart) from:

Main results of the calculation such as orbital energies are included in C2H2_info.data. Explanations of the C2H2_info.data and other output files are below:

C2H2_info.data

Calculated orbital and total energies as well as parameters specified in the input file are shown in this file.

C2H2_eigen.data

1 particle energies.

#esp: single-particle energies (eigen energies)
#occ: occupation numbers, io: orbital index
# 1:io, 2:esp[eV], 3:occ

C2H2_trj.xyz

The atomic coordinates during the geometry optimization in xyz format.

C2H2_k.data

k-point distribution(for isolated systems, only gamma point is described).

# ik: k-point index
# kx,ky,kz: Reduced coordinate of k-points
# wk: Weight of k-point
# 1:ik[none] 2:kx[none] 3:ky[none] 4:kz[none] 5:wk[none]
# coefficients (2*pi/a [a.u.]) in kx, ky, kz

Exercise-9: Ehrenfest molecular dynamics of C2H2 molecule

In this exercise, we learn the calculation of the molecular dynamics in the acetylene (C2H2) molecule under a pulsed electric field, solving the time-dependent Kohn-Sham equation and the Newtonian equation. As outputs of the calculation, time-evolution of the electron density as well as molecular structures and associated quantities such as the electron and ion kinetic energies, the electric dipole moment of the system and temperature as functions of time are calculated.. This tutorial should be carried out after finishing the geometry optimization that was explained in Exercise-8. In the calculation, a pulsed electric field that has cos^2 envelope shape is applied. The parameters that characterize the pulsed field such as magnitude, frequency, polarization direction, and carrier envelope phase are specified in the input file.

Input files

To run the code, following files in samples are used. The directory restart is created in the ground state calculation as data_for_restart. Pseudopotential files are already used in the geometry optimization. Therefore, C2H2_md.inp that specifies input keywords and their values for the pulsed electric field and molecular dynamics calculations is the only file that the users need to prepare.

file name

description

C2H2_md.inp

input file that contain input keywords and their values.

C_rps.dat

pseodupotential file for carbon

H_rps.dat

pseudopotential file for hydrogen

restart

directory created in the geometry optimization (rename the directory from data_for_restart to restart)

In the input file C2H2_md.inp, input keywords are specified. Most of them are mandatory to execute the calculation of electron dynamics induced by a pulsed electric field. This will help you to prepare the input file for other systems and other pulsed electric fields with molecular dynamics calculation that you want to calculate. A complete list of the input keywords that can be used in the input file can be found in List of input keywords.

!########################################################################################!
! Excercise 09: Ehrenfest molecular dynamics of C2H2 molecule                            !
!----------------------------------------------------------------------------------------!
! * The detail of this excercise is expained in our manual(see chapter: 'Exercises').    !
!   The manual can be obtained from: https://salmon-tddft.jp/documents.html              !
! * Input format consists of group of keywords like:                                     !
!     &group                                                                             !
!       input keyword = xxx                                                              !
!     /                                                                                  !
!   (see chapter: 'List of all input keywords' in the manual)                            !
!----------------------------------------------------------------------------------------!
! * Conversion from unit_system = 'a.u.' to 'A_eV_fs':                                   !
!   Length: 1 [a.u.] = 0.52917721067    [Angstrom]                                       !
!   Energy: 1 [a.u.] = 27.21138505      [eV]                                             !
!   Time  : 1 [a.u.] = 0.02418884326505 [fs]                                             !
!----------------------------------------------------------------------------------------!
! * Ehrenfest-MD option is still trial.                                                  !
! * Copy the ground state data directory ('data_for_restart') (or make symbolic link)    !
!   calculated in 'samples/exercise_08_C2H2_opt/' and rename the directory to 'restart/' !
!   in the current directory.                                                            !
!########################################################################################!

&calculation
  !type of theory
  theory = 'tddft_pulse'

  !molecular dynamics option
  yn_md  = 'y'
/
theory specifies which theoretical method is used in the calculation.
yn_md is a switch for Ehrenfest molecular dynamics.
&control
  !common name of output files
  sysname = 'C2H2'
/
sysname is a prefix for filenames of output files.
&units
  !units used in input and output files
  unit_system = 'A_eV_fs'
/
unit_system specifies which unit system is used in the input and output files.
&system
  !periodic boundary condition
  yn_periodic = 'n'

  !grid box size(x,y,z)
  al(1:3) = 12.0d0, 12.0d0, 16.0d0

  !number of elements, atoms, electrons and states(orbitals)
  nelem  = 2
  natom  = 4
  nelec  = 10
  nstate = 6
/
yn_periodic specifies whether or not periodic boundary condition is applied.
al(i) specifies the spatial box size of the cubiod cell.
nelem is the number of elements in the system.
natom is the number of atoms in the system.
nelec is the number of electrons in the system.
nstate is the number of orbitals that are used in the calculation.
&pseudo
  !name of input pseudo potential file
  file_pseudo(1) = './C_rps.dat'
  file_pseudo(2) = './H_rps.dat'

  !atomic number of element
  izatom(1) = 6
  izatom(2) = 1

  !angular momentum of pseudopotential that will be treated as local
  lloc_ps(1) = 1
  lloc_ps(2) = 0
  !--- Caution ---------------------------------------!
  ! Indices must correspond to those in &atomic_coor. !
  !---------------------------------------------------!
/
file_pseudo(n) specifies the filename of the pseudopotential file of the n-th element.
izatom(n) is the atomic number of the n-th element.
lloc_ps(n) specifies which angular momentum component is chosen as the local potential for the n-th element.
&functional
  !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).)
  xc = 'PZ'
/
xc specifies the exchange-correlation potential to be used in the calculation.
&rgrid
  !spatial grid spacing(x,y,z)
  dl(1:3) = 0.20d0, 0.20d0, 0.20d0
/
dl(i) specifies the spatial grid spacing in i-th direction.
&tgrid
  !time step size and number of time grids(steps)
  dt = 1.00d-3
  nt = 5000
/
dt specifies the time step.
nt is the number of time steps for the time propagation.
&emfield
  !envelope shape of the incident pulse('Ecos2': cos^2 type envelope for scalar potential)
  ae_shape1 = 'Ecos2'

  !peak intensity(W/cm^2) of the incident pulse
  I_wcm2_1 = 1.00d8

  !duration of the incident pulse
  tw1 = 6.00d0

  !mean photon energy(average frequency multiplied by the Planck constant) of the incident pulse
  omega1 = 9.28d0

  !polarization unit vector(real part) for the incident pulse(x,y,z)
  epdir_re1(1:3) = 0.00d0, 0.00d0, 1.00d0

  !carrier emvelope phase of the incident pulse
  !(phi_cep1 must be 0.25 + 0.5 * n(integer) when ae_shape1 = 'Ecos2')
  phi_cep1 = 0.75d0
  !--- Caution ---------------------------------------------------------!
  ! Defenition of the incident pulse is wrriten in:                     !
  ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 !
  !---------------------------------------------------------------------!
/
ae_shape1 specifies the envelope of the field.
I_wcm2_1 specify the intensity of the pulse in unit of W/cm2.
tw1 specifies the duration of the pulse.
omega1 specifies the mean photon energy of the pulse.
epdir_re1(i) specifies the i-th component of the real part of the polarization unit vector.
phi_cep1 specifies the carrier-envelope phase of the pulse.
&md
  !ensemble
  ensemble = 'NVE'

  !set of initial velocities
  yn_set_ini_velocity = 'y'

  !setting temperature [K] for NVT ensemble, velocity scaling,
  !and generating initial velocities
  temperature0_ion_k = 300.0d0

  !time step interval for updating pseudopotential
  step_update_ps = 20
/
ensemble specifies the choice of the ensemble.
yn_set_ini_velocity is a switch to prepare initial velocity for atoms.
temperature0_ion_k specifies the temperature that is used to generate initial velocity of ions.
step_update_ps specifies the time step interval to update projector for the nonlocal pseudopotential.

Output files

After the calculation, following output files are created in the directory that you run the code,

file name

description

C2H2_pulse.data

dipole moment as functions of energy

C2H2_rt.data

components of change of dipole moment (electrons/plus definition) and total dipole moment (electrons/minus + ions/plus) as functions of time

C2H2_rt_energy.data

components of total energy and difference of total energy as functions of time

C2H2_trj.xyz

Trajectory of atoms(ions): Atomic coordinates, velocities, and forces are printed

PS_C_KY_n.dat

information on pseodupotential file for carbon atom

PS_H_KY_n.dat

information on pseodupotential file for hydrogen atom

You may download the above files (zipped file) from:

Explanations of the files are described below:

C2H2_pulse.data

Time-frequency Fourier transformation of the dipole moment.

# Fourier-transform spectra:
# energy: Frequency
# dm: Dopile moment
# 1:energy[eV] 2:Re(dm_x)[fs*Angstrom] 3:Re(dm_y)[fs*Angstrom] 4:Re(dm_z)[fs*Angstrom] 5:Im(dm_x)[fs*Angstrom] 6:Im(dm_y)[fs*Angstrom] 7:Im(dm_z)[fs*Angstrom] 8:|dm_x|^2[fs^2*Angstrom^2] 9:|dm_y|^2[fs^2*Angstrom^2] 10:|dm_z|^2[fs^2*Angstrom^2]

C2H2_rt.data

Results of time evolution calculation for vector potential, electric field, and dipole moment.

# Real time calculation:
# Ac_ext: External vector potential field
# E_ext: External electric field
# Ac_tot: Total vector potential field
# E_tot: Total electric field
# ddm_e: Change of dipole moment (electrons/plus definition)
# dm: Total dipole moment (electrons/minus + ions/plus)
# 1:Time[fs] 2:Ac_ext_x[fs*V/Angstrom] 3:Ac_ext_y[fs*V/Angstrom] 4:Ac_ext_z[fs*V/Angstrom] 5:E_ext_x[V/Angstrom] 6:E_ext_y[V/Angstrom] 7:E_ext_z[V/Angstrom] 8:Ac_tot_x[fs*V/Angstrom] 9:Ac_tot_y[fs*V/Angstrom] 10:Ac_tot_z[fs*V/Angstrom] 11:E_tot_x[V/Angstrom] 12:E_tot_y[V/Angstrom] 13:E_tot_z[V/Angstrom] 14:ddm_e_x[Angstrom] 15:ddm_e_y[Angstrom] 16:ddm_e_z[Angstrom] 17:dm_x[Angstrom] 18:dm_y[Angstrom] 19:dm_z[Angstrom]

C2H2_rt_energy.data

Eall and Eall-Eall0 are total energy and electronic excitation energy, respectively.

# Real time calculation:
# Eall: Total energy
# Eall0: Initial energy
# Tion: Kinetic energy of ions
# Temperature_ion: Temperature of ions
# E_work: Work energy of ions(sum f*dr)
# 1:Time[fs] 2:Eall[eV] 3:Eall-Eall0[eV] # 4:Tion[eV] 5:Temperature_ion[K] 6:E_work[eV]

C2H2_trj.xyz

Atomic coordinates [Angstrom], velocities [a.u.] and forces [a.u.] are printed along the time evolution in xyz format.

FDTD simulation(electromagnetic analysis)

Exercise-10: Pulsed electric field response of a metallic nanosphere in classical electromagnetism(FDTD simulation)

In this exercise, we learn the pulsed electric field response in the metallic nanosphere, solving the time-dependent Maxwell equations. As outputs of the calculation, the time response of the electromagnetic field is calculated. A pulsed electric field that has cos^2 envelope shape is applied. The parameters that characterize the pulsed field such as magnitude, frequency, polarization direction, and carrier envelope phase are specified in the input file.

Input files

To run the code, the input file classicEM_rt_pulse.inp that contains input keywords and their values for the pulsed electric field calculation is required. The shape file of the metallic nanosphere shape.cube is also required.

The shape file can be generated by program FDTD_make_shape in SALMON utilities: https://salmon-tddft.jp/utilities.html

'shape.inp' is an input file for 'FDTD_make_shape' to generate 'shape.cube'.

The input files are in samples

file name

description

classicEM_rt_pulse.inp

input file that contain input keywords and their values.

shape.cube

shape file for fdtd

shape.inp

input file for FDTD_make_shape

In the input file classicEM_rt_pulse.inp, input keywords are specified. Most of them are mandatory to execute the linear response calculation. This will help you to prepare the input file for other systems that you want to calculate. A complete list of the input keywords that can be used in the input file can be found in List of input keywords.

!########################################################################################!
! Excercise 10: Pulsed electric field response of a metallic nanosphere                  !
!               in classical electromagnetism(FDTD simulation)                           !
!----------------------------------------------------------------------------------------!
! * The detail of this excercise is expained in our manual(see chapter: 'Exercises').    !
!   The manual can be obtained from: https://salmon-tddft.jp/documents.html              !
! * Input format consists of group of keywords like:                                     !
!     &group                                                                             !
!       input keyword = xxx                                                              !
!     /                                                                                  !
!   (see chapter: 'List of all input keywords' in the manual)                            !
!----------------------------------------------------------------------------------------!
! * Conversion from unit_system = 'a.u.' to 'A_eV_fs':                                   !
!   Length: 1 [a.u.] = 0.52917721067    [Angstrom]                                       !
!   Energy: 1 [a.u.] = 27.21138505      [eV]                                             !
!   Time  : 1 [a.u.] = 0.02418884326505 [fs]                                             !
!----------------------------------------------------------------------------------------!
! * The read-in file 'shape_file' in &maxwell category can be generated by program       !
!   'FDTD_make_shape' in SALMON utilities(https://salmon-tddft.jp/utilities.html).       !
!   'shape.inp' is an input file for 'FDTD_make_shape' to generate 'shape.cube'.         !
! * Results can be visualized by program 'FDTD_make_figani' in SALMON utilities.         !
!########################################################################################!

&calculation
  !type of theory
  theory = 'maxwell'
/
theory specifies which theoretical method is used in the calculation.
&control
  !name of directory where output files are contained
  base_directory = 'result'
/
base_directory specifies the directory name where output files are generated.
&units
  !units used in input and output files
  unit_system = 'A_eV_fs'
/
unit_system specifies which unit system is used in the input and output files.
&system
  !periodic boundary condition
  yn_periodic = 'n'
/
yn_periodic specifies whether or not periodic boundary condition is applied.
&emfield
  !envelope shape of the incident pulse('Ecos2': cos^2 type envelope for scalar potential)
  ae_shape1 = 'Ecos2'

  !peak intensity(W/cm^2) of the incident pulse
  I_wcm2_1 = 1.00d8

  !duration of the incident pulse
  tw1 = 4.60d0

  !mean photon energy(average frequency multiplied by the Planck constant) of the incident pulse
  omega1 = 5.49d0

  !polarization unit vector(real part) for the incident pulse(x,y,z)
  epdir_re1(1:3) = 0.00d0, 0.00d0, 1.00d0

  !carrier emvelope phase of the incident pulse
  !(phi_cep1 must be 0.25 + 0.5 * n(integer) when ae_shape1 = 'Ecos2')
  phi_cep1 = 0.75d0
  !--- Caution ---------------------------------------------------------!
  ! Defenition of the incident pulse is wrriten in:                     !
  ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 !
  !---------------------------------------------------------------------!
/
ae_shape1 specifies the envelope of the field.
I_wcm2_1 specify the intensity of the pulse in unit of W/cm2.
tw1 specifies the duration of the pulse.
omega1 specifies the mean photon energy of the pulse.
epdir_re1(i) specifies the i-th component of the real part of the polarization unit vector.
phi_cep1 specifies the carrier-envelope phase of the pulse.
&maxwell
  !box size and spacing of spatial grid(x,y,z)
  al_em(1:3) = 120d0, 120d0, 120d0
  dl_em(1:3) = 1.2d0, 1.2d0, 1.2d0

  !time step size and number of time grids(steps)
  dt_em = 2.30d-4
  nt_em = 20000

  !name of input shape file and number of media in the file
  shape_file = './shape.cube'
  media_num  = 1

  !*** MEDIA INFORMATION(START) **************************************!
  !type of media(media ID)
  media_type(1) = 'lorentz-drude'
  !--- Au described by Lorentz-Drude model ---------------------------!
  ! The parameters are determined from:                               !
  ! (https://www.osapublishing.org/ao/abstract.cfm?uri=ao-37-22-5271) !
  !-------------------------------------------------------------------!

  !number of poles and plasma frequency of media(media ID)
  pole_num_ld(1) = 6
  omega_p_ld(1)  = 9.030d0

  !oscillator strength, collision frequency,
  !and oscillator frequency of media(media ID,pole ID)
  f_ld(1,1:6)     = 0.760d0, 0.024d0, 0.010d0, 0.071d0, 0.601d0, 4.384d0
  gamma_ld(1,1:6) = 0.053d0, 0.241d0, 0.345d0, 0.870d0, 2.494d0, 2.214d0
  omega_ld(1,1:6) = 0.000d0, 0.415d0, 0.830d0, 2.969d0, 4.304d0, 13.32d0
  !*** MEDIA INFORMATION(END) ****************************************!

  !*** SOURCE INFORMATION(START) *************************************!
  !type of method to generate the incident pulse
  !('source': incident current source)
  wave_input = 'source'

  !location of source(x,y,z)
  source_loc1(1:3) = -37.8d0, 0.0d0, 0.0d0

  !propagation direction of the incident pulse(x,y,z)
  ek_dir1(1:3) = 1.0d0, 0.0d0, 0.0d0
  !*** SOURCE INFORMATION(END) ***************************************!

  !*** OBSERVATION INFORMATION(START) ********************************!
  !number of observation points
  obs_num_em = 1

  !time step interval for sampling
  obs_samp_em = 20

  !location of observation point(observation ID,x,y,z)
  obs_loc_em(1,1:3) = 0.0d0, 0.0d0, 0.0d0

  !output flag for electrmagnetic field distribution(observation ID)
  yn_obs_plane_em(1) = 'n'
  !--- Make of animation file ----------------------------------------!
  ! When yn_obs_plane_em(1) = 'y', animation file can be made         !
  ! by program 'FDTD_make_figani' in SALMON utilities.                !
  ! The animation file visualizes electromagnetic field distributions !
  ! on the cross-section including the observation point              !
  ! whose location is determined by obs_loc_em.                       !
  !-------------------------------------------------------------------!
  !*** OBSERVATION INFORMATION(END) **********************************!
/
al_em(i) specifies the lengths of three sides of the cuboid where the grid points are prepared.
dl_em(i) specifies the grid spacings in three Cartesian directions.
dt_em specifies the time step of the time evolution calculation.
nt_em specifies the number of time steps in the calculation.
shape_file specifies the filename of the shape file.
media_num specifies the number of the types of media that is provided in the shape file.
media_type(n) specifies the type of the n-th media.
pole_num_ld(n) and omega_p_ld(n) specify the number of poles and the plasmal frequency of the n-th media, respectively.
f_ld(n,m), omega_ld(n,m), gamma_ld(n,m) specify the oscillator strength, oscillator frequency, and collision frequency of the m-th pole of the n-th media, respectively.
wave_input specifies an electric current source that is used for the generation of the pulse.
source_loc1(i) specifies the coordinate of the current source.
ek_dir1(i) specifies the propagation direction of the pulse.
obs_num_em specifies the number of the observing point.
obs_samp_em specifies the sampling interval.
obs_loc_em(n,i) specifies the coordinate of n-th observing point.
yn_obs_plane_em(n) is a switch to output the electromagnetic fields on the xy, yz, and xz planes that include the n-th observation point.

Output files

After the calculation, following output files are created in the directory 'result',

file name

description

obs0_info.data

information to generate animation

obs1_at_point_rt.data

components of electric and magnetic fields as functions of time

You may download the above files (zipped file) from:

Explanations of the files are described below:

obs0_info.data

This file is used to generate animation files by using SALMON utilities: https://salmon-tddft.jp/utilities.html

obs1_at_point_rt.data

Results of time evolution calculation for electric and magnetic fields at observation point 1.

# Real time calculation:
# E: Electric field
# H: Magnetic field
# 1:Time[fs] 2:E_x[V/Angstrom] 3:E_y[V/Angstrom] 4:E_z[V/Angstrom] 5:H_x[A/Angstrom] 6:H_y[A/Angstrom] 7:H_z[A/Angstrom]