# Inputs¶

We here summarize namelists that appear in this Tutorial. A thorough list of the namelist variables may be found in the downloaded file in ‘SALMON/manual/input_variables.md’.

## &units¶

Mandatory: none

```
&units
unit_system='A_eV_fs'
/
```

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

For isolated systems (specified by `iperiodic = 0`

in `&system`

),
the unit of 1/eV is used for the output files of DOS and PDOS if
`unit_system = 'A_eV_fs'`

is specified, while atomic unit is used if
not. For other output files, the Angstrom/eV/fs units are used
irrespective of the namelist value.

For periodic systems (specified by `iperiodic =3`

in `&system`

), the
unit system specified by this namelist variable is used for most output
files. See the first few lines of output files to confirm the unit
system adopted in the file.

## &calculation¶

Mandatory: calc_mode

```
&calculation
calc_mode = 'GS'
/
```

The value of the `calc_mode`

should be one of `'GS'`

, `'RT'`

, and
`'GS-RT'`

. For isolated systems (specified by `iperiodic = 3`

in
`&system`

), the ground state (`'GS'`

) and the real time (`'RT'`

) calculations should be done separately and sequentially.
For periodic systems (specified by `iperiodic = 3`

in `&system`

), both ground state and real time calculations should be carried out
as a single task (`calc_mode = 'GS_RT'`

).

For Maxwell + TDDFT multi-scale calculation, add the following namelist, `use_ms_maxwell = 'y'`

.

## &control¶

Mandatory: none

```
&control
sysname = 'C2H2'
/
```

‘C2H2’ defined by `sysname = 'C2H2'`

will be used in the filenames of
output files. If you do not specify it, the file name will start with
‘default’.

## &functional¶

```
&functional
xc ='PZ'
/
```

`xc ='PZ'`

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

For isolated systems (specified by `iperiodic = 0`

in `&system`

),
only the default choice of ‘PZ’ is available at present.

For periodic systems (specified by `iperiodic = 3`

in `&system`

),
the following functionals may be available in addition to ‘PZ’,
`xc = 'PZM'`

Perdew-Zunger LDA with modification to improve sooth connection between
high density form and low density one, `xc = 'TBmBJ' cval = 1.0`

:J. P. Perdew and Alex Zunger, Phys. Rev. B 23, 5048 (1981).

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

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

and `alibc`

separately. If the exchange and
correlation potentials are given as a combined set, you need to specify
`alibxc`

. We show below an example:

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

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

Note that, the hybrid functionals (hybrid gga/mgga) are not supported in the current (version 1.1.0) of SALMON.

## &system¶

Mandatory: iperiodic, al, nstate, nelem, natom

**For an isolated molecule (Tutorial-1, 2, 3)**:

```
&system
iperiodic = 0
al = 16d0, 16d0, 16d0
nstate = 5
nelem = 2
natom = 4
nelec = 10
/
```

`iperiodic = 0`

indicates that the isolated boundary condition will be
used in the calculation. `al = 16d0, 16d0, 16d0`

specifies the lengths
of three sides of the rectangular parallelepiped where the grid points
are prepared. `nstate = 8`

indicates the number of Kohn-Sham orbitals
to be solved. `nelec = 10`

indicate the number of valence electrons in
the system. Since the present code assumes that the system is spin
saturated, `nstate`

should be equal to or larger than `nelec/2`

.
`nelem = 2`

and `natom = 4`

indicate the number of elements and the
number of atoms in the system, respectively.

**For a periodic system (Tutorial-4, 5)**:

```
&system
iperiodic = 3
al = 10.26d0,10.26d0,10.26d0
nstate = 32
nelec = 32
nelem = 1
natom = 8
/
```

`iperiodic = 3`

indicates that three dimensional periodic boundary
condition (bulk crystal) is assumed. `al = 10.26d0, 10.26d0, 10.26d0`

specifies the lattice constans of the unit cell. `nstate = 32`

indicates the number of Kohn-Sham orbitals to be solved. `nelec = 32`

indicate the number of valence electrons in the system. `nelem = 1`

and `natom = 8`

indicate the number of elements and the number of
atoms in the system, respectively.

**For Maxwell - TDDFT multi scale calculation (Tutorial-6)**:

```
&system
iperiodic = 3
al = 10.26d0,10.26d0,10.26d0
isym = 8
crystal_structure = 'diamond'
nstate = 32
nelec = 32
nelem = 1
natom = 8
/
```

The difference from the above case is the variables, `isym = 8`

and
`crystal_structure = 'diamond'`

, which indicates that the spatial
symmetry of the unit cell is used in the calculation. Although the use
of the symmetry substantially reduces the computational cost, it should
be used very carefully. At present, the spatial symmetry has been
implemented only for the case of the diamond structure.

## &pseudo¶

Mandatory: pseudo_file, izatom

**For C2H2 molecule**:

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

Parameters related to atomic species and pseudopotentials.
`izatom(1) = 6`

specifies the atomic number of the element #1.
`pseudo_file(1) = 'C_rps.dat'`

indicates the filename of the
pseudopotential of element #1. `lmax_ps(1) = 1`

and `lloc_ps(1) = 1`

specify the maximum angular momentum of the pseudopotential projector
and the angular momentum of the pseudopotential that will be treated as
local, respectively.

**For crystalline Si**:

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

`izatom(1) = 14`

indicates the atomic number of the element #1.
`pseudo_file(1) = 'Si_rps.dat'`

indicates the pseudopotential filename
of element #1. `lloc_ps(1) = 2`

indicate the angular momentum of the
pseudopotential that will be treated as local.

## &atomic_coor¶

Mandatory: atomic_coor or atomic_red_coor (they may be provided as a separate file)

**For C2H2 molecule**:

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

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

## &atomic_red_coor¶

Mandatory: atomic_coor or atomic_red_coor (they may be provided as a separate file)

**For a crystalline silicon**:

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

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

## &rgrid¶

Mandatory: dl or num_rgrid

This namelist provides grid spacing of Cartesian coordinate system.
`dl(3)`

specify the grid spacing in three Cartesian coordinates. This
is adopted for C2H2 calculation (Tutorial-1).

```
&rgrid
dl = 0.25d0, 0.25d0, 0.25d0
/
```

`num_rgrid(3)`

specify the number of grid points in each Cartesian
direction. This is adopted for crystalline Is calculation (Tutorial-4,
5, 6).

```
&rgrid
num_rgrid = 12,12,12
/
```

## &kgrid¶

Mandatory: none

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

```
&kgrid
num_kgrid = 4,4,4
/
```

## &scf¶

Mandatory: nscf

This namelists specify parameters related to the self-consistent field calculation.

```
&scf
ncg = 4
nscf = 1000
convergence = 'norm_rho_dng'
threshold_norm_rho = 1.d-15
/
```

`ncg = 4`

is the number of conjugate-gradient iterations in solving
the Kohn-Sham equation. Usually this value should be 4 or 5.
`nscf = 1000`

is the number of scf iterations. For isolated systems
specified by `&system/iperiodic = 0`

, the scf loop in the ground state
calculation ends before the number of the scf iterations reaches
`nscf`

, if a convergence criterion is satisfied. There are several
options to examine the convergence. If the value of `norm_rho_dng`

is
specified, the convergence is examined by the squared difference of the
electron density,

## &hartree¶

Mandatory: none

```
&hartree
meo = 3
num_pole_xyz = 2,2,2
/
```

`meo`

specifies the order of multipole expansion of electron density
that is used to prepare boundary condition for the Hartree potential.

`meo=1`

: Monopole expansion (spherical boundary condition).`meo=2`

: Multipole expansions around each atom.`meo=3`

: Multipole expansion around the center of mass of electrons in cubits that are defined by`num_pole_xyz`

.

`num_pole_xyz(3)`

defines the division of space when `meo = 3`

is
specified.

A default for `meo`

is `3`

, and defaults for `num_pole_xyz`

are
`(0,0,0)`

. When default is set for `num_pole_xyz`

, the division of
space is carried out using a prescribed method.

## &tgrid¶

Mandatory: dt, Nt

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

`dt=1.25d-3`

specifies the time step of the time evolution
calculation. `nt=5000`

specifies the number of time steps in the
calculation.

## &propagation¶

This namelist specifies the numerical method for time evolution calculations of electron orbitals.

```
&propagation
propagator='etrs'
/
```

`propagator = 'etrs'`

indicates the use of enforced time-reversal
symmetry propagator. M.A.L. Marques, A. Castro, G.F. Bertsch, and A.
Rubio, Comput. Phys. Commun., 151 60
(2003).

```
&propagation
propagator='middlepoint'
/
```

`propagation='middlepoint'`

indicates that Hamiltonian at midpoint of
two-times is used.

The default is *middlepoint*.

## &emfield¶

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

### Linear response calculations¶

A weak impulsive field is applied at *t=0*. For this case,
`ae_shape1 = 'impulse'`

should be described.

Mandatory: ae_shape1

```
&emfield
ae_shape1 = 'impulse'
epdir_re1 = 0.d0,0.d0,1.d0
/
```

`epdir_rel(3)`

specify a unit vector that indicates the direction of
the impulse.

For a periodic system specified by `iperiodic = 3`

, one may add
`trans_longi`

. It has the value, `'tr'`

(transverse) or
`'lo'`

(longitudinal), that specifies the treatment of the
polarization in the time evolution calculation. The default is `'tr'`

.

```
&emfield
trans_longi = 'tr'
ae_shape1 = 'impulse'
epdir_re1 = 0.,0.,1.
/
```

The magnitude of the impulse of the pulse may be explicitly specified
by, for example, `e_impulse = 1d-2`

. The default is ‘1d-2’ in atomic
unit.

### Pulsed electric field calculations¶

A Pulsed electric field of finite time duration is applied. For this
case, `as_shape1`

should be specified. It indicates the shape of the
envelope of the pulse. The options include ‘Acos2’ and ‘Ecos2’ (See
below for other options).

Mandatory: ae_shape1, epdir_re1, {rlaser_int1 or amplitude1}, omega1, pulse_tw1, phi_cep1

```
&emfield
ae_shape1 = 'Ecos2'
epdir_re1 = 0.d0,0.d0,1.d0
rlaser_int_wcm2_1 = 1.d8
omega1=9.28d0
pulse_tw1=6.d0
phi_cep1=0.75d0
/
```

`ae_shape1 = 'Ecos2'`

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

`epdir_re1 = 0.d0,0.d0,1.d0`

specifies the real part of the unit
polarization vector of the pulsed electric field. If only the real part
is specified, it describes a linearly polarized pulse. Using both real
(‘epdir_re1’) and imaginary (‘epdir_im1’) parts of the polarization
vector, circularly (and general ellipsoidary) polarized pulses may be
described.

`laser_int_wcm2_1 = 1.d8`

specifies the maximum intensity of the
applied electric field in unit of W/cm^2. It is also possible to specify
the maximum intensity of the pulse by `amplitude1`

.

`omega1=9.26d0`

specifies the average photon energy (frequency
multiplied with hbar).

`pulse_tw1=6.d0`

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

`phi_cep1=0.75d0`

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

It is possible to use two pulses simultaneously to simulate pump-probe
experiments, adding information for two pulses. To specify the second
pulse, change from 1 to 2 in the namelist variables, like `ae_shape2`

.
The time delay between two pulses is specified by the variable ‘t1_t2’.

For a periodic system specified by `iperiodic = 3`

, one may add
`trans_longi`

. It has the value, `'tr'`

(transverse) or
`'lo'`

(longitudinal), that specifies the treatment of the
polarization in the time evolution calculation. The default is `'tr'`

.
For a periodic system, it is also specify ‘Acos3’, ‘Acos4’, ‘Acos6’,
‘Acos8’ for `ae_shape1`

.

## &analysis¶

Mandatory: none

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

```
&analysis
out_psi = 'y'
out_dns = 'y'
out_dos = 'y'
out_pdos = 'y'
out_elf = 'y'
/
```

In the time evolution calculation of isolated systems (Tutorial-3):

```
&analysis
out_dns_rt = 'y'
out_elf_rt = 'y'
out_estatic_rt = 'y'
/
```

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

```
&analysis
nenergy=1000
de=0.001
/
```

`nenergy=1000`

specifies the number of energy steps, and `de=0.001`

specifies the energy spacing in the time-frequency Fourier
transformation.

## &multiscale¶

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

```
&multiscale
fdtddim = '1D'
twod_shape = 'periodic'
nx_m = 4
ny_m = 1
hX_m = 250d0
nxvacl_m = -2000
nxvacr_m = 256
/
```

`fdtddim`

specifies the spatial dimension of the macro system.
`fdtddim='1D'`

indicates that one-dimensional equation is solved for
the macroscopic vector potential.

`nx_m = 4`

specifies the number of the macroscopic grid points in for
x-direction in the spatial region where the material exists.

`hx_m = 250d0`

specifies the grid spacing of the macroscopic grid in
x-direction.

`nxvacl_m = -2000`

and `nxvacr_m = 256`

indicate the number of grid
points in the vacuum region, `nxvacl_m`

for the left and `nxvacr_m`

for the right from the surface of the material.

## ¶llel¶

When you execute a job with MPI parallelization, you are not required to specify any parameters that describe the assignment of the parallelization; the assignment is carried out automatically. You may also specify the parameters explicitly as below.

Mandatory: none

```
¶llel
nproc_ob = 1
nproc_domain = 1,1,1
nproc_domain_s = 1,1,1
/
```

`nproc_ob`

specifies the number of MPI parallelization to divide the electron orbitals. The default value is 0 (automatic parallelization).`nproc_domain(3)`

specifies the number of MPI parallelization to divide the spatial grids of the electron orbitals in three Cartesian directions. The default values are (0/0/0) (automatic parallelization).`nproc_domain_s(3)'`

specifies the number of MPI parallelization to divide the spatial grids related to the electron density in three Cartesian directions. The default values are (0/0/0) (automatic parallelization).

The following conditions must be satisfied.

- The total number of processors must be equal to both
`nproc_ob * nproc_domain(1) * nproc_domain(2) * nproc_domain(3)`

and also`nproc_domain_s(1) * nproc_domain_s(2) * nproc_domain_s(3)`

. `nproc_domain_s(1)`

is a multiple of`nproc_domain(1)`

, and the same relations to the second and third components.