# Input Keywords for Exercises¶

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

## &calculation¶

Mandatory: theory

```
&calculation
theory = 'dft'
/
```

The value of the `theory`

should be one of `'dft'`

, `'dft_md'`

, `'tddft_response'`

, `'tddft_pulse'`

,
`'single_scale_maxwell_tddft'`

, `'multi_scale_maxwell_tddft'`

, `'maxwell'`

, and `'dft_k_expand'`

.

`dft`

: ground state calculation based on DFT

`dft_md`

: adiabatic ab initio MD simulations based on DFT

`tddft_response`

: simulations based on TDDFT to obtain linear-response

`tddft_pulse`

: simulations based on TDDFT using pulsed light

`single_scale_maxwell_tddft`

: coupled Maxwell and TDDFT single-scale simulation

`multi_scale_maxwell_tddft`

: coupled Maxwell and TDDFT multi-scale simulation

`maxwell`

: electromagnetic simulations based on the Maxwell's equations

`dft_k_expand`

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

## &units¶

Mandatory: none

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

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

For isolated systems (specified by `yn_periodic = 'n'`

in `&system`

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

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

For periodic systems (specified by `yn_periodic = 'y'`

in `&system`

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

## &control¶

Mandatory: none

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

'C2H2' defined by `sysname = 'C2H2'`

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

## &system¶

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

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

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

`yn_periodic = 'n'`

indicates that the isolated boundary condition will be used in the calculation.
`al(1:3) = 16.0d0, 16.0d0, 16.0d0`

specifies the lengths of three sides of the rectangular parallelepiped
where the grid points are prepared.
`nelem = 2`

and `natom = 4`

indicate the number of elements and the number of atoms in the system, respectively.
`nelec = 10`

indicate the number of valence electrons in the system.

`nstate = 6`

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

`nstate`

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

.

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

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

`yn_periodic = 'y'`

indicates that three dimensional periodic boundary condition (bulk crystal) is assumed.
`al(1:3) = 10.26d0, 10.26d0, 10.26d0`

specifies the lattice constans of the unit cell.
`nelem = 1`

and `natom = 8`

indicate the number of elements and the number of atoms in the system, respectively.
`nelec = 32`

indicate the number of valence electrons in the system.
`nstate = 32`

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

## &pseudo¶

Mandatory: pseudo_file, izatom

**For C2H2 molecule**:

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

Parameters related to atomic species and pseudopotentials.
`pseudo_file(1) = './C_rps.dat'`

indicates the filename of the pseudopotential of element.
`izatom(1) = 6`

specifies the atomic number of the element.

**For crystalline Si**:

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

`file_pseudo(1) = './Si_rps.dat'`

indicates the pseudopotential filename of element.
`izatom(1) = 14`

indicates the atomic number of the element.

## &functional¶

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

`xc ='PZ'`

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

For isolated systems (specified by `yn_periodic = 'n'`

in `&system`

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

For periodic systems (specified by ```yn_periodic = 'y'`

in `&system`

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

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

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

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

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

and `alibc`

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

. We show below an example:

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

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

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

## &rgrid¶

Mandatory: dl or num_rgrid

`dl(1:3) = 0.25d0, 0.25d0, 0.25d0`

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

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

`num_rgrid(1:3) = 12, 12, 12`

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

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

## &kgrid¶

Mandatory: none

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

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

## &scf¶

Mandatory: nscf

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

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

`nscf = 200`

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

,
if a convergence criterion is satisfied.

## &analysis¶

Mandatory: none

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

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

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

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

`de = 1.0d-2`

specifies the energy spacing,
and `nenergy = 3000`

specifies the number of energy steps
in the time-frequency Fourier transformation.

## &tgrid¶

Mandatory: dt, nt

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

`dt = 1.25d-3`

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

specifies the number of time steps in the calculation.

## &emfield¶

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

### Linear response calculations¶

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

should be described.

Mandatory: ae_shape1

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

`epdir_re1(1:3) = 0.0d0, 0.0d0, 1.0d0`

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

For a periodic system specified by `yn_periodic = 'y'`

,
one may add `trans_longi`

.
It has the value, `'tr'`

(transverse) or `'lo'`

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

.

The magnitude of the impulse of the pulse may be explicitly specified by,
for example, `e_impulse = 1.00d-2`

.
The default is '1.00d-2' in atomic unit.

### Pulsed electric field calculations¶

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

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

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

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

`ae_shape1 = 'Ecos2'`

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

`I_wcm2_1 = 1.00d8`

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

.

`tw1 = 6.00d0`

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

`omega1 = 9.28d0`

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

`epdir_re1(1:3) = 0.00d0, 0.00d0, 1.00d0`

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

`phi_cep1 = 0.75d0`

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

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

.
The time delay between two pulses is specified by the input keyword 't1_t2'.

For a periodic system specified by `yn_periodic = 'y'`

, one may add `trans_longi`

.
It has the value, `'tr'`

(transverse) or `'lo'`

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

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

.

## &multiscale¶

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

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

`nx_m = 8`

specifies the number of the macroscopic grid points for x-direction
in the spatial region where the material exists.
`ny_m = 1`

and `nz_m = 1`

are those for y- and z-directions.

`hx_m = 100.0d0`

specifies the grid spacing of the macroscopic grid for x-direction.
`hy_m = 100.0d0`

and `hz_m = 100.0d0`

are those for y- and z-directions.

`nxvacl_m = 1000`

and `nxvacr_m = 1000`

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

for the left and `nxvacr_m`

for the right from the surface of the material.

## &atomic_coor¶

Mandatory: atomic_coor or atomic_red_coor

**For C2H2 molecule**:

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

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

## &atomic_red_coor¶

Mandatory: atomic_coor or atomic_red_coor

**For a crystalline silicon**:

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

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