# Exercises

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## 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 namelist variables 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 6 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. This is illustrated in Exercise-1. After finishing the ground state calculation, two exercises of electron dynamics calculations 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 2 exercises (Exercise-4 ~ 5) are for a crystalline solid, silicon. If you are interested in learning electron dynamics calculations in extended periodic systems, please look into these exercises. Since ground state calculations of small unit-cell systems are not computationally expensive and a time evolution calculation is usually much more time-consuming than the ground state calculation, we recommend to run the ground and the time evolution calculations as a single job. The following two exercises are organized in that way. Exercise-4 illustrates the calculation of linear response properties of crystalline silicon to obtain the dielectric function. Exercise-5 illustrates the calculation of electron dynamics in the crystalline silicon induced by a pulsed electric field.

The final exercise (Exercise-6) is for an irradiation and a propagation of a pulsed light in a bulk silicon, coupling Maxwell equations for the electromagnetic fields of the pulsed light and the electron dynamics in the unit cells. This calculation is quite time-consuming and is recommended to execute using massively parallel supercomputers. Exercise-6 illustrates the calculation of a pulsed, linearly polarized light irradiating normally on a surface of a bulk silicon.

## C2H2 (isolated molecules)

### Exercise-1: Ground state of C2H2 molecule

In this exercise, we learn the calculation of the ground state solution 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. It should be noted that at present it is not possible to carry out the geometry optimization in SALMON. Therefore, atomic positions of the molecule are specified in the input file and are fixed during the calculations.

#### Input files

To run the code, following files are used:

 file name description C2H2_gs.inp input file that contains namelist variables and their values C_rps.dat pseodupotential file for carbon atom H_rps.dat pseudopotential file for hydrogen atom

You may download the above 3 files (zipped file) from:

Download zipped input and pseudopotential files


In the input file C2H2_gs.inp, namelists variables are specified. Most of them are mandatory to execute the ground state calculation. We present their explanations below:

Explanations of input files (ground state of C2H2 molecule)


This will help you to prepare an input file for other systems that you want to calculate. A complete list of the namelist variables that can be used in the input file can be found in the downloaded file SALMON/manual/input_variables.md.

#### Output files

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

 file name description C2H2_info.data information on ground state solution dns.cube a cube file for electron density elf.cube electron localization function (ELF) psi1.cube, psi2.cube, ... electron orbitals dos.data density of states pdos1.data, pdos2.data, ... projected density of states C2H2_gs.bin binary output file to be used in the real-time calculation

You may download the above files (zipped file, except for the binary file C2H2_gs.bin) from:

Download zipped output files


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 described in:

Explanations of output files (ground state of C2H2 molecule)


#### Images

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

 image files used to create the image highest occupied molecular orbital (HOMO) psi1.cube, psi2.cube, ... electron density dns.cube electron localization function elf.cube

### 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 namelist variables and their values for the linear response calculation is required. The binary file C2H2_gs.bin that is created in the ground state calculation and pseudopotential files are also required. The pseudopotential files should be the same as those used in the ground state calculation.

 file name description C2H2_rt_response.inp input file that contains namelist variables and their values C_rps.dat pseodupotential file for carbon H_rps.dat pseudopotential file for hydrogen C2H2_gs.bin binary file created in the ground state calculation

You may download the C2H2_rt_response.inp file (zipped file) from:

Download zipped input file


In the input file C2H2_rt_response.inp, namelists variables are specified. Most of them are mandatory to execute the linear response calculation. We present their explanations below:

Explanations of input files (polarizability and photoabsorption of C2H2 molecule)


This will help you to prepare the input file for other systems that you want to calculate. A complete list of the namelist variables that can be used in the input file can be found in the downloaded file SALMON/manual/input_variables.md.

#### Output files

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

 file name description C2H2_lr.data polarizability and oscillator strength distribution as functions of energy C2H2_p.data components of dipole moment as functions of time

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

Download zipped output files


Explanations of the output files are given in:

Explanations of output files (polarizability and photoabsorption of C2H2 molecule)


### 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 are used. The C2H2_gs.bin file is created in the ground state calculation. Pseudopotential files are already used in the ground state calculation. Therefore, C2H2_rt_pulse.inp that specifies namelist variables 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 namelist variables and their values. C_rps.dat pseodupotential file for Carbon H_rps.dat pseudopotential file for Hydrogen C2H2_gs.bin binary file created in the ground state calculation

You may download the C2H2_rt_pulse.inp file (zipped file) from:

Download zipped input file


In the input file C2H2_rt_pulse.inp, namelists variables are specified. Most of them are mandatory to execute the calculation of electron dynamics induced by a pulsed electric field. We present explanations of the namelist variables that appear in the input file in:

Explanations of input files (C2H2 molecule under 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 namelist variables that can be used in the input file can be found in the downloaded file SALMON/manual/input_variables.md.

#### Output files

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

 file name description C2H2_p.data components of the electric dipole moment as functions of time C2H2_ps.data power spectrum that is obtained by a time-frequency Fourier transformation of the electric dipole moment

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

Download zipped output files


Explanations of the files are described in:

Explanations of output files (C2H2 molecule under a pulsed electric field)


## Crystalline silicon (periodic solids)

### Exercise-4: 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. Since the ground state calculation costs much less computational time than the time evolution calculation, both calculations are successively executed. After finishing the ground state calculation, 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 are used:

 file name description Si_gs_rt_response.inp input file that contain namelist variables and their values. Si_rps.dat pseodupotential file of silicon

You may download the above 2 files (zipped file) from:

Download zipped input and pseudopotential files


In the input file Si_gs_rt_response.inp, namelists variables are specified. Most of them are mandatory to execute the calculation. We present explanations of the namelist variables that appear in the input file in:

Explanations of input files (dielectric function of crystalline silicon)


This will help you to prepare the input file for other systems that you want to calculate. A complete list of the namelist variables that can be used in the input file can be found in the downloaded file SALMON/manual/input_variables.md.

#### Output files

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

 file name description Si_gs_info.data information of ground state calculation Si_eigen.data energy eigenvalues of orbitals Si_k.data information on k-points Si_rt.data electric field, vector potential, and current as functions of time Si_force.data force acting on atoms Si_lr.data Fourier spectra of the dielectric functions Si_gs_rt_response.out standard output file

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

Download zipped output files


Explanations of the output files are described in:

Explanation of output fiels (dielectric function of crystalline silicon)


### Exercise-5: 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. Since the ground state calculation costs much less computational time than the time evolution calculation, both calculations are successively executed. After finishing the ground state 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, and carrier envelope phase are specified in the input file.

#### Input files

To run the code, following files are used:

 file name description Si_gs_rt_pulse.inp input file that contain namelist variables and their values. Si_rps.dat pseodupotential file for Carbon

You may download the above 2 files (zipped file) from:

Download zipped input and pseudopotential files


In the input file Si_gs_rt_pulse.inp, namelists variables are specified. Most of them are mandatory to execute the calculation. We present explanations of the namelist variables that appear in the input file in:

Explanation of input files (crystalline silicon under a pulsed electric field)


This will help you to prepare the input file for other systems that you want to calculate. A complete list of the namelist variables that can be used in the input file can be found in the downloaded file SALMON/manual/input_variables.md.

#### Output files

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

 file name description Si_gs_info.data information of ground state calculation Si_eigen.data energy eigenvalues of orbitals Si_k.data information on k-points Si_rt.data electric field, vector potential, and current as functions of time Si_force.data force acting on atoms Si_lr.data Fourier transformations of various quantities Si_gs_rt_pulse.out standard output file

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

Download zipped output files


Explanations of the output files are described in:

Explanation of output files (crystalline silicon under a pulsed electric field)


## Maxwell + TDDFT multiscale simulation

### Exercise-6: 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 ?? nm thickness, and an irradiation of a few-cycle, linearly polarized pulsed light normally on the thin film. First, to set up initial orbitals, the ground state calculation is carried out. 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. The calculation ends when the reflected and transmitted pulses reach the vacuum region.

#### Input files

To run the code, following files are used:

 file name description Si_gs_rt_multiscale.inp input file that contain namelist variables and their values. Si_rps.dat pseodupotential file for silicon

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

Download zipped input and pseudopotential files


In the input file Si_gs_rt_multiscale.inp, namelists variables are specified. Most of them are mandatory to execute the calculation. We present explanations of the namelist variables that appear in the input file in:

Explanation of input files (pulsed-light propagation through a silicon thin film)


This will help you to prepare the input file for other systems that you want to calculate. A complete list of the namelist variables that can be used in the input file can be found in the downloaded file SALMON/manual/input_variables.md.

#### Output files

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

 file name description Si_gs_info.data results of the ground state as well as input parameters Si_eigen.data orbital energies in the ground state calculation Si_k.data information on k-points Si_Ac_xxxxxx.data various quantities at a time as functions of macroscopic position Si_Ac_M_xxxxxx.data various quantities at a macroscopic point as functions of time Si_Ac_vac.data vector potential at vacuum position adjacent to the medium Si_gs_rt_multiscale.out standard output file

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

Download zipped output files


Explanations of the output files are described in:

Explanation of output files (pulsed-light propagation through a silicon thin film)