SALMON document
Release v.1.1.0

SALMON developers

Sep 29, 2018

CONTENTS

1

Introduction
1.1 About SALMON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 SALMON features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 License . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 SALMON at Github . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 List of developers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Acknowledgements for SALMON developments . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3
3
3
4
4
4
5

2

Install and Run
2.1 Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Download . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Build and Install . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Files necessary to run SALMON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Run SALMON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Troubleshooting of the Installation Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7
7
7
8
9
10
11
12

3

Inputs
3.1 &units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 &calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 &control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 &functional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 &system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 &pseudo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 &atomic_coor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 &atomic_red_coor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 &rgrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.10 &kgrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.11 &scf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 &hartree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.13 &tgrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.14 &propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15 &emfield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.16 &analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.17 &multiscale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.18 &parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15
15
15
15
16
16
17
18
18
19
19
19
20
20
20
21
22
23
23

4

Exercises
4.1 Getting started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 C2H2 (isolated molecules) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25
25
26

i

4.3
4.4

Crystalline silicon (periodic solids) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Maxwell + TDDFT multiscale simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Bibliography

ii

41
64
75

SALMON document, Release v.1.1.0

Sep 29, 2018
SALMON is an open-source software based on first-principles time-dependent density functional theory to describe
optical responses and electron dynamics in matters induced by light electromagnetic fields.

CONTENTS

1SALMON document, Release v.1.1.0

2

CONTENTSCHAPTERONEINTRODUCTION

1.1 About SALMONSALMON is an open-source computer program for ab-initio quantum-mechanical calculations of electron dynamics atthe nanoscale that takes place in various situations of light-matter interactions. It is based on time-dependent density
functional theory, solving time-dependent Kohn-Sham equation in real time and real space with norm-conserving
pseudopotentials.
SALMON was born by unifying two scientific programs: ARTED, developed by Univ. Tsukuba group, that describes
electron dynamics in crystalline solids, and GCEED, developed by Institute for Molecular Science group, that describes electron dynamics in molecules and nanostructures. It can thus describe electron dynamics in both isolated andperiodic systems. It can also describe coupled dynamics of electrons and light-wave electromagnetic fields.
To run the program, SALMON requires MPI Fortran/C compiller with LAPACK libraries. SALMON has been tested
and optimized to run in a number of platforms, including Linux PC Cluster with x86-64 CPU, Fujitsu FX100 supercomputer system, K-computer, and supercomputer system with Intel Xeon Phi (Knights Landing).

1.2 SALMON features
SALMON describes electron dynamics in both isolated (molecules and nanostructures) and periodic (crystalline
solids) systems. SALMON first carries out ground-state calculations in the density functional theory to prepare initialconfigurations. SALMON then calculates electron dynamics induced by applied electric field. Employing a weak
impulsive external field, SALMON can be used to calculate linear response properties such as a polarizability ofmolecules and a dielectric function of crystalline solids. Using pulsed electric fields, SALMON describes electron
dynamics in matters induced by intense and ultrashort laser pulses.
• Ground state calculations– Kohn-Sham orbitals and energies– density of states– projected density of states– electron localization function• Optical properties– Oscillator strength distribution (absorption spectrum)– dielectric function• Light-induced electron dynamics– time evolution of Kohn-Sham orbitals

3

SALMON document, Release v.1.1.0– density, current– excitation energy– number density of excited carriers• Simultaneous description of electron dynamics and light pulse propagation– light pulse propagation as well as time evolution of Kohn-Sham orbitals– energy transfer from pulsed light to electrons

1.3 License
SALMON is available under Apache License version 2.0.
Copyright 2017 SALMON developers
Licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except incompliance with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
express or implied. See the License for the specific language governing permissions and limitations under
the License.

1.4 SALMON at Github
SALMON is developed at GitHub.com

1.5 List of developers(Alphabetic order)• Isabella Floss (TU Wien, Austria)• Yuta Hirokawa (University of Tsukuba, Japan)• Kenji Iida (Institute for Molecular Science, Japan)• Kazuya Ishimura (Institute for Molecular Science, Japan)• Kyung-Min Lee (Max Planck Institute for the Structure and Dynamics of Matter, Germany)• Katsuyuki Nobusada (Institute for Molecular Science, Japan)• Masashi Noda (University of Tsukuba, Japan)• Tomohito Otobe (National Institutes for Quantum and Radiological Science and Technology, Japan)• Shunsuke Sato (Max Planck Institute for the Structure and Dynamics of Matter, Germany)• Yasushi Shinohara (University of Tokyo, Japan)• Takashi Takeuchi (University of Tsukuba, Japan)• Xiao-Min Tong (University of Tsukuba, Japan)

4

Chapter 1. Introduction

SALMON document, Release v.1.1.0• Mitsuharu Uemoto (University of Tsukuba, Japan)• Kazuhiro Yabana (University of Tsukuba, Japan)• Atsushi Yamada (University of Tsukuba, Japan)• Shunsuke Yamada (University of Tsukuba, Japan)• Maiku Yamaguchi (University of Tokyo, Japan)

1.6 Acknowledgements for SALMON developments
SALMON has been developed by the SALMON developers under supports by Center for Computational Sciences,
University of Tsukuba, and Institute for Molecular Science. SALMON has been supported by Strategic Basic Research Programs, CREST, Japan Science and Technology Agency, under the Grand Number JPMJCR16N5, in the
research area of Advanced core technology for creation and practical utilization of innovative properties and functions
based upon optics and photonics. SALMON has been also supported by Ministry of Education, Culture, Sports andTechnology of Japan as a social and scientific priority issue (Creation of new functional devices and high-performancematerials to support next-generation industries: CDMSI) to be tackled by using post-K computer.

1.6. Acknowledgements for SALMON developments

5

SALMON document, Release v.1.1.0

6

Chapter 1. Introduction

CHAPTERTWOINSTALL AND RUN

2.1 Prerequisites
In this guide, it is assumed that readers have a basic knowledge of Unix and its command line operations. For the
installation of SALMON, following packages are required.
• Fortran90/C compiler. SALMON assumes users have one of the following compilers:– GCC (Gnu Compiler Collection)– Intel Fortran/C Compiler– Fujitsu Compiler (at FX100 / K-Computer)• One of the following library packages for linear algebra:– BLAS/LAPACK– Intel Math Kernel Library (MKL)– Fujitsu Scientific Subroutine Library 2 (SSL-II)• Build tools:– CMakeIf you use other compilers, you may need to change build scripts (CMake). See Additional options in configure.py
script. If no numerical library is installed on your computer system, you may need to install BLAS/LAPACK by
yourself. See Troubleshooting of the Installation Process.
For the installation of SALMON, we adopt the CMake tools as the first option. If there were any problems to use
CMake tools in your environment, you may use the GNU make tools. See Troubleshooting of the Installation Process.

2.2 Download
The newest version of SALMON can be downloaded from download page. To extract files from the downloaded filesalmon-<VERSION>.tar.gz, type the following command in the command-line:$ tar -zxvf ./salmon-<VERSION>.tar.gz

After the extraction, the following directories will be created:
SALMON|- src|- example

Source codes
Samples(continues on next page)

7

SALMON document, Release v.1.1.0(continued from previous page)|- cmakefiles
CMake related files|- gnumakefiles GNU Makefiles for building

2.3 Build and Install
To compile SALMON to create executable the binary files, we adopt to use CMake tools as the first option. In case you
fail to build SALMON using CMake in your environment, we may use Gnu Make. See Build using GNU Makefile.

2.3.1 Checking CMake availability
First, examine whether CMake is usable in your environment or not. Type the following in Unix command-line:$ cmake --version

If CMake is not installed in your system, an error message such as cmake: command not found will appear.
If CMake is installed on your system, the version number will be shown. To build SALMON, CMake of version 3.0.2
or later is required. If you confirm that CMake of version 3.0.2 or later is installed in your system, proceed to Build
using CMake. However, we realize that old versions of CMake are installed in many systems. If CMake is not installed
or CMake of older versions is installed in your system, you need to install the new version by yourself. It is a simple
procedure and explained below.

2.3.2 Installation of CMake
CMake is a cross-platform build tool. The simplest way to make CMake usable in your environment is to get
the binary distribution of CMake from the download page. (The file name of the binary distribution will be
cmake-<VERSION>-<PLATFORM>.tar.gz). In standard Unix environment, a file for the platform of Linuxx86_64 will be appropriate.
To download the file, proceed as follows: We assume that you are in the directory that you extracted files from thedownloaded file of SALMON, and that you will use the version 3.8.2. First get the URL of the download link fromyour browser, and use wget command in your Unix command-line:$ wget https://cmake.org/files/v3.8/cmake-3.8.2-Linux-x86_64.tar.gz

Next, unpack the archive by:$ tar -zxvf cmake-3.8.2-Linux-x86_64.tar.gz

and you will have the binary make-3.8.2-Linux-x86_64/bin/cmake in your directory.
To make the cmake command usable in your command-line, you need to modify the environment variable $PATH
so that the executable of CMake are settled inside the directory specified in your $PATH. If you use the bash shell,
you need to modify the file ~/.bashrc that specifies the $PATH variable. It can be done by typing the following
command in your login directory:$ export PATH=<SALMON_INSTALLATION_DIRECTORY>/cmake-3.8.2-Linux-x86_64/bin:$PATH

and then reload the configuration by typing:$ source ~/.bashrc

8

Chapter 2. Install and Run

SALMON document, Release v.1.1.0

2.3.3 Build using CMake
Confirming that CMake of version 3.0.2 or later can be usable in your environment, proceed the following steps. We
assume that you are in the directory SALMON.
1. Create a new temporary directory build and move to the directory:$ mkdir build$ cd build

2. Execute the python script ‘’configure.py” and then make:$ python ../configure.py --arch=ARCHITECTURE --prefix=../$ make$ make install

In executing the python script, you need to specify ARCHITECTURE that indicates the architecture of the CPU in yourcomputer system such as intel-avx. The options of the ARCHITECUTRE are as follows:archintel-knl
intel-knc
intel-avx
intel-avx2
intel-avx512
fujitsu-fx100
fujitsu-k

DetailIntel Knights LandingIntel Knights Corner
Intel Processer (Ivy-, Sandy-Bridge)
Intel Processer (Haswell, Broadwell ..)Intel Processer (Skylake-SP)
FX100 Supercomputer
Fujitsu FX100 / K-computer

CompilerIntel Compiler
Intel Compiler
Intel Compiler
Intel Compiler
Intel Compiler
Fujitsu Compiler
Fujitsu Compiler

Numerical LibraryIntel MKLIntel MKLIntel MKLIntel MKLIntel MKL
SSL-II
SSL-II

If the build is successful, you will get a file salmon.cpu at the directory salmon/bin. If you specify manycore architechtures, intel-knl or intel-knc, you find a file salmon.mic or both files salmon.cpu andsalmon.mic.

2.4 Files necessary to run SALMON
To run SALMON, at least two kinds of files are required for any calculations. One is an input file with the filename
extension *.inp that should be read from the standard input stdin. This file should be prepared in the Fortran90
namelist format. Pseudopotential files of relevant elements are also required. Depending on your purpose, some otherfiles may also be necessary. For example, coordinates of atomic positions of the target material may be either written
in the input file or prepared as a separate file.

2.4.1 Pseudopotentials
SALMON utilizes norm-conserving pseudpotentials. You may find pseudopotentials of some elements in the samples
prepared in exercises-calc. In SALMON, several formats of pseudopotentials may be usable. Pseudopotentials
with an extension .fhi can be obtained from the website listed below. (This is a part of previous atomic data files for
the ABINIT code.)
Pseudopotential
Pseudopotentials for the ABINIT
code

Websitehttps://www.abinit.org/sites/default/files/PrevAtomicData/psp-links/
psp-links/lda_fhi

Filenames of the pseudopotentials should be written in the input file.
2.4. Files necessary to run SALMON

9SALMON document, Release v.1.1.0

2.4.2 input file
Input files are composed of several blocks of namelists:&namelist1
variable1 = int_value
variable2 = 'char_value'/&namelist2
variable1 = real8_value
variable2 = int_value1, int_value2, int_value3/

A block of namelists starts with &namelist line and ends with / line. The blocks may appear in any order.
Between two lines of &namelist and /, descriptions of variables and their values appear. Note that many variables
have their default values so that it is not necessary to give values for all variables. Descriptions of the variables may
appear at any position if they are between &namelist and /.
SALMON describes electron dynamics in systems with both isolated and periodic boundary conditions. The boundary
condition is specified by the variable iperiodic in the namelist &system.
Calculations are usually achieved in two steps; first, the ground state calculation is carried out and then electron dynamics calculations in real time is carried out. A choice of the calculation mode is specified by the variable calc_mode in
the namelist &calculation. For isolated systems, the ground state and the electron dynamics calculations should
be carried out as two separate executions. First the ground state calculation is carried out specifying calc_mode ='GS'. Then the real-time electron dynamics calculation is carried out specifying calc_mode = 'RT'. For periodic
systems, two calculations should be carried out as a single execution specifying calc_mode = 'GS_RT'.
In exercises-calc, we prepare six exercises that cover typical calculations feasible by SALMON. We prepare
explanations of the input files of the exercises that will help to prepare input files of your own interests.
There are more than 20 groups of namelists. A complete list of namelist variables is given in the file
SALMON/manual/input_variables.md. Namelist variables that are used in our exercises are explained at
input-variables.

2.5 Run SALMON
Before running SALMON, the following preparations are required as described above: The executable file ofsalmon.cpu and salmon.mic (if your system is the many-core machine) should be built from the source fileof SALMON. An input file inputfile.inp and pseudopotential files should also be prepared.
The execution of the calculation can be done as follows: In single process environment, type the following command:$ salmon.cpu < inputfile.inp > fileout.out

In multiprocess environment in which the command to execute parallel calculations using MPI is mpiexec, type thefollowing command:$ mpiexec -n NPROC salmon.cpu < inputfile.inp > fileout.out

where NPROC is the number of MPI processes that you will use. In many-core processor (e.g. intel-knl) environment,
the execution command is:$ mpiexec.hydra -n NPROC salmon.mic < inputfile.inp > fileout.out

10

Chapter 2. Install and Run

SALMON document, Release v.1.1.0

The execution command and the job submission procedure depends much on local environment. We summarize
general conditions to execute SALMON:• SALMON runs in both single-process and multi-process environments using MPI.
• executable files are prepared as /salmon/bin/salmon.cpu and/or /salmon/bin/salmon.mic in thestandard build procedure.
• to start calculations, inputfile.inp should be read through stdin.

2.6 Appendix
2.6.1 Additional options in configure.py script
Manual specifications of compiler and environment variables
In executing configure.py, you may manually specify compiler and environment variables instead of specifying
the architecture, for example:$ python ../configure.py FC=mpiifort CC=mpiicc FFLAGS="-xAVX" CFLAGS="-restrict -xAVX"The major options of configure.py are as follows:
Commandline switch-a ARCH, –arch=ARCH–enable-mpi, –disable-mpi–enable-scalapack, –disable-scalapack–enable-libxc, –with-libxc
FC, FFLAGS

DetailTarget architecture
enable/disable MPI parallelization
enable/disable computations with ScaLAPACK library
see To use Libxc
User-defined Fortran Compiler, and the compiler options

To use Libxc
In SALMON, you may use Libxc functional library. To use the Libxc library, some adittional procedures are necessary.
First you need to download the source files in your system as follows:$ wget http://www.tddft.org/programs/octopus/down.php?file=libxc/4.2.1/libxc-4.2.1.
,→tar.gz$ tar -zxvf libxc-4.2.1.tar.gz

Then, enter the libxc source directory and make the library as follows:$ ./configure --prefix=INSTALL/PATH/OF/LIBXC$ make && make install

Finally, enter the SALMON directory and execute configure.py script specifying the Libxc directory:$ configure.py --arch=ARCHITECTURE --prefix=PREFIX --with-libxc=INSTALL/PATH/OF/LIBXC$ make && make install

Build for single process calculations
If you use a single processor machine, specify --disable-mpi in executing the python script:

2.6. Appendix

11

SALMON document, Release v.1.1.0$ python ../configure.py --arch=<ARCHITECTURE> --disable-mpi

Build in GCC/GFortran environemnt
If you use GCC/GFortran compiler, specify the following flags in executing the python script:$ python ../configure.py FC=gfortran CC=gcc FFLAG=-O3 CFLAG=-O3

2.6.2 Build using GNU Makefile
If CMake build fails in your environment, we recommend you to try to use Gnu Make for the build process. First,
enter the directory makefiles:$ cd SALMON/makefiles

In the directory, Makefile files are prepared for several architectures:• fujitsu• gnu• gnu-without-mpi• intel• intel-avx• intel-avx2• intel-knc• intel-knl• intel-without-mpi
Makefile files with *-without-mpi indicate that they are for single processor environment. Choose Makefile
appropriate for your environment, and execute the make command:$ make -f Makefile.PLATFORM

If the make proceeds successful, a binary file is created in the directory SALMON/bin/.

2.7 Troubleshooting of the Installation Process
2.7.1 Installation of CMake
The CMake is a cross-platform build tool. In order to build the SALMON from the source code, the CMake of version
3.0.2 or later is required. You may install it following one of the three instructions below.
Installation of pre-compiled binary
You can get the binary distribution from the download page. First, move to the directory that you installed SALMON,

12

Chapter 2. Install and Run

SALMON document, Release v.1.1.0

cd <SALMON_INSTALLATION_DIRECTORY>

and download the binary distribution (cmake-<VERSION>-<PLATFORM>.tar.gz) appropriate for your platform. You can do it by copy the URL of download link from the browser, and use wget command:
wget https://cmake.org/files/v3.8/cmake-3.8.2-Linux-x86_64.tar.gz

In this document, we will use version 3.8.2 as an example. You can unpack the downloaded archivetar -zxvf cmake-3.8.2-Linux-x86_64.tar.gz

and you will have the binary make-3.8.2-Linux-x86_64/bin/cmake.
Next, to utilize the cmake command, it is required that the executable are settled inside the directory specified in your
$PATH. If you use the bash shell, edit ~/.bashrc and append the line:
export PATH=<SALMON_INSTALLATION_DIRECTORY>/cmake-3.8.2-Linux-x86_64/bin:$PATH

and reload the configuration:
source ~/.bashrc

Installation by package manager
If your system has a built-in package manager, you may conveniently install the CMake tools as below:
Debian/Ubuntu Linuxsudo apt-get install cmake

Fedora Linux/CentOS
sudo yum install cmake

openSUSE Linuxsudo zypper install cmake

Installation from source code
You can get the source code distribution from the download page. In this time, we will use the cmake version 3.8.2 asan example. Download the archive by wget comamnd and unpack it as below:
wget https://cmake.org/files/v3.8/cmake-3.8.2.tar.gz
tar -zxvf cmake-3.8.2.tar.gz

And, move to the unpacked directory and build.
cd cmake-3.8.2./configure --prefix=INSTALLATION_DIRECTORY
make
make install

2.7. Troubleshooting of the Installation Process

13

SALMON document, Release v.1.1.0(replace INSTALLATION_DIRECTORY to your installation directory.)
Next, to utilize the cmake command, it is required that the executable are settled inside the directory specified in your
$PATH. If you use the bash shell, edit ~/.bashrc and append the line:
export PATH=INSTALLATION_DIRECTORY/bin:$PATH

and reload the configuration:
source ~/.bashrc

2.7.2 Installation of BLAS/LAPACK

14

Chapter 2. Install and Run

CHAPTER

THREE

INPUTSWe 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’.

3.1 &units
Mandatory: none
&unitsunit_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.

3.2 &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 byiperiodic = 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'.

3.3 &control
Mandatory: none
15

SALMON document, Release v.1.1.0&controlsysname = 'C2H2'/‘C2H2’ defined by sysname = 'C2H2' will be used in the filenames of output files. If you do not specify it, thefile name will start with ‘default’.

3.4 &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 atpresent.
For periodic systems (specified by iperiodic = 3 in &system), the following functionals may be available inaddition 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 theoriginal 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/) havebeen usable in SALMON. At present, usable functionals are limited to LDA and GGA. For periodic systems, metaGGA 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.

3.5 &system
Mandatory: iperiodic, al, nstate, nelem, natom
For an isolated molecule (Tutorial-1, 2, 3):16

Chapter 3. Inputs

SALMON document, Release v.1.1.0&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 ofvalence electrons in the system. Since the present code assumes that the system is spin saturated, nstate should beequal to or larger than nelec/2. nelem = 2 and natom = 4 indicate the number of elements and the number ofatoms 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 thenumber 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.

3.6 &pseudo
Mandatory: pseudo_file, izatom
For C2H2 molecule:3.6. &pseudo

17

SALMON document, Release v.1.1.0&pseudoizatom(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 theelement #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:&pseudoizatom(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 thepseudopotential that will be treated as local.

3.7 &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.

3.8 &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(continues on next page)

18

Chapter 3. Inputs

SALMON document, Release v.1.1.0(continued from previous page)'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.

3.9 &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).
&rgriddl = 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).
&rgridnum_rgrid = 12,12,12/

3.10 &kgrid
Mandatory: none
This namelist provides grid spacing of k-space for periodic systems.
&kgridnum_kgrid = 4,4,4/

3.11 &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/

3.9. &rgrid

19

SALMON document, Release v.1.1.0

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,

3.12 &hartree
Mandatory: none
&hartreemeo = 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.

3.13 &tgrid
Mandatory: dt, Nt&tgriddt=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.

3.14 &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).

20

Chapter 3. Inputs

SALMON document, Release v.1.1.0&propagation
propagator='middlepoint'/

propagation='middlepoint' indicates that Hamiltonian at midpoint of two-times is used.
The default is middlepoint.

3.15 &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.

3.15.1 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'.
&emfieldtrans_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.

3.15.2 Pulsed electric field calculations
A Pulsed electric field of finite time duration is applied. For this case, as_shape1 should be specified. It indicatesthe 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/

3.15. &emfield

21

SALMON document, Release v.1.1.0

ae_shape1 = 'Ecos2' specifies the envelope of the pulsed electric field, ‘Ecos2’ for the cos^2 envelope for theelectric 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 notvanish. 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 (or0.25) if one employs ‘Ecos2’ pulse shape, since otherwise the time integral of the electric field does not vanish. Thereis 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.

3.16 &analysis
Mandatory: none
The following namelists specify whether the output files are created or not after the calculation. In the ground statecalculation 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(continues on next page)

22

Chapter 3. Inputs

SALMON document, Release v.1.1.0(continued from previous page)

de=0.001/

nenergy=1000 specifies the number of energy steps, and de=0.001 specifies the energy spacing in the timefrequency Fourier transformation.

3.17 &multiscaleThis namelist specifies information necessary for Maxwell - TDDFT multiscale calculations.
&multiscale
fdtddim = '1D'
twod_shape = 'periodic'
nx_m = 4ny_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 thematerial 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.

3.18 &parallel
When you execute a job with MPI parallelization, you are not required to specify any parameters that describe theassignment of the parallelization; the assignment is carried out automatically. You may also specify the parameters
explicitly as below.
Mandatory: none&parallel
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 theelectron density in three Cartesian directions. The default values are (0/0/0) (automatic parallelization).
The following conditions must be satisfied.
3.17. &multiscale

23

SALMON document, Release v.1.1.0• The total number of processors must be equal to both nproc_ob * nproc_domain(1)andalso
nproc_domain_s(1) ** nproc_domain(2) * nproc_domain(3)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.

24

Chapter 3. Inputs

CHAPTER

FOUR

EXERCISES

4.1 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/LinuxOS. 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 theground state solution first. This is illustrated in Exercise-1. After finishing the ground state calculation, two exercisesof electron dynamics calculations are prepared. Exercise-2 illustrates the calculation of linear optical responses in realtime, 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 timeconsuming than the ground state calculation, we recommend to run the ground and the time evolution calculations asa 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 ofelectron 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.

25

SALMON document, Release v.1.1.0

4.2 C2H2 (isolated molecules)
4.2.1 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 thegeometry 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
C2H2_gs.inp
C_rps.dat
H_rps.dat

description
input file that contains namelist variables and their values
pseodupotential file for carbon atom
pseudopotential file for hydrogen atom

You may download the above 3 files (zipped file) from:https://salmon-tddft.jp/webmanual/v_1_1_0/exercise_zip_files/C2H2_gs_input.zip(zipped input and pseudopotential files)

In the input file C2H2_gs.inp, namelists variables are specified. Most of them are mandatory to execute the groundstate calculation. 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.
&unitsunit_system='A_eV_fs'/&calculation
calc_mode = 'GS'/
&controlsysname = 'C2H2'/&system
iperiodic = 0
al = 16d0, 16d0, 16d0
nstate = 5
nelem = 2
natom = 4
nelec = 10/
&pseudoizatom(1)=6
izatom(2)=1
pseudo_file(1)='C_rps.dat'
pseudo_file(2)='H_rps.dat'
lmax_ps(1)=1(continues on next page)

26

Chapter 4. Exercises

SALMON document, Release v.1.1.0(continued from previous page)lmax_ps(2)=0
lloc_ps(1)=1
lloc_ps(2)=0/&rgriddl = 0.25d0, 0.25d0, 0.25d0/&scf
ncg = 4
nscf = 1000
convergence = 'norm_rho_dng'
threshold_norm_rho = 1.d-15/&analysis
out_psi = 'y'out_dos = 'y'out_pdos = 'y'out_dns = 'y'out_elf = 'y'/&atomic_coor'C'
0.000000
0.000000
0.599672'H'
0.000000
0.000000
1.662257'C'
0.000000
0.000000-0.599672'H'
0.000000
0.000000-1.662257
/

1
2
1
2

We present their explanations below:
Required and recommened variables&unitsMandatory: none
&unitsunit_system='A_eV_fs'/

This namelist specifies the unit system to be used in the input file. If you do not specify it, atomic unit will be used.
See &units in Inputs for detail.
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.
&calculation
Mandatory: calc_mode&calculation
calc_mode = 'GS'/

This indicates that the ground state (GS) calculation is carried out in the present job. See &calculation in Inputs fordetail.
&control
Mandatory: none
4.2. C2H2 (isolated molecules)

27

SALMON document, Release v.1.1.0&controlsysname = 'C2H2'/‘C2H2’ defined by sysname = 'C2H2' will be used in the filenames of output files.
&system
Mandatory: iperiodic, al, nstate, nelem, natom&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 ofvalence electrons in the system. Since the present code assumes that the system is spin saturated, nstate should beequal to or larger than nelec/2. nelem = 2 and natom = 4 indicate the number of elements and the number ofatoms in the system, respectively. See &system in Inputs for more information.
&pseudoMandatory: pseudo_file, izatom&pseudoizatom(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 theelement #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.
&rgridMandatory: dl or num_rgrid&rgriddl = 0.25d0, 0.25d0, 0.25d0/

dl = 0.25d0, 0.25d0, 0.25d0 specifies the grid spacings in three Cartesian directions. See &rgrid in Inputs
for more information.
&scf
Mandatory: nscf
28

Chapter 4. Exercises

SALMON document, Release v.1.1.0&scf
ncg = 4
nscf = 1000
convergence = 'norm_rho_dng'
threshold_norm_rho = 1.d-15/

ncg is the number of CG iterations in solving the Khon-Sham equation. nscf 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 forthe convergence check. If the value of norm_rho_dng is specified, the convergence is examined by the squared
difference of the electron density,&analysis
The following namelists specify whether the output files are created or not after the calculation.
&analysis
out_psi = 'y'out_dos = 'y'out_pdos = 'y'out_dns = 'y'out_elf = 'y'/&atomic_coor
Mandatory: atomic_coor or atomic_red_coor (it may be provided as a separate file)&atomic_coor'C'
0.000000'H'
0.000000'C'
0.000000'H'
0.000000/

0.000000
0.000000
0.000000
0.000000

0.599672
1.662257-0.599672-1.6622571212

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.
Output files
After the calculation, following output files are created in the directory that you run the code,
file name
C2H2_info.data
dns.cube
elf.cube
psi1.cube, psi2.cube, . . .
dos.data
pdos1.data, pdos2.data, . . .
C2H2_gs.bin

description
information on ground state solution
a cube file for electron density
electron localization function (ELF)
electron orbitals
density of states
projected density of statesbinary 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:https://salmon-tddft.jp/webmanual/v_1_1_0/exercise_zip_files/C2H2_gs_output.zip

4.2. C2H2 (isolated molecules)

29

SALMON document, Release v.1.1.0(zipped output files)

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

Explanations of theC2H2_info.data
Calculated orbital and total energies as well as parameters specified in the input file are shown in this file.
Total number of iteration = 49
Number of states = 5
Number of electrons = 5
Total energy (eV) = -339.7041368688747
1-particle energies (eV)1-18.4492
2-13.98843-12.3935
5-7.3310Size of the box (A) =15.99999363
15.99999363
15.99999363
Grid spacing (A)=0.24999990
0.24999990
0.24999990
Number of atoms =4iZatom( 1)=6iZatom( 2)=1
Ref. and max angular momentum and pseudo-core radius of PP (A)( 1)Ref, Max, Rps =
1
1
0.800
( 2)
Ref, Max, Rps =
0
0
0.800

4

-7.3310dns.cube
A cube file for electron density. For isolated systems (specified by iperiodic = 0 in &system), atomic unit isadopted in all cube files.
elf.cube
A cube file for electron localization function (ELF).
psi1.cube, psi2.cube, . . .
Cube files for electron orbitals. The number in the filename indicates the index of the orbital..
dos.data
A file for density of states. The units used in this file are affected by the input parameter, unit_energy in &unit.
# Density of States# Energy[eV] DOS[1/eV]#-----------------------21.22853
0.00000000-21.20073
0.00000000-21.17294
0.00000000-21.14514
0.00000000-21.11735
0.00000000...
-7.38656-7.35876-7.33097-7.30317-7.27538

13.67306519
15.35302960
15.95769122
15.35301925
13.67304675...
(continues on next page)

30

Chapter 4. Exercises

SALMON document, Release v.1.1.0(continued from previous page)-4.66264-4.63484-4.60705-4.57925-4.55146

0.00000000
0.00000000
0.00000000
0.00000000
0.00000000

pdos1.data, pdos2.data, . . .
Files for projected density of states. The units used in this file are affected by the input parameter, unit_energy in&unit. The number in the filename indicates the order of atoms specified in &atomic_coor.
# Projected Density of States# Energy[eV] PDOS(l=0)[1/eV] PDOS(l=1)[1/eV]#-----------------------21.22853
0.00000000
0.00000000-21.20073
0.00000000
0.00000000-21.17294
0.00000000
0.00000000-21.14514
0.00000000
0.00000000-21.11735
0.00000000
0.00000000...
-7.38656-7.35876-7.33097-7.30317-7.27538

0.00000000
0.00000000
0.00000000
0.00000000
0.00000000

18.33035096
20.58254071
21.39316068
20.58252684
18.33032625

0.00000000
0.00000000
0.00000000
0.00000000
0.00000000

0.00000000
0.00000000
0.00000000
0.00000000
0.00000000...
-4.66264-4.63484-4.60705-4.57925-4.55146

We show several image that are created from the output files.
• Highest occupied molecular orbital (HOMO)
The output files psi1.cube, psi2.cube, . . . are used to create the image.

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

4.2. C2H2 (isolated molecules)

31

SALMON document, Release v.1.1.0• Electron localization function
The output files elf.cube, . . . are used to create the image.

4.2.2 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 distributionof the molecule. This exercise should be carried out after finishing the ground state calculation that was explainedin 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 andthe 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 andpseudopotential files are also required. The pseudopotential files should be the same as those used in the ground statecalculation.
file name
C2H2_rt_response.inp
C_rps.dat
H_rps.dat
C2H2_gs.bin

description
input file that contains namelist variables and their values
pseodupotential file for carbon
pseudopotential file for hydrogenbinary file created in the ground state calculation

You may download the C2H2_rt_response.inp file (zipped file) from:https://salmon-tddft.jp/webmanual/v_1_1_0/exercise_zip_files/C2H2_rt_response_input.zip(zipped input file)In the input file C2H2_rt_response.inp, namelists variables are specified. Most of them are mandatory to executethe 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 namelist variables that can be used in the input file can be found in the downloaded file
SALMON/manual/input_variables.md.

32

Chapter 4. Exercises

SALMON document, Release v.1.1.0&unitsunit_system='A_eV_fs'/&calculation
calc_mode='RT'/&controlsysname = 'C2H2'/&system
iperiodic = 0
al = 16d0, 16d0, 16d0
nstate = 5
nelem = 2
natom = 4
nelec = 10/
&pseudoizatom(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/&tgriddt=1.25d-3
nt=5000/&emfield
ae_shape1 = 'impulse'
epdir_re1 = 0.d0,0.d0,1.d0/&atomic_coor'C'
0.000000
0.000000'H'
0.000000
0.000000'C'
0.000000
0.000000'H'
0.000000
0.000000/

0.599672
1.662257-0.599672-1.662257

1
2
1
2

We present their explanations below:
Required and recommended variables&unitsMandatory: none
&unitsunit_system='A_eV_fs'/

This namelist specifies the unit system to be used in the input file. If you do not specify it, atomic unit will be used.
See &units in Inputs for detail.
&calculation
Mandatory: calc_mode
4.2. C2H2 (isolated molecules)

33

SALMON document, Release v.1.1.0&calculation
calc_mode = 'RT'/This indicates that the real time (RT) calculation is carried out in the present job. See &calculation in Inputs for detail.
&control
Mandatory: none&controlsysname = 'C2H2'/‘C2H2’ defined by sysname = 'C2H2' will be used in the filenames of output files.
&system
Mandatory: iperiodic, al, nstate, nelem, natom&system
iperiodic = 0
al = 16d0, 16d0, 16d0
nstate = 5
nelem = 2
natom = 4
nelec = 10/

These namelists and their values should be the same as those used in the ground state calculation. See &system in
Exercise-1.
&pseudoMandatory: pseudo_file, izatom&pseudoizatom(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/These namelists and their values should be the same as those used in the ground state calculation. See &pseudo in
Exercise-1.
&tgridMandatory: dt, Nt&tgriddt=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.
34

Chapter 4. Exercises

SALMON document, Release v.1.1.0&emfield
Mandatory: ae_shape1&emfield
ae_shape1 = 'impulse'
epdir_re1 = 0.d0,0.d0,1.d0/

ae_shape1 = 'impulse' indicates that a weak impulse is applied to all electrons at t=0 epdir_re1(3) specify a unit vector that indicates the direction of the impulse. See &emfield in Inputs for details.
&atomic_coor
Mandatory: atomic_coor or atomic_red_coor (it may be provided as a separate file)&atomic_coor'C'
0.000000'H'
0.000000'C'
0.000000'H'
0.000000/

0.000000
0.000000
0.000000
0.000000

0.599672
1.662257-0.599672-1.6622571212

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. They must be the same as those in the groundstate calculation.
Output files
After the calculation, following output files are created in the directory that you run the code,
file name
C2H2_lr.data
C2H2_p.data

description
polarizability and oscillator strength distribution as functions of energy
components of dipole moment as functions of time

You may download the above files (zipped file) from:https://salmon-tddft.jp/webmanual/v_1_1_0/exercise_zip_files/C2H2_rt_response_output.zip(zipped output files)

Explanations of the output files are below:
C2H2-p.data
For time steps from 1 to nt,• 1 column: time• 2-4 columns: x,y,z components of the dipole moment• 5 column: total energy of the system# time[fs],dipoleMoment(x,y,z)[A],
0.12500E-02 0.20197641E-09 0.12143673E-09
0.25000E-02 -0.23127543E-09 -0.38283389E-09
0.37500E-02 -0.24342401E-08 -0.25180060E-08

Energy[eV]0.27407578E-02 -0.33969042E+03
0.54651286E-02 -0.33969040E+03
0.81587485E-02 -0.33969039E+03(continues on next page)

4.2. C2H2 (isolated molecules)

35

SALMON document, Release v.1.1.0(continued from previous page)

0.50000E-02 -0.63429482E-08 -0.62611945E-08
0.62500E-02 -0.11655064E-07 -0.11294666E-07

0.10810857E-01 -0.33969038E+03
0.13413805E-01 -0.33969038E+03...
0.62450E+01 -0.21648194E-05 -0.12589717E-05 -0.15217299E-02 -0.33969011E+03
0.62463E+01 -0.22246530E-05 -0.12919132E-05 -0.14111473E-02 -0.33969011E+03
0.62475E+01 -0.22836011E-05 -0.13244333E-05 -0.12951690E-02 -0.33969011E+03
0.62488E+01 -0.23416512E-05 -0.13565206E-05 -0.11738782E-02 -0.33969011E+03
0.62500E+01 -0.23987916E-05 -0.13881638E-05 -0.10473800E-02 -0.33969011E+03

C2H2_lr.data
For energy steps from 0 to nenergy,• 1 column: energy• 2-4 columns: x,y,z components of real part of the polarizability (time-frequency Fourier transformation of thedipole moment)• 5-7 columns: x,y,z components of imaginary part of the polarizability (time-frequency Fourier transformationof the dipole moment)• 8-10 columns: x,y,z components of power spectrum of the dipole moment# energy[eV], Re[alpha](x,y,z)[A**3], Im[alpha](x,y,z)[A**3], S(x,y,z)[1/eV]
0.00000E+00 0.90041681E-02 0.42900323E-02 0.47230167E+01 0.00000000E+00 0.
,→00000000E+00
0.00000000E+00 0.00000000E+00 0.00000000E+00 0.00000000E+00
0.10000E-01 0.89986618E-02 0.42874031E-02 0.47230192E+01 0.25932415E-03 0.
,→12379226E-03
0.18663776E-03 0.15045807E-07 0.71823406E-08 0.10828593E-07
0.20000E-01 0.89821593E-02 0.42795232E-02 0.47230267E+01 0.51808569E-03 0.
,→24731589E-03
0.37320742E-03 0.60117942E-07 0.28698192E-07 0.43306470E-07
0.30000E-01 0.89547084E-02 0.42664157E-02 0.47230393E+01 0.77572398E-03 0.
,→37030322E-03
0.55964230E-03 0.13502090E-06 0.64454205E-07 0.97410171E-07
0.40000E-01 0.89163894E-02 0.42481186E-02 0.47230569E+01 0.10316824E-02 0.
,→49248844E-03
0.74587862E-03 0.23942997E-06 0.11429535E-06 0.17310143E-06
0.50000E-01 0.88673137E-02 0.42246853E-02 0.47230796E+01 0.12854100E-02 0.
,→61360857E-03
0.93185683E-03 0.37289297E-06 0.17800571E-06 0.27032843E-06...
0.99601E+01 0.15674984E-03 0.37403402E-04 -0.44437601E+00 -0.10631864E-03 -0.
,→14544171E-03
0.27060202E+01 -0.61438595E-05 -0.84046729E-05 0.15637340E+00
0.99701E+01 0.15448331E-03 0.37400902E-04 -0.14920113E+00 -0.10649714E-03 -0.
,→14698080E-03
0.25947889E+01 -0.61603535E-05 -0.85021406E-05 0.15009620E+00
0.99801E+01 0.15224601E-03 0.37478652E-04 0.14911900E+00 -0.10665066E-03 -0.
,→14847068E-03
0.24965858E+01 -0.61754213E-05 -0.85969375E-05 0.14456047E+00
0.99901E+01 0.15003254E-03 0.37632621E-04 0.45012407E+00 -0.10678183E-03 -0.
,→14990965E-03
0.24115316E+01 -0.61892122E-05 -0.86889561E-05 0.13977547E+00
0.10000E+02 0.14783807E-03 0.37858911E-04 0.75334591E+00 -0.10689373E-03 -0.
,→15129625E-03
0.23397373E+01 -0.62019000E-05 -0.87781030E-05 0.13574993E+00

4.2.3 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 thetotal energy and the electric dipole moment of the system as functions of time are calculated. This tutorial should be

36

Chapter 4. Exercises

SALMON document, Release v.1.1.0

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
C2H2_rt_pulse.inp
C_rps.dat
H_rps.dat
C2H2_gs.bin

description
input file that contain namelist variables and their values.
pseodupotential file for Carbon
pseudopotential file for Hydrogenbinary file created in the ground state calculation

You may download the C2H2_rt_pulse.inp file (zipped file) from:https://salmon-tddft.jp/webmanual/v_1_1_0/exercise_zip_files/C2H2_rt_pulse_input.zip

In the input file C2H2_rt_pulse.inp, namelists variables are specified. Most of them are mandatory to execute thecalculation of electron dynamics induced by a pulsed electric field. This will help you to prepare the input file forother systems and other pulsed electric fields that you want to calculate. A complete list of the namelist variables thatcan be used in the input file can be found in the downloaded file SALMON/manual/input_variables.md.
&unitsunit_system='A_eV_fs'/&calculation
calc_mode='RT'/&controlsysname = 'C2H2'/&system
iperiodic = 0
al = 16d0, 16d0, 16d0
nstate = 5
nelem = 2
natom = 4
nelec = 10/
&pseudoizatom(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/&tgrid(continues on next page)

4.2. C2H2 (isolated molecules)

37

SALMON document, Release v.1.1.0(continued from previous page)

dt=1.25d-3
nt=4800/&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/&atomic_coor'C'
0.000000
0.000000'H'
0.000000
0.000000'C'
0.000000
0.000000'H'
0.000000
0.000000/

0.599672
1.662257-0.599672-1.662257

1
2
1
2

We present explanations of the namelist variables that appear in the input file below:
required and recommended variables&unitsMandatory: none
&unitsunit_system='A_eV_fs'/

This namelist specifies the unit system to be used in the input file. If you do not specify it, atomic unit will be used.
See &units in Inputs for detail.
&calculation
Mandatory: calc_mode&calculation
calc_mode = 'RT'/This indicates that the real time (RT) calculation is carried out in the present job. See &calculation in Inputs for detail.
&control
Mandatory: none&controlsysname = 'C2H2'/‘C2H2’ defined by sysname = 'C2H2' will be used in the filenames of output files.
&system
Mandatory: iperiodic, al, nstate, nelem, natom&system
iperiodic = 0
al = 16d0, 16d0, 16d0
(continues on next page)

38

Chapter 4. Exercises

SALMON document, Release v.1.1.0(continued from previous page)

nstate = 5
nelem = 2
natom = 4
nelec = 10/

These namelists and their values should be the same as those used in the ground state calculation. See &system in
Exercise-1.
&pseudoMandatory: pseudo_file, izatom&pseudoizatom(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/These namelists and their values should be the same as those used in the ground state calculation. See &pseudo in
Exercise-1.
&tgridMandatory: dt, Nt&tgriddt=1.25d-3
nt=4800/

dt=1.25d-3 specifies the time step of the time evolution calculation. Nt=4800 specifies the number of time steps
in the calculation.
&emfield
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' indicates that the envelope of the pulsed electric field has a cos^2 shape.
epdir_re1 = 0.d0,0.d0,1.d0 specifies the real part of the unit polarization vector of the pulsed electric field.
Using the real polarization vector, it describes a linearly polarized pulse.
laser_int_wcm2_1 = 1.d8 specifies the maximum intensity of the applied electric field in unit of W/cm^2.
omega1=9.26d0 specifies the average photon energy (frequency multiplied with hbar).

4.2. C2H2 (isolated molecules)

39

SALMON document, Release v.1.1.0

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 (or0.25) if one employs ‘Ecos2’ pulse shape, since otherwise the time integral of the electric field does not vanish.
See &emfield in Inputs for details.
&atomic_coor
Mandatory: atomic_coor or atomic_red_coor (it may be provided as a separate file)&atomic_coor'C'
0.000000'H'
0.000000'C'
0.000000'H'
0.000000/

0.000000
0.000000
0.000000
0.000000

0.599672
1.662257-0.599672-1.6622571212

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. They must be the same as those in the groundstate calculation.
Output files
After the calculation, following output files are created in the directory that you run the code,
file namedescription
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:https://salmon-tddft.jp/webmanual/v_1_1_0/exercise_zip_files/C2H2_rt_pulse_output.zip

Explanations of the files are described below:
C2H2_p.data
For time steps from 1 to nt,• 1 column: time• 2-4 columns: x,y,z components of the dipole moment• 5 column: total energy of the system# time[fs],0.12500E-02
0.25000E-02
0.37500E-02
0.50000E-02
0.62500E-02

dipoleMoment(x,y,z)[A],
0.18257556E-09 0.11097584E-09
0.91251666E-09 0.54016872E-09
0.24945802E-08 0.14520397E-08
0.50230110E-08 0.29055651E-08
0.83018473E-08 0.48072377E-08

Energy[eV]0.48217422E-09 -0.33970414E+03
0.19424475E-08 -0.33970414E+03
0.43921301E-08 -0.33970414E+03
0.78162260E-08 -0.33970414E+03
0.12178890E-07 -0.33970413E+03...
(continues on next page)

40

Chapter 4. Exercises

SALMON document, Release v.1.1.0(continued from previous page)

0.59950E+01
0.59963E+01
0.59975E+01
0.59988E+01
0.60000E+01

0.10101410E-04
0.10109316E-04
0.10115053E-04
0.10118632E-04
0.10120064E-04

0.55756362E-05
0.55775491E-05
0.55780512E-05
0.55771582E-05
0.55748807E-05

0.32250943E-03 -0.33970394E+03
0.38471398E-03 -0.33970394E+03
0.44680913E-03 -0.33970394E+03
0.50877609E-03 -0.33970394E+03
0.57059604E-03 -0.33970394E+03

C2H2_ps.data
For energy steps from 0 to nenergy,• 1 column: energy• 2-4 columns: x,y,z components of the real part of the time-frequency Fourier transformation of the dipole
moment• 5-7 columns: x,y,z components of imaginary part of the time-frequency Fourier transformation of the dipole
moment• 8-10 columns: x,y,z components of power spectrum of the dipole moment# energy[eV], Re[alpha](x,y,z)[A*fs], Im[alpha](x,y,z)[A*fs], I(x,y,z)[A**2*fs**2]0.00000E+00 0.12836214E-01 0.60771681E-02 -0.28240863E-02 0.00000000E+00 0.
,→00000000E+00
0.00000000E+00 0.16476838E-03 0.36931972E-04 0.79754632E-05
0.10000E-01 0.12829079E-01 0.60737829E-02 -0.28241953E-02 0.35253318E-03 0.
,→16719128E-03 -0.41437502E-04
0.16470954E-03 0.36918792E-04 0.79777964E-05
0.20000E-01 0.12807693E-01 0.60636364E-02 -0.28245142E-02 0.70436985E-03 0.
,→33405211E-03 -0.83009748E-04
0.16453313E-03 0.36879277E-04 0.79847710E-05
0.30000E-01 0.12772113E-01 0.60467557E-02 -0.28250177E-02 0.10548158E-02 0.
,→50025311E-03 -0.12484976E-03
0.16423951E-03 0.36813507E-04 0.79963126E-05
0.40000E-01 0.12722434E-01 0.60231857E-02 -0.28256644E-02 0.14031812E-02 0.
,→66546701E-03 -0.16708711E-03
0.16382925E-03 0.36721612E-04 0.80122973E-05
0.50000E-01 0.12658789E-01 0.59929893E-02 -0.28263966E-02 0.17487830E-02 0.
,→82936975E-03 -0.20984627E-03
0.16330319E-03 0.36603775E-04 0.80325532E-05...
0.99601E+01 0.38757368E-03 0.19783358E-03 0.11087376E+01 -0.27465428E-03 -0.
,→29515838E-03
0.10183658E+01 0.22564833E-06 0.12625659E-06 0.22663679E+01
0.99701E+01 0.38446279E-03 0.19754997E-03 0.10416956E+01 -0.27241140E-03 -0.
,→29512921E-03
0.10381647E+01 0.22201960E-06 0.12612724E-06 0.21629157E+01
0.99801E+01 0.38136406E-03 0.19733388E-03 0.97519659E+00 -0.27017795E-03 -0.
,→29508231E-03
0.10542348E+01 0.21843467E-06 0.12601423E-06 0.20624194E+01
0.99901E+01 0.37827032E-03 0.19718146E-03 0.90943725E+00 -0.26795413E-03 -0.
,→29501502E-03
0.10666811E+01 0.21488785E-06 0.12591439E-06 0.19648847E+01
0.10000E+02 0.37517469E-03 0.19708886E-03 0.84460457E+00 -0.26574105E-03 -0.
,→29492512E-03
0.10756186E+01 0.21137435E-06 0.12582485E-06 0.18703122E+01

4.3 Crystalline silicon (periodic solids)
4.3.1 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

4.3. Crystalline silicon (periodic solids)

41

SALMON document, Release v.1.1.0

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 nameSi_gs_rt_response.inp
Si_rps.dat

description
input file that contain namelist variables and their values.
pseodupotential file of silicon

You may download the above 2 files (zipped file) from:https://salmon-tddft.jp/webmanual/v_1_1_0/exercise_zip_files/Si_gs_rt_response_input.zip

In the input file Si_gs_rt_response.inp, namelists variables 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 namelist variables that can be used in the input file can be found in the downloaded file
SALMON/manual/input_variables.md.
&calculation
calc_mode = 'GS_RT'/&controlsysname = 'Si'/&unitsunit_system = 'a.u.'/&system
iperiodic = 3
al = 10.26d0, 10.26d0, 10.26d0
nstate = 32
nelec = 32
nelem = 1
natom = 8/
&pseudoizatom(1) = 14
pseudo_file(1) = './Si_rps.dat'
lloc_ps(1) = 2/&functional
xc = 'PZ'/&rgridnum_rgrid = 12, 12, 12/&kgridnum_kgrid = 4, 4, 4/
&tgrid(continues on next page)

42

Chapter 4. Exercises

SALMON document, Release v.1.1.0(continued from previous page)nt = 3000
dt = 0.16/&propagation
propagator = 'etrs'/&scf
ncg = 5
nscf = 120/&emfieldtrans_longi = 'tr'
ae_shape1 = 'impulse'
epdir_re1 = 0., 0., 1.
/&analysis
nenergy = 1000
de = 0.001/&atomic_red_coor
'Si'
.0
.0
'Si'
.25
.25
'Si'
.5
.0
'Si'
.0
.5
'Si'
.5
.5
'Si'
.75
.25
'Si'
.25
.75
'Si'
.75
.75
/

.0
.25
.5
.5
.0
.75
.75
.25

1
1
1
1
1
1
1
1

We present explanations of the namelist variables that appear in the input file below:&calculation
Mandatory: calc_mode&calculation
calc_mode = 'GS_RT'/

This indicates that the ground state (GS) and the real time (RT) calculations are carried out sequentially in the present
job. See &calculation in Inputs for detail.
&control
Mandatory: none&controlsysname = 'Si'/

‘Si’ defined by sysname = 'C2H2' will be used in the filenames of output files.
&system
Mandatory: periodic, al, state, nelem, natom&system
iperiodic = 3(continues on next page)

4.3. Crystalline silicon (periodic solids)

43

SALMON document, Release v.1.1.0(continued from previous page)

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 thenumber 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.
See &system in Inputs for more information.
&pseudo&pseudoizatom(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 thepseudopotential that will be treated as local.
&functional&functional
xc = 'PZ'/

This indicates that the adiabatic local density approximation with the Perdew-Zunger functional is used. We note thatmeta-GGA functionals that reasonably reproduce the band gap of various insulators may also be used in the calculationof periodic systems. See &functional in Inputs for detail.
&rgridMandatory: dl or num_rgrid&rgridnum_rgrid = 12,12,12/

num_rgrid=12,12,12 specifies the number of the grids for each Cartesian direction. See &rgrid in Inputs formore information.
&kgridMandatory: none
This namelist provides grid spacing of k-space for periodic systems.
&kgridnum_kgrid = 4,4,4/&tgrid44

Chapter 4. Exercises

SALMON document, Release v.1.1.0&tgridnt=3000
dt=0.16/dt=0.16 specifies the time step of the time evolution calculation. nt=3000 specifies the number of time steps inthe calculation.
&propagation&propagation
propagator='etrs'/

propagator = 'etrs' indicates the use of enforced time-reversal symmetry propagator. See &propagation in
Inputs for more information.
&scf
Mandatory: nscf
This namelists specify parameters related to the self-consistent field calculation.
&scf
ncg = 5
nscf = 120/

ncg = 5 is the number of conjugate-gradient iterations in solving the Kohn-Sham equation. Usually this value
should be 4 or 5. nscf = 120 is the number of scf iterations.
&emfield
Mandatory:ae_shape1&emfieldtrans_longi = 'tr'
ae_shape1 = 'impulse'
epdir_re1 = 0.,0.,1.
/

as_shape1 = 'impulse' indicates that a weak impulsive field is applied to all electrons at t=0
epdir_re1(3) specify a unit vector that indicates the direction of the impulse.
trans_longi = 'tr' specifies the treatment of the polarization in the time evolution calculation, transverse for‘tr’ and longitudinal for ‘lo’.
See &emfield in Inputs for detail.
&analysis&analysis
nenergy=1000
de=0.001/

nenergy=1000 specifies the number of energy steps, and de=0.001 specifies the energy spacing in the timefrequency Fourier transformation.
&atomic_red_coor

4.3. Crystalline silicon (periodic solids)

45

SALMON document, Release v.1.1.0

Mandatory: atomic_coor or atomic_red_coor (they may be provided as a separate file)&atomic_red_coor
'Si'
.0
.0
'Si'
.25
.25
'Si'
.5
.0
'Si'
.0
.5
'Si'
.5
.5
'Si'
.75
.25
'Si'
.25
.75
'Si'
.75
.75
/

.0
.25
.5
.5
.0
.75
.75
.25

1
1
1
1
1
1
1
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.
Output files
After the calculation, following output files are created in the directory that you run the code,
file nameSi_gs_info.data
Si_eigen.data
Si_k.data
Si_rt.data
Si_force.data
Si_lr.data
Si_gs_rt_response.out

description
information of ground state calculationenergy eigenvalues of orbitals
information on k-points
electric field, vector potential, and current as functions of timeforce acting on atoms
Fourier spectra of the dielectric functions
standard output file

You may download the above files (zipped file) from:https://salmon-tddft.jp/webmanual/v_1_1_0/exercise_zip_files/Si_gs_rt_response_output.zip

Explanations of the output files are described below:
Si_gs_info.data
Results of the ground state as well as input parameters are provided.
#--------------------------------------------------------#grid information----------------------------------------#aL =10.2600000000000
10.2600000000000
10.2600000000000#al(1),al(2),al(3) =10.2600000000000
10.2600000000000
10.2600000000000#aLx,aLy,aLz =10.2600000000000
10.2600000000000
10.2600000000000#bLx,bLy,bLz = 0.612396228769940
0.612396228769940
0.612396228769940#Nd =4#NLx,NLy,NLz=
12
12
12
#NL =
1728
#Hx,Hy,Hz = 0.855000000000000
0.855000000000000
0.855000000000000#(pi/max(Hx,Hy,Hz))**2 =13.5010490764192(continues on next page)46

Chapter 4. Exercises

SALMON document, Release v.1.1.0(continued from previous page)#(pi/Hx)**2+(pi/Hy)**2+(pi/Hz)**2 =40.5031472292576#Hxyz = 0.625026375000000#NKx,NKy,NKz=
4
4
4#NKxyz =
64
#Sym=
1
#NK =
64
#NEwald, aEwald =4 0.500000000000000#--------------------------------------------------------#GS calc. option-----------------------------------------#FSset_option =n#Ncg=
5#Nmemory_MB,alpha_MB =8 0.750000000000000#NFSset_start,NFSset_every =75
25#Nscf=
120#Nscf_conv=
120#NI,NE=
8
1#Zatom=14#Lref=
2#i,Kion(ia)(Rion(j,a),j=1,3)#
1
1# 0.000000000000000E+000 0.000000000000000E+000 0.000000000000000E+000#
21#2.56500000000000
2.56500000000000
2.56500000000000#
31#5.13000000000000
0.000000000000000E+000
5.13000000000000#
41# 0.000000000000000E+000
5.13000000000000
5.13000000000000#
51#5.13000000000000
5.13000000000000
0.000000000000000E+000#
61#
7.69500000000000
2.56500000000000
7.69500000000000#
71#2.56500000000000
7.69500000000000
7.69500000000000#
81#7.69500000000000
7.69500000000000
2.56500000000000#--------------------------------------------------------#GS information------------------------------------------#NB,Nelec=
32
32#Eall = -31.2658878806236#ddns(iter = Nscf_conv) 2.798849279746559E-010#ddns_abs_1e(iter = Nscf_conv) 2.364732236264119E-010#esp_var_ave(iter = Nscf_conv) 1.196976937606010E-009#esp_var_max(iter = Nscf_conv) 4.031276129792963E-009#NBoccmax is
16#--------------------------------------------------------#band information----------------------------------------#Bottom of VB -0.194802063980608#Top of VB 0.216731478175047#Bottom of CB 0.255681914576368#Top of CB 0.533214678236198#Fundamental gap 3.895043640132098E-002#Fundamental gap[eV]1.05990369517819#BG between same k-point 3.895043648321342E-002#BG between same k-point[eV]1.05990369740661#Physicaly upper bound of CB for DOS 0.454100922291231#Physicaly upper bound of CB for eps(omega) 0.609752486428134#--------------------------------------------------------(continues on next page)

4.3. Crystalline silicon (periodic solids)

47

SALMON document, Release v.1.1.0(continued from previous page)

#iter
1
2
3
4
5

total-energy-0.2059780903E+02-0.2600097163E+02-0.2866336088E+02-0.3006244467E+02-0.3096872596E+02

ddns/nelec
0.5134199377E+00
0.3186108570E+00
0.1363849859E+00
0.1245614607E+00
0.7495214064E-01

esp_var_ave
0.1332473220E-01
0.1526707771E-01
0.6359704895E-02
0.5868323970E-02
0.2566344769E-02

esp_var_max
0.1986049398E-01
0.2520724900E-01
0.1247448390E-01
0.1942874074E-01
0.1102001262E-01-0.3126588788E+02-0.3126588788E+02-0.3126588788E+02-0.3126588788E+02-0.3126588788E+02-0.3126588788E+02

0.1355175468E-09
0.1452261250E-09
0.1419175726E-09
0.1686476198E-09
0.2159059511E-09
0.2364732236E-09

0.1208579378E-08
0.1204317051E-08
0.1198067051E-08
0.1198945057E-08
0.1200809994E-08
0.1196976938E-08

0.4031265522E-08
0.4031272647E-08
0.4031255783E-08
0.4031251395E-08
0.4666412657E-08
0.4031276130E-08

...
115
116
117
118
119
120

Si_eigen.data
Orbital energies in the ground state calculation.
# Ground state eigenenergies# ik: k-point index# ib: Band index# energy: Eigenenergy# occup: Occupation# 1:ik[none] 2:ib[none] 3:energy[a.u.] 4:occup[none]1
1 -1.38676447625070E-001 2.00000000000000E+000
1
2 -1.10783431105032E-001 2.00000000000000E+000
1
3 -1.10783428207470E-001 2.00000000000000E+000
1
4 -1.10783427594037E-001 2.00000000000000E+000
1
5 -1.57456296850928E-002 2.00000000000000E+000
...
64
64
64
64
64

28
29
30
31
32

3.68051950109468E-001
4.91528586750629E-001
4.91528587785578E-001
4.91528588058071E-001
5.14831956233275E-001

0.00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000

Si_k.data
Information on k-points.
# 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]
1 -3.75000000000000E-001 -3.75000000000000E-001 -3.75000000000000E-001,→00000000000000E+000
2 -3.75000000000000E-001 -3.75000000000000E-001 -1.25000000000000E-001,→00000000000000E+000
3 -3.75000000000000E-001 -3.75000000000000E-001 1.25000000000000E-001,→00000000000000E+000
4 -3.75000000000000E-001 -3.75000000000000E-001 3.75000000000000E-001,→00000000000000E+000

1.
1.
1.
1.

(continues on next page)48

Chapter 4. Exercises

SALMON document, Release v.1.1.0(continued from previous page)

5 -3.75000000000000E-001 -1.25000000000000E-001 -3.75000000000000E-001,→00000000000000E+000

1.

...
60 3.75000000000000E-001
00000000000000E+000
61 3.75000000000000E-001,→00000000000000E+000
62 3.75000000000000E-001,→00000000000000E+000
63 3.75000000000000E-001,→00000000000000E+000
64 3.75000000000000E-001,→00000000000000E+000

1.25000000000000E-001

3.75000000000000E-001

1.

3.75000000000000E-001 -3.75000000000000E-001

1.

3.75000000000000E-001 -1.25000000000000E-001

1.

3.75000000000000E-001

1.25000000000000E-001

1.

3.75000000000000E-001

3.75000000000000E-001

1.

,→

Si_rt.data
Results of time evolution calculation. Ac_ext_x,y,z are applied vector potential. For transverse calculation specified bytrans_longi = ‘tr’, Ac_tot_x,y,z are equal to Ac_ext_x,y,z. For longitudinal calculation specified by trans_longi ='lo', Ac_tot_x,y,z are the sum of Ac_ext_x,y,z and the induced polarization. The same relation holds for electric fields
of E_ext_x,y,z and E_tot_x,y,z. Jm_x,y,z are macroscopic current. Eall and Eall-Eall0 are total energy and electronic
excitation energy, respectively. ‘’Tion’ is the kinetic energy of atoms. Temperature_ion is the temperature estimatedfrom the atomic motion.
# 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# Eall: Total energy# Eall0: Initial energy# Tion: Kinetic energy of ions
# 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.] 17:Eall[a.u.] 18:Eall-Eall0[a.u.] 19:Tion[a.u.] 20:Temperature_ion[K]0.00000000 0.00000000000000E+000 0.00000000000000E+000 1.00000000000000E-002,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 1.00000000000000E-002 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 -8.
,→65860214541267E-013
1.04880923197437E-012 2.79610491078699E-004 -3.
,→12643773655041E+001
1.51051511945255E-003 0.00000000000000E+000 0.
,→00000000000000E+000
0.16000000 0.00000000000000E+000 0.00000000000000E+000 1.00000000000000E-002,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 1.00000000000000E-002 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 -7.
,→80220609595942E-013
1.25669598865900E-012 2.77640461612200E-004 -3.
,→12643780708603E+001
1.50980976327020E-003 0.00000000000000E+000 0.
,→00000000000000E+000
0.32000000 0.00000000000000E+000 0.00000000000000E+000 1.00000000000000E-002,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 1.00000000000000E-002 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 -6.
,→65469342838961E-013
1.44166600383436E-012 2.72256619397668E-004 -3.
,→12643780794812E+001
1.50980114240440E-003 0.00000000000000E+000 0. (continues on next page),→00000000000000E+000

4.3. Crystalline silicon (periodic solids)

49

SALMON document, Release v.1.1.0(continued from previous page)

0.48000000 0.00000000000000E+000 0.00000000000000E+000 1.00000000000000E-002,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 1.00000000000000E-002 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 -5.
,→07694047189471E-013
1.65330407801294E-012 2.65100129464106E-004 -3.
,→12643780384343E+001
1.50984218925032E-003 0.00000000000000E+000 0.
,→00000000000000E+000
0.64000000 0.00000000000000E+000 0.00000000000000E+000 1.00000000000000E-002,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 1.00000000000000E-002 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 -3.
,→21400178809861E-013
1.87627749522222E-012 2.57460045574299E-004 -3.
,→12643779799564E+001
1.50990066720169E-003 0.00000000000000E+000 0.
,→00000000000000E+000...
479.36000000 0.00000000000000E+000 0.00000000000000E+000 1.00000000000000E-002
0.00000000000000E+000 0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 1.00000000000000E-002 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 -7.
,→94263263896610E-013
3.79557494087330E-012 -3.59285386087180E-006 -3.
,→12643819342307E+001
1.50594639281820E-003 0.00000000000000E+000 0.
,→00000000000000E+000
479.52000000 0.00000000000000E+000 0.00000000000000E+000 1.00000000000000E-002,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 1.00000000000000E-002 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 -5.
,→67828280529921E-013
3.78374121551490E-012 -2.90523320634650E-006 -3.
,→12643819351033E+001
1.50594552028593E-003 0.00000000000000E+000 0.
,→00000000000000E+000
479.68000000 0.00000000000000E+000 0.00000000000000E+000 1.00000000000000E-002,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 1.00000000000000E-002 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 -3.
,→61839313869103E-013
3.74173331529800E-012 -2.24958911411780E-006 -3.
,→12643819359872E+001
1.50594463632103E-003 0.00000000000000E+000 0.
,→00000000000000E+000
479.84000000 0.00000000000000E+000 0.00000000000000E+000 1.00000000000000E-002,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 1.00000000000000E-002 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 -1.
,→73847971134404E-013
3.66573716775167E-012 -1.63591499831827E-006 -3.
,→12643819368722E+001
1.50594375133295E-003 0.00000000000000E+000 0.
,→00000000000000E+000
480.00000000 0.00000000000000E+000 0.00000000000000E+000 1.00000000000000E-002,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 1.00000000000000E-002 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 3.
,→16688678319438E-016
3.55459629253500E-012 -1.06271326454723E-006 -3.
,→12643819377811E+001
1.50594284247063E-003 0.00000000000000E+000 0.
,→00000000000000E+000,→

Si_force.data
Force acting on each atom during time evolution.

50

Chapter 4. Exercises

SALMON document, Release v.1.1.0# Force calculatio# force: Force# time[a.u.] force[a.u.]
0.000000E+000 -0.663815E-008
0.381467E-008
0.178186E-002
0.280496E-008
0.
,→236613E-009
0.178187E-002
0.190620E-008
0.346038E-008
0.178186E-002 -0.
,→255965E-008
0.162582E-008
0.178187E-002 -0.713246E-009 -0.607621E-008
0.
,→178187E-002-0.124821E-008
0.434748E-008
0.178187E-002 -0.932639E-008 -0.
,→112168E-007
0.178187E-002 -0.505708E-008 -0.289586E-008
0.178187E-002
0.160000E+001 -0.131290E-008
0.165516E-008
0.339940E-002 -0.941496E-009 -0.
,→767670E-009
0.339940E-002
0.138786E-008
0.172143E-008
0.339940E-002 -0.
,→451825E-009-0.106362E-008
0.339940E-002
0.298232E-009
0.383164E-009
0.
,→339940E-002-0.296521E-009 -0.195556E-008
0.339940E-002
0.348404E-009 -0.
,→849494E-009
0.339940E-002 -0.297429E-009
0.578589E-009
0.339940E-002
0.320000E+001
0.615410E-008 -0.278186E-008
0.457711E-002 -0.486320E-008 -0.
,→116861E-008
0.457711E-002 -0.112143E-008 -0.166802E-008
0.457711E-002
0.
,→253122E-008-0.368112E-008
0.457710E-002
0.935799E-009
0.830658E-008
0.
,→457711E-002
0.621491E-009 -0.804263E-008
0.457710E-002
0.123310E-007
0.
,→130141E-007
0.457711E-002
0.636436E-008
0.330898E-008
0.457710E-002
0.480000E+001
0.635332E-008 -0.357991E-008
0.446307E-002 -0.388157E-008 -0.
,→157542E-008
0.446307E-002 -0.193530E-008 -0.255271E-008
0.446308E-002
0.
,→230966E-008-0.227850E-008
0.446306E-002 -0.341100E-009
0.746659E-008
0.
,→446307E-002
0.734950E-009 -0.635113E-008
0.446307E-002
0.943051E-008
0.
,→126831E-007
0.446307E-002
0.494958E-008
0.330406E-008
0.446306E-002
0.640000E+001
0.407644E-009
0.406484E-010
0.320569E-002
0.134973E-008 -0.
,→648732E-009
0.320569E-002 -0.148635E-009 -0.650159E-009
0.320569E-002 -0.
,→231759E-009
0.163276E-008
0.320569E-002 -0.961535E-009 -0.941812E-009
0.
,→320569E-002
0.847442E-009
0.130553E-008
0.320569E-002 -0.264725E-008 -0.
,→351407E-009
0.320569E-002 -0.141512E-008
0.421806E-009
0.320569E-002...
0.473600E+003
0.246506E-009
0.251205E-009 -0.148216E-003 -0.416554E-011
0.
779853E-009 -0.148215E-003 -0.115879E-009
0.104374E-008 -0.148217E-003
0.
,→913004E-009-0.465967E-009 -0.148217E-003
0.176729E-009 -0.270103E-009 -0.
,→148216E-003
0.962326E-009
0.799398E-009 -0.148218E-003
0.220066E-009 -0.
,→152063E-008-0.148216E-003
0.571304E-009 -0.132336E-008 -0.148217E-003
0.475200E+003 -0.504521E-009 -0.437234E-010 -0.316399E-003 -0.459509E-009
0.
,→105940E-008-0.316398E-003
0.105290E-009
0.547364E-009 -0.316401E-003
0.
,→181887E-009-0.343314E-009 -0.316399E-003 -0.804290E-010 -0.500340E-009 -0.
,→316400E-003
0.372911E-009
0.141733E-008 -0.316401E-003 -0.244574E-009 -0.
,→259207E-008-0.316400E-003
0.202885E-009 -0.147976E-008 -0.316400E-003
0.476800E+003 -0.475521E-009 -0.161693E-009 -0.415900E-003 -0.925954E-009
0.
,→240941E-009-0.415900E-003
0.291237E-009 -0.453400E-009 -0.415902E-003 -0.
,→580783E-009-0.751060E-010 -0.415900E-003 -0.683807E-009 -0.202391E-010 -0.
,→415902E-003-0.618227E-011
0.138283E-008 -0.415902E-003 -0.274419E-009 -0.
,→218740E-008-0.415901E-003
0.175364E-009 -0.657477E-009 -0.415900E-003
0.478400E+003
0.303920E-009 -0.402101E-009 -0.439830E-003 -0.134116E-008 -0.
,→816066E-009-0.439830E-003
0.318015E-009 -0.927198E-009 -0.439831E-003 -0.
,→150791E-008-0.169799E-009 -0.439831E-003 -0.702142E-009
0.881452E-009 -0.
,→439831E-003-0.618720E-009
0.779075E-009 -0.439831E-003
0.540736E-009
0.
,→352559E-009-0.439830E-003
0.382572E-009
0.794098E-009 -0.439830E-003
0.480000E+003
0.957060E-009 -0.635421E-009 -0.336591E-003 -0.873698E-009 -0.
,→134192E-008-0.336592E-003 -0.660852E-010 -0.282862E-009 -0.336591E-003 -0.
,→156118E-008-0.398368E-009 -0.336593E-003 -0.480887E-010
0.961042E-009 -0.
,→336592E-003-0.121634E-008 -0.277887E-009 -0.336591E-003
0.104632E-008
0.
,→244269E-008-0.336591E-003
0.412975E-009
0.133042E-008 -0.336591E-003,→

Si_lr_data

4.3. Crystalline silicon (periodic solids)

51

SALMON document, Release v.1.1.0

In transverse calculation specified by trans_longi = 'tr', 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:Frequency[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]
0.00100000 -1.03308449903699E-010 -2.55685769383253E-011 3.36356888185559E-005,→ 9.38757700305135E-010
2.38405472055867E-010 -1.31839196070590E-003 -1.
,→17967771791178E-005 -2.99589151834528E-006
1.75674019932220E+001 -1.
,→29821226908484E-006 -3.21304213888753E-007
4.22678531563230E-001
0.00200000 -4.05463997396279E-010 -1.00459000515141E-010 1.32405016849080E-004,→ 1.82449482725124E-009
4.64061580393162E-010 -2.62118275831395E-003 -1.
,→14636390916102E-005 -2.91578490355285E-006
1.74693769944707E+001 -2.
,→54760543103060E-006 -6.31202516010683E-007
8.31925256463007E-001
0.00300000 -8.83952914849078E-010 -2.19401192737277E-010 2.90077713140610E-004,→ 2.60896580505206E-009
6.65304400028214E-010 -3.89397682658909E-003 -1.
,→09284104088247E-005 -2.78682055403947E-006
1.73110519888816E+001 -3.
,→70269331121220E-006 -9.19025567056355E-007
1.21507468343022E+000
0.00400000 -1.50380858485809E-009 -3.74177620806077E-010 4.96861248105049E-004,→ 3.25293966934794E-009
8.32525470173577E-010 -5.12467699872510E-003 -1.
,→02194113677943E-005 -2.61545590102370E-006
1.70996476112154E+001 -4.
,→72435400259545E-006 -1.17551366466208E-006
1.56093564690028E+000
0.00500000 -2.22112273174113E-009 -5.54404046892706E-010 7.40224957578435E-004,→ 3.72943718693087E-009
9.58925096932178E-010 -6.30436402916416E-003 -9.
,→37309797478928E-006 -2.41004163189201E-006
1.68445949756623E+001 -5.
,→58229028540739E-006 -1.39336934467086E-006
1.86038823098578E+000...

0.99600000 -2.76735852669967E-009 -1.50791378263185E-009 4.18549443295463E-003-3.48281730295103E-010 -2.38950132823120E-011 2.58042637047465E-002 4.
,→39421415772947E-009
3.01479510783703E-010 6.74431785999496E-001 -3.
,→49153141258183E-008 -1.90251038625021E-008
5.28077050691215E-002
0.99700000 -2.79907084112808E-009 -1.43228946145853E-009 4.21502473100264E-003,→-4.64190825344567E-010 -1.65916319932293E-010
2.58406831005378E-002 5.
,→85074618562197E-009
2.09123968629867E-009 6.74299297121799E-001 -3.
,→52800015701720E-008 -1.80528387158764E-008
5.31269437497179E-002
0.99800000 -2.80549388829912E-009 -1.33123845334775E-009 4.22285528976820E-003,→-5.93339164267705E-010 -2.85965452283521E-010
2.58784739372621E-002 7.
,→47106196212637E-009
3.60074935500759E-009 6.74149805180691E-001 -3.
,→53255270107077E-008 -1.67623605018579E-008
5.31723092405153E-002
0.99900000 -2.78217278629315E-009 -1.21099840604532E-009 4.20947560905717E-003,→-7.28526525583285E-010 -3.79100172729291E-010
2.59111098101567E-002 9.
,→16409842129228E-009
4.76868195243629E-009 6.74065456552766E-001 -3.
,→49968111569009E-008 -1.52330878716353E-008
5.29507813768946E-002
1.00000000 -2.72693112746934E-009 -1.07872277288261E-009 4.17738539625698E-003,→-8.61256547421816E-010 -4.42238226589537E-010
2.59324188318589E-002 1.
,→08228689689459E-008
5.55732945516107E-009 6.74123614032074E-001 -3.
,→42676271876120E-008 -1.35556301541920E-008
5.24945730883769E-002,→

Si_gs_rt_response.out
Standard output file.

52

Chapter 4. Exercises

SALMON document, Release v.1.1.0

4.3.2 Exercise-5: Electron dynamics in crystalline silicon under a pulsed electricfield
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 parametersthat 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 nameSi_gs_rt_pulse.inp
Si_rps.dat

description
input file that contain namelist variables and their values.
pseodupotential file for Carbon

You may download the above 2 files (zipped file) from:https://salmon-tddft.jp/webmanual/v_1_1_0/exercise_zip_files/Si_gs_rt_pulse_input.zip

In the input file Si_gs_rt_pulse.inp, namelists variables are specified. Most of them are mandatory to executethe calculation. 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.
&calculation
calc_mode = 'GS_RT'/&controlsysname = 'Si'/&unitsunit_system = 'a.u.'/&system
iperiodic = 3
al = 10.26d0, 10.26d0, 10.26d0
nstate = 32
nelec = 32
nelem = 1
natom = 8/
&pseudoizatom(1) = 14
pseudo_file(1) = './Si_rps.dat'
lloc_ps(1) = 2/&functional
xc = 'PZ'/&rgrid(continues on next page)

4.3. Crystalline silicon (periodic solids)

53

SALMON document, Release v.1.1.0(continued from previous page)num_rgrid = 12, 12, 12/&kgridnum_kgrid = 4, 4, 4/
&tgridnt = 3000
dt = 0.16/&propagation
propagator = 'etrs'/&scf
ncg = 5
nscf = 120/&emfieldtrans_longi = 'tr'
ae_shape1 = 'Acos2'
rlaser_int_wcm2_1 = 1d14
pulse_tw1 = 441.195136248d0
omega1 = 0.05696145187d0
epdir_re1 = 0., 0., 1.
/&atomic_red_coor
'Si'
.0
.0
.0
'Si'
.25
.25
.25
'Si'
.5
.0
.5
'Si'
.0
.5
.5
'Si'
.5
.5
.0
'Si'
.75
.25
.75
'Si'
.25
.75
.75
'Si'
.75
.75
.25
/

1
1
1
1
1
1
1
1

We present explanations of the namelist variables that appear in the input file below:
XXXX hoge input exe5 XXXXX&calculation
Mandatory: calc_mode&calculation
calc_mode = 'GS_RT'/

This indicates that the ground state (GS) and the real time (RT) calculations are carried out sequentially in the present
job. See &calculation in Inputs for detail.
&control
Mandatory: none&controlsysname = 'Si'/

‘Si’ defined by sysname = 'C2H2' will be used in the filenames of output files.
54

Chapter 4. Exercises

SALMON document, Release v.1.1.0&system
Mandatory: periodic, al, state, nelem, natom&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 thenumber 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.
See &system Inputs for more information.
&pseudo&pseudoizatom(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 thepseudopotential that will be treated as local.
&functional&functional
xc = 'PZ'/

This indicates that the adiabatic local density approximation with the Perdew-Zunger functional is used. We note thatmeta-GGA functionals that reasonably reproduce the band gap of various insulators may also be used in the calculationof periodic systems. See &functional in Inputs for detail.
&rgridMandatory: dl or num_rgrid&rgridnum_rgrid = 12,12,12/

num_rgrid=12,12,12 specifies the number of the grids for each Cartesian direction. See &rgrid in Inputs formore information.
&kgridMandatory: none
This namelist provides grid spacing of k-space for periodic systems.

4.3. Crystalline silicon (periodic solids)

55

SALMON document, Release v.1.1.0&kgridnum_kgrid = 4,4,4/&tgrid&tgridnt=3000
dt=0.16/dt=0.16 specifies the time step of the time evolution calculation. nt=3000 specifies the number of time steps inthe calculation.
&propagation&propagation
propagator='etrs'/

propagator = 'etrs' indicates the use of enforced time-reversal symmetry propagator. See &propagation in
Inputs for more information.
&scf
Mandatory: nscf
This namelists specify parameters related to the self-consistent field calculation.
&scf
ncg = 5
nscf = 120/

ncg = 5 is the number of conjugate-gradient iterations in solving the Kohn-Sham equation. Usually this value
should be 4 or 5. nscf = 120 is the number of scf iterations.
&emfield&emfieldtrans_longi = 'tr'
ae_shape1 = 'Acos2'
rlaser_int_wcm2_1 = 1d14
pulse_tw1 = 441.195136248d0
omega1 = 0.05696145187d0
epdir_re1 = 0.,0.,1.
/

This namelist specifies the pulsed electric field applied to the systemae_shape1 = 'Acos2' specifies the envelope of the pulsed electric field, cos^2 envelope for the vector potential.
epdir_re1 = 0.,0.,1. specify the real part of the unit polarization vector of the pulsed electric field. Specifying
only the real part, it describes a linearly polarized pulse.
laser_int_wcm2_1 = 1d14 specifies the maximum intensity of the applied electric field in unit of W/cm^2.
omega1=0.05696145187d0 specifies the average photon energy (frequency multiplied with hbar).
pulse_tw1=441.195136248d0 specifies the pulse duration. Note that it is not the FWHM but a full duration of
the cos^2 envelope.

56

Chapter 4. Exercises

SALMON document, Release v.1.1.0

trans_longi = 'tr' specifies the treatment of the polarization in the time evolution calculation, ‘tr’ indicatingtransverse.
See &emfield in Inputs for detail.
&atomic_red_coor
Mandatory: atomic_coor or atomic_red_coor (they may be provided as a separate file)&atomic_red_coor
'Si'
.0
.0
'Si'
.25
.25
'Si'
.5
.0
'Si'
.0
.5
'Si'
.5
.5
'Si'
.75
.25
'Si'
.25
.75
'Si'
.75
.75
/

.0
.25
.5
.5
.0
.75
.75
.25

1
1
1
1
1
1
1
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.
Output files
After the calculation, following output files are created in the directory that you run the code,
file nameSi_gs_info.data
Si_eigen.data
Si_k.data
Si_rt.data
Si_force.data
Si_lr.data
Si_gs_rt_pulse.out

description
information of ground state calculationenergy eigenvalues of orbitals
information on k-points
electric field, vector potential, and current as functions of timeforce acting on atoms
Fourier transformations of various quantities
standard output file

You may download the above files (zipped file) from:https://salmon-tddft.jp/webmanual/v_1_1_0/exercise_zip_files/Si_gs_rt_pulse_output.zip

Explanations of the output files are described below:
Si_gs_info.data
Results of the ground state as well as input parameters are provided.
#--------------------------------------------------------#grid information----------------------------------------#aL =10.2600000000000
10.2600000000000
10.2600000000000#al(1),al(2),al(3) =10.2600000000000
10.2600000000000
10.
,→2600000000000#aLx,aLy,aLz =10.2600000000000
10.2600000000000
10.2600000000000#bLx,bLy,bLz = 0.612396228769940
0.612396228769940
0.612396228769940#Nd =4#NLx,NLy,NLz=
121212(continues on next page)

4.3. Crystalline silicon (periodic solids)

57

SALMON document, Release v.1.1.0(continued from previous page)

#NL =
1728
#Hx,Hy,Hz = 0.855000000000000
0.855000000000000
0.855000000000000#(pi/max(Hx,Hy,Hz))**2 =13.5010490764192#(pi/Hx)**2+(pi/Hy)**2+(pi/Hz)**2 =40.5031472292576#Hxyz = 0.625026375000000#NKx,NKy,NKz=
4
4
4#NKxyz =
64
#Sym=
1
#NK =
64
#NEwald, aEwald =4 0.500000000000000#--------------------------------------------------------#GS calc. option-----------------------------------------#FSset_option =n#Ncg=
5#Nmemory_MB,alpha_MB =8 0.750000000000000#NFSset_start,NFSset_every =75
25#Nscf=
120#Nscf_conv=
120#NI,NE=
8
1#Zatom=14#Lref=
2#i,Kion(ia)(Rion(j,a),j=1,3)#
1
1# 0.000000000000000E+000 0.000000000000000E+000 0.000000000000000E+000#
21#2.56500000000000
2.56500000000000
2.56500000000000#
31#5.13000000000000
0.000000000000000E+000
5.13000000000000#
41# 0.000000000000000E+000
5.13000000000000
5.13000000000000#
51#5.13000000000000
5.13000000000000
0.000000000000000E+000#
61#
7.69500000000000
2.56500000000000
7.69500000000000#
71#2.56500000000000
7.69500000000000
7.69500000000000#
81#7.69500000000000
7.69500000000000
2.56500000000000#--------------------------------------------------------#GS information------------------------------------------#NB,Nelec=
32
32#Eall = -31.2658878806236#ddns(iter = Nscf_conv) 2.798849279746559E-010#ddns_abs_1e(iter = Nscf_conv) 2.364732236264119E-010#esp_var_ave(iter = Nscf_conv) 1.196976937606010E-009#esp_var_max(iter = Nscf_conv) 4.031276129792963E-009#NBoccmax is
16#--------------------------------------------------------#band information----------------------------------------#Bottom of VB -0.194802063980608#Top of VB 0.216731478175047#Bottom of CB 0.255681914576368#Top of CB 0.533214678236198#Fundamental gap 3.895043640132098E-002#Fundamental gap[eV]1.05990369517819#BG between same k-point 3.895043648321342E-002#BG between same k-point[eV]1.05990369740661(continues on next page)

58

Chapter 4. Exercises

SALMON document, Release v.1.1.0(continued from previous page)#Physicaly upper bound of CB for DOS 0.454100922291231#Physicaly upper bound of CB for eps(omega) 0.609752486428134#--------------------------------------------------------#iter
total-energy
ddns/nelec
esp_var_ave
1-0.2059780903E+02
0.5134199377E+00
0.1332473220E-01
2-0.2600097163E+02
0.3186108570E+00
0.1526707771E-01
3-0.2866336088E+02
0.1363849859E+00
0.6359704895E-02
4-0.3006244467E+02
0.1245614607E+00
0.5868323970E-02
5-0.3096872596E+02
0.7495214064E-01
0.2566344769E-02

esp_var_max
0.1986049398E-01
0.2520724900E-01
0.1247448390E-01
0.1942874074E-01
0.1102001262E-01

...
115
116
117
118
119
120

-0.3126588788E+02-0.3126588788E+02-0.3126588788E+02-0.3126588788E+02-0.3126588788E+02-0.3126588788E+02

0.1355175468E-09
0.1452261250E-09
0.1419175726E-09
0.1686476198E-09
0.2159059511E-09
0.2364732236E-09

0.1208579378E-08
0.1204317051E-08
0.1198067051E-08
0.1198945057E-08
0.1200809994E-08
0.1196976938E-08

0.4031265522E-08
0.4031272647E-08
0.4031255783E-08
0.4031251395E-08
0.4666412657E-08
0.4031276130E-08

Si_eigen.data
Orbital energies in the ground state calculation.
# Ground state eigenenergies# ik: k-point index# ib: Band index# energy: Eigenenergy# occup: Occupation# 1:ik[none] 2:ib[none] 3:energy[a.u.] 4:occup[none]1
1 -1.38676447625070E-001 2.00000000000000E+000
1
2 -1.10783431105032E-001 2.00000000000000E+000
1
3 -1.10783428207470E-001 2.00000000000000E+000
1
4 -1.10783427594037E-001 2.00000000000000E+000
1
5 -1.57456296850928E-002 2.00000000000000E+000
...
64
64
64
64
64

28
29
30
31
32

3.68051950109468E-001
4.91528586750629E-001
4.91528587785578E-001
4.91528588058071E-001
5.14831956233275E-001

0.00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000

Si_k.data
Information on k-points.
# 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]
1 -3.75000000000000E-001 -3.75000000000000E-001 -3.75000000000000E-001,→00000000000000E+000
2 -3.75000000000000E-001 -3.75000000000000E-001 -1.25000000000000E-001,→00000000000000E+000
3 -3.75000000000000E-001 -3.75000000000000E-001 1.25000000000000E-001,→00000000000000E+000

1.
1.
1.

(continues on next page)

4.3. Crystalline silicon (periodic solids)

59

SALMON document, Release v.1.1.0(continued from previous page)

4 -3.75000000000000E-001 -3.75000000000000E-001 3.75000000000000E-001,→00000000000000E+000
5 -3.75000000000000E-001 -1.25000000000000E-001 -3.75000000000000E-001,→00000000000000E+000

1.
1.

...
60 3.75000000000000E-001
00000000000000E+000
61 3.75000000000000E-001,→00000000000000E+000
62 3.75000000000000E-001,→00000000000000E+000
63 3.75000000000000E-001,→00000000000000E+000
64 3.75000000000000E-001,→00000000000000E+000

1.25000000000000E-001

3.75000000000000E-001

1.

3.75000000000000E-001 -3.75000000000000E-001

1.

3.75000000000000E-001 -1.25000000000000E-001

1.

3.75000000000000E-001

1.25000000000000E-001

1.

3.75000000000000E-001

3.75000000000000E-001

1.

,→

Si_rt.data
Results of time evolution calculation. Ac_ext_x,y,z are applied vector potential. For transverse calculation specified bytrans_longi = ‘tr’, Ac_tot_x,y,z are equal to Ac_ext_x,y,z. For longitudinal calculation specified by trans_longi ='lo', Ac_tot_x,y,z are the sum of Ac_ext_x,y,z and the induced polarization. The same relation holds for electric fields
of E_ext_x,y,z and E_tot_x,y,z. Jm_x,y,z are macroscopic current. Eall and Eall-Eall0 are total energy and electronic
excitation energy, respectively. ‘’Tion’ is the kinetic energy of atoms. Temperature_ion is the temperature estimatedfrom the atomic motion.
# 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# Eall: Total energy# Eall0: Initial energy# Tion: Kinetic energy of ions
# 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.] 17:Eall[a.u.] 18:Eall-Eall0[a.u.] 19:Tion[a.u.] 20:Temperature_ion[K]0.00000000 0.00000000000000E+000 0.00000000000000E+000 0.00000000000000E+000,→ 0.00000000000000E+000
0.00000000000000E+000 3.77331308204139E-008 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 3.77331308204139E-008 -8.
,→70901886780464E-013
1.04477060852801E-012 2.05240902737187E-014 -3.
,→12658878806237E+001 -1.13686837721616E-013
0.00000000000000E+000 0.
,→00000000000000E+000
0.16000000 0.00000000000000E+000 0.00000000000000E+000 -1.20746018625324E-008,→ 0.00000000000000E+000
0.00000000000000E+000 2.89492697662796E-007 0.
,→00000000000000E+000
0.00000000000000E+000 -1.20746018625324E-008 0.
,→00000000000000E+000
0.00000000000000E+000 2.89492697662796E-007 -7.
,→85903272323908E-013
1.25651122959738E-012 -3.36584280927329E-010 -3.
,→12658878806202E+001
3.36797256750287E-012 0.00000000000000E+000 0.
,→00000000000000E+000
0.32000000 0.00000000000000E+000 0.00000000000000E+000 -9.26376632520948E-008,→ 0.00000000000000E+000
0.00000000000000E+000 9.25330085901344E-007 0.
,→00000000000000E+000
0.00000000000000E+000 -9.26376632520948E-008 0.
,→00000000000000E+000
0.00000000000000E+000 9.25330085901344E-007 -6. (continues on next page),→72570067469639E-013
1.44513383464745E-012 -2.58015152519122E-009 -3.
,→12658878805859E+001
3.76836339910369E-011 0.00000000000000E+000 0.
60
Chapter 4. Exercises,→00000000000000E+000

SALMON document, Release v.1.1.0(continued from previous page)

0.48000000 0.00000000000000E+000 0.00000000000000E+000 -3.08180229350963E-007,→ 0.00000000000000E+000
0.00000000000000E+000 1.97661471359977E-006 0.
,→00000000000000E+000
0.00000000000000E+000 -3.08180229350963E-007 0.
,→00000000000000E+000
0.00000000000000E+000 1.97661471359977E-006 -5.
,→16188379881674E-013
1.65999923818627E-012 -8.55700433990977E-009 -3.
,→12658878804485E+001
1.75052861095537E-010 0.00000000000000E+000 0.
,→00000000000000E+000
0.64000000 0.00000000000000E+000 0.00000000000000E+000 -7.25154371604021E-007,→ 0.00000000000000E+000
0.00000000000000E+000 3.44304368307922E-006 0.
,→00000000000000E+000
0.00000000000000E+000 -7.25154371604021E-007 0.
,→00000000000000E+000
0.00000000000000E+000 3.44304368307922E-006 -3.
,→31706377656679E-013
1.88556925268305E-012 -2.00507097518009E-008 -3.
,→12658878800854E+001
5.38197042487809E-010 0.00000000000000E+000 0.
,→00000000000000E+000...
479.36000000 0.00000000000000E+000 0.00000000000000E+000 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 -5.
,→55195781926435E-013 -3.96119870066348E-012
8.12847438945111E-005 -5.
,→27018855348676E+000
2.59956993271368E+001 0.00000000000000E+000 0.
,→00000000000000E+000
479.52000000 0.00000000000000E+000 0.00000000000000E+000 0.00000000000000E+000,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 -3.
,→02810565250972E-013 -3.64518553366057E-012
5.63898060743298E-005 -5.
,→27028126908996E+000
2.59956066115336E+001 0.00000000000000E+000 0.
,→00000000000000E+000
479.68000000 0.00000000000000E+000 0.00000000000000E+000 0.00000000000000E+000,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 -7.
,→16671188540074E-014 -3.26226560875438E-012
2.80138979239849E-005 -5.
,→27037369552727E+000
2.59955141850963E+001 0.00000000000000E+000 0.
,→00000000000000E+000
479.84000000 0.00000000000000E+000 0.00000000000000E+000 0.00000000000000E+000,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 1.
,→25642145342234E-013 -2.83144546563755E-012 -1.41212701168313E-006 -5.
,→27046577678837E+000
2.59954221038352E+001 0.00000000000000E+000 0.
,→00000000000000E+000
480.00000000 0.00000000000000E+000 0.00000000000000E+000 0.00000000000000E+000,→ 0.00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 2.
,→93865192596554E-013 -2.36028795847010E-012 -2.94243971611215E-005 -5.
,→27055732569162E+000
2.59953305549319E+001 0.00000000000000E+000 0.
,→00000000000000E+000,→

Si_force.data
Force acting on each atom during time evolution.

4.3. Crystalline silicon (periodic solids)

61

SALMON document, Release v.1.1.0# Force calculatio# force: Force# time[a.u.] force[a.u.]
0.000000E+000 -0.663696E-008
0.381594E-008
0.147786E-006
0.280111E-008
0.
,→228130E-009
0.152372E-006
0.190603E-008
0.347020E-008
0.144454E-006 -0.
,→255639E-008
0.162309E-008
0.157887E-006 -0.715186E-009 -0.607023E-008
0.
,→150657E-006-0.125193E-008
0.434347E-008
0.154377E-006 -0.932342E-008 -0.
,→112253E-007
0.150918E-006 -0.505492E-008 -0.289610E-008
0.158433E-006
0.160000E+001 -0.131252E-008
0.164755E-008
0.796703E-004 -0.945892E-009 -0.
,→762583E-009
0.796709E-004
0.139448E-008
0.172324E-008
0.796683E-004 -0.
,→452537E-009-0.106913E-008
0.796682E-004
0.302666E-009
0.384512E-009
0.
,→796698E-004-0.295296E-009 -0.194915E-008
0.796704E-004
0.357413E-009 -0.
,→849344E-009
0.796713E-004 -0.289642E-009
0.582711E-009
0.796703E-004
0.320000E+001
0.611719E-008 -0.279866E-008
0.299229E-003 -0.482069E-008 -0.
,→108492E-008
0.299224E-003 -0.113705E-008 -0.180657E-008
0.299232E-003
0.
,→249663E-008-0.365775E-008
0.299214E-003
0.894693E-009
0.822775E-008
0.
,→299225E-003
0.674776E-009 -0.800682E-008
0.299222E-003
0.122632E-007
0.
,→130955E-007
0.299227E-003
0.634943E-008
0.330482E-008
0.299216E-003
0.480000E+001
0.632236E-008 -0.360316E-008
0.625960E-003 -0.380678E-008 -0.
,→149542E-008
0.625956E-003 -0.195847E-008 -0.271155E-008
0.625964E-003
0.
,→224789E-008-0.225876E-008
0.625950E-003 -0.416507E-009
0.737796E-008
0.
,→625958E-003
0.788341E-009 -0.633137E-008
0.625955E-003
0.936024E-008
0.
,→128155E-007
0.625960E-003
0.491902E-008
0.331005E-008
0.625950E-003
0.640000E+001
0.402103E-009
0.205061E-010
0.102016E-002
0.136956E-008 -0.
,→668489E-009
0.102016E-002 -0.133472E-009 -0.624741E-009
0.102016E-002 -0.
,→272159E-009
0.161549E-008
0.102016E-002 -0.993343E-009 -0.896691E-009
0.
,→102016E-002
0.819106E-009
0.130318E-008
0.102016E-002 -0.262966E-008 -0.
,→314962E-009
0.102016E-002 -0.140244E-008
0.427951E-009
0.102016E-002...
0.473600E+003
0.597367E-009
0.387050E-009 -0.348389E-002
0.605905E-009 -0.
465705E-009 -0.348389E-002 -0.641806E-009 -0.394485E-009 -0.348389E-002 -0.
,→964505E-009
0.116781E-008 -0.348389E-002 -0.589312E-009
0.786468E-009 -0.
,→348389E-002-0.237343E-009
0.194589E-009 -0.348389E-002 -0.120897E-008 -0.
,→693231E-009-0.348389E-002
0.229921E-009 -0.733008E-009 -0.348389E-002
0.475200E+003 -0.168428E-009 -0.115247E-008
0.473981E-002 -0.265453E-009 -0.
,→760895E-010
0.473981E-002
0.442756E-009 -0.106813E-009
0.473981E-002
0.
,→875680E-009
0.104699E-008
0.473981E-002 -0.870002E-009
0.234294E-009
0.
,→473982E-002
0.694922E-009
0.543690E-009
0.473981E-002
0.694120E-009
0.
,→135771E-009
0.473981E-002 -0.233819E-009
0.444395E-009
0.473981E-002
0.476800E+003
0.102600E-008
0.751831E-009 -0.162791E-002
0.826826E-009
0.
,→101675E-008-0.162791E-002
0.656143E-009 -0.777523E-009 -0.162791E-002
0.
,→379311E-010
0.158618E-008 -0.162791E-002 -0.375430E-009
0.123075E-008 -0.
,→162791E-002
0.363301E-009 -0.428326E-009 -0.162792E-002
0.297257E-009 -0.
,→713355E-009-0.162791E-002 -0.253648E-010
0.813094E-010 -0.162791E-002
0.478400E+003
0.101572E-008
0.116909E-008 -0.663462E-002 -0.435127E-010 -0.
,→480843E-009-0.663462E-002
0.122317E-008
0.313588E-009 -0.663462E-002 -0.
,→951952E-010-0.156395E-008 -0.663462E-002
0.528331E-009 -0.200449E-009 -0.
,→663462E-002-0.593208E-009
0.104932E-009 -0.663462E-002
0.293176E-009 -0.
,→106265E-008-0.663462E-002 -0.144531E-009
0.662959E-010 -0.663462E-002
0.480000E+003
0.378024E-009 -0.244626E-009
0.169685E-002
0.792446E-009 -0.
,→137457E-008
0.169684E-002 -0.267886E-009
0.231108E-009
0.169684E-002 -0.
,→568326E-009
0.242847E-011
0.169684E-002
0.803904E-010 -0.153003E-009
0.
,→169684E-002-0.698906E-009 -0.493838E-009
0.169684E-002 -0.201697E-009 -0.
,→515273E-009
0.169684E-002 -0.182781E-009 -0.848598E-009
0.169684E-002,→

Si_lr_data

62

Chapter 4. Exercises

SALMON document, Release v.1.1.0

Fourier transformations of various quantities.
# Fourier-transform spectra# Jm: Matter current density# E_ext: External electric field# E_tot: Total electric potential field# 1:Frequency[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:Re(E_ext_x)[a.u.] 9:Re(E_ext_y)[a.u.] 10:Re(E_,→ext_z)[a.u.] 11:Im(E_ext_x)[a.u.] 12:Im(E_ext_y)[a.u.] 13:Im(E_ext_z)[a.u.] 14:Re(E_,→tot_x)[a.u.] 15:Re(E_tot_y)[a.u.] 16:Re(E_tot_z)[a.u.] 17:Im(E_tot_x)[a.u.] 18:Im(E_,→tot_y)[a.u.] 19:Im(E_tot_z)[a.u.]
0.00036749 -2.84895463680408E-013 5.15173051622877E-014 -3.52107345483375E-005,→ 4.48903005613079E-012 -2.32288812334531E-012
6.75568020279512E-004 0.
,→00000000000000E+000
0.00000000000000E+000 4.97953467812365E-004 0.
,→00000000000000E+000
0.00000000000000E+000 3.58501823355665E-004 0.
,→00000000000000E+000
0.00000000000000E+000 4.97953467812365E-004 0.
,→00000000000000E+000
0.00000000000000E+000 3.58501823355665E-004
0.00073499 -1.13540774534206E-012 2.07937929182977E-013 -1.40798553922957E-004,→ 8.90861768500183E-012 -4.65722890058464E-012
1.34678502951777E-003 0.
,→00000000000000E+000
0.00000000000000E+000 4.63469055289272E-004 0.
,→00000000000000E+000
0.00000000000000E+000 7.13528955721859E-004 0.
,→00000000000000E+000
0.00000000000000E+000 4.63469055289272E-004 0.
,→00000000000000E+000
0.00000000000000E+000 7.13528955721859E-004
0.00110248 -2.53907962392519E-012 4.74814744878412E-013 -3.16626882537289E-004,→ 1.31903398564115E-011 -7.01379574946040E-012
2.00927257456496E-003 0.
,→00000000000000E+000
0.00000000000000E+000 4.07013867440069E-004 0.
,→00000000000000E+000
0.00000000000000E+000 1.06169736359997E-003 0.
,→00000000000000E+000
0.00000000000000E+000 4.07013867440069E-004 0.
,→00000000000000E+000
0.00000000000000E+000 1.06169736359997E-003
0.00146997 -4.47536487471274E-012 8.61226149017987E-013 -5.62456776380136E-004,→ 1.72677949815665E-011 -9.40201922497097E-012
2.65859850138268E-003 0.
,→00000000000000E+000
0.00000000000000E+000 3.30095592579552E-004 0.
,→00000000000000E+000
0.00000000000000E+000 1.39980301776817E-003 0.
,→00000000000000E+000
0.00000000000000E+000 3.30095592579552E-004 0.
,→00000000000000E+000
0.00000000000000E+000 1.39980301776817E-003
0.00183747 -6.91594776469286E-012 1.37951536625165E-012 -8.77930263458079E-004,→ 2.10775706012377E-011 -1.18293542969418E-011
3.29025303683963E-003 0.
,→00000000000000E+000
0.00000000000000E+000 2.34784059348594E-004 0.
,→00000000000000E+000
0.00000000000000E+000 1.72490861730070E-003 0.
,→00000000000000E+000
0.00000000000000E+000 2.34784059348594E-004 0.
,→00000000000000E+000
0.00000000000000E+000 1.72490861730070E-003...

0.36602326 -1.34089639696033E-011 -1.39416295506675E-010 1.78132697555994E-003-4.82428771517963E-011 2.46762847283247E-012 -1.61143602449332E-004 0.
,→00000000000000E+000
0.00000000000000E+000 4.45170812023321E-006 0.
,→00000000000000E+000
0.00000000000000E+000 -3.65224569772520E-004 0.
,→00000000000000E+000
0.00000000000000E+000 4.45170812023321E-006 0.
,→00000000000000E+000
0.00000000000000E+000 -3.65224569772520E-004
0.36639076 -1.24360432096437E-011 -1.36245370206982E-010 1.73864190682382E-003,→-5.21816299182567E-011 -3.50916159867163E-012 -7.77023817604767E-005
0.
,→00000000000000E+000
0.00000000000000E+000 5.11905824950650E-006 0.
,→00000000000000E+000
0.00000000000000E+000 -3.63173718411360E-004 0.
,→00000000000000E+000
0.00000000000000E+000 5.11905824950650E-006 0.
,→00000000000000E+000
0.00000000000000E+000 -3.63173718411360E-004
0.36675825 -1.12274531733429E-011 -1.32788988742883E-010 1.69384196276721E-003,→-5.60444962150072E-011 -9.12174813252230E-012 -2.15275586453434E-006
0.
(continues on next page),→00000000000000E+000
0.00000000000000E+000 5.62963567554736E-006 0.
,→00000000000000E+000
0.00000000000000E+000 -3.61035199699344E-004 0.
,→00000000000000E+000
0.00000000000000E+000
5.62963567554736E-006 0.
4.3.
Crystalline silicon (periodic
solids)63,→00000000000000E+000
0.00000000000000E+000 -3.61035199699344E-004,→

SALMON document, Release v.1.1.0(continued from previous page)

0.36712574 -9.79019347225448E-012 -1.29082073143664E-010 1.64792403884542E-003,→-5.98140679681705E-011 -1.43564301457731E-011
6.57920339739901E-005 0.
,→00000000000000E+000
0.00000000000000E+000 5.97107609420323E-006 0.
,→00000000000000E+000
0.00000000000000E+000 -3.58835797250056E-004 0.
,→00000000000000E+000
0.00000000000000E+000 5.97107609420323E-006 0.
,→00000000000000E+000
0.00000000000000E+000 -3.58835797250056E-004
0.36749324 -8.13273340472761E-012 -1.25159803753324E-010 1.60180907923576E-003,→-6.34737299655122E-011 -1.92028837998549E-011
1.26529960616246E-004 0.
,→00000000000000E+000
0.00000000000000E+000 6.13554270900561E-006 0.
,→00000000000000E+000
0.00000000000000E+000 -3.56603849256161E-004 0.
,→00000000000000E+000
0.00000000000000E+000 6.13554270900561E-006 0.
,→00000000000000E+000
0.00000000000000E+000 -3.56603849256161E-004

Si_gs_rt_pulse.out
Standard output file.

4.4 Maxwell + TDDFT multiscale simulation
4.4.1 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 53 nm thickness, and an irradiation of a few-cycle, linearly polarized pulsed lightnormally 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 nameSi_gs_rt_multiscale.inp
Si_rps.dat

description
input file that contain namelist variables and their values.
pseodupotential file for silicon

You may download the above two files (zipped file) from:https://salmon-tddft.jp/webmanual/v_1_1_0/exercise_zip_files/Si_gs_rt_multiscale_input.zip

In the input file Si_gs_rt_multiscale.inp, namelists variables 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 namelist variables that can be used in the input file can be found in the downloaded file
SALMON/manual/input_variables.md.
&calculation
calc_mode = 'GS_RT'
use_ms_maxwell = 'y'/&control(continues on next page)

64

Chapter 4. Exercises

SALMON document, Release v.1.1.0(continued from previous page)

sysname = 'Si'/&system
iperiodic = 3
al = 10.26d0, 10.26d0, 10.26d0
nstate = 32
nelec = 32
nelem = 1
natom = 8/
&pseudoizatom(1) = 14
pseudo_file(1) = './Si_rps.dat'
lloc_ps(1) = 2/&functional
xc = 'PZ'/&rgridnum_rgrid = 12, 12, 12/&kgridnum_kgrid = 2, 2, 2/
&tgridnt = 4000
dt = 0.08/&propagation
propagator = 'middlepoint'/&scf
ncg = 5
nscf = 100/&emfield
ae_shape1 = 'Acos2'
rlaser_int_wcm2_1 = 1d12
pulse_tw1 = 441.195136248d0
omega1 = 0.05696145187d0
epdir_re1 = 0., 0., 1.
/&multiscale
fdtddim = '1d'twod_shape = 'periodic'
nx_m = 4ny_m = 1
hx_m = 250d0
nxvacl_m = -2000
nxvacr_m = 256/&atomic_red_coor
'Si'
.0
.0
.0
'Si'
.25
.25
.25
'Si'
.5
.0
.5
'Si'
.0
.5
.5
'Si'
.5
.5
.0

1
1
1
1
1
(continues on next page)

4.4. Maxwell + TDDFT multiscale simulation

65

SALMON document, Release v.1.1.0(continued from previous page)

'Si'
'Si'
'Si'

.75
.25
.75

.25
.75
.75

.75
.75
.25

1
1
1

/

We present explanations of the namelist variables that appear in the input file below:&calculation
Mandatory: calc_mode&calculation
calc_mode = 'GS_RT'
use_ms_maxwell = 'y'/calc_mode = 'GS_RT' indicates that the ground state (GS) and the real time (RT) calculations are carried out
sequentially in the present job. use_ms_maxwell = 'y' indicates the multi-scale Maxwell - TDDFT calculation.
See &calculation in Inputs for detail.
&control
Mandatory: none&controlsysname = 'Si'/

‘Si’ defined by sysname = 'C2H2' will be used in the filenames of output files.
&system&system
iperiodic = 3
al = 10.26d0,10.26d0,10.26d0
isym = 8
crystal_structure = 'diamond'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 thenumber 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.
isym = 8 and crystal_structure = 'diamond', which indicates that the spatial symmetry of the unit cellis 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.
See &system in Inputs for more information.
&pseudo&pseudoizatom(1)=14
pseudo_file(1) = './Si_rps.dat'(continues on next page)

66

Chapter 4. Exercises

SALMON document, Release v.1.1.0(continued from previous page)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 thepseudopotential that will be treated as local.l&functional&functional
xc='PZ'/

This indicates that the adiabatic local density approximation with the Perdew-Zunger functional is used. We note thatmeta-GGA functionals that reasonably reproduce the band gap of various insulators may also be used in the calculationof periodic systems. See &functional in Inputs for detail.
&rgridMandatory: dl or num_rgrid&rgridnum_rgrid = 12,12,12/

num_rgrid=12,12,12 specifies the number of the grids for each Cartesian direction. See &rgrid in Inputs formore information.
&kgridMandatory: none
This namelist provides grid spacing of k-space for periodic systems.
&kgridnum_kgrid = 2,2,2/&tgrid&tgridnt=4000
dt=0.08/

dt=0.08 specifies the time step of the time evolution calculation. nt=4000 specifies the number of time steps inthe calculation.
&propagation&propagation
propagator='middlepoint'/

propagator = 'middlepoint' indicates that Hamiltonian at midpoint of two-times is used. See &propagationin Inputs for more information.
&scf
Mandatory: nscf
4.4. Maxwell + TDDFT multiscale simulation

67

SALMON document, Release v.1.1.0

This namelists specify parameters related to the self-consistent field calculation.
&scf
ncg = 5
nscf = 120/

ncg = 5 is the number of conjugate-gradient iterations in solving the Kohn-Sham equation. Usually this value
should be 4 or 5. nscf = 120 is the number of scf iterations.
&emfield&emfield
ae_shape1 = 'Acos2'
rlaser_int_wcm2_1 = 1d12
pulse_tw1 = 441.195136248d0
omega1 = 0.05696145187d0
epdir_re1 = 0.,0.,1.
/

This namelist specifies the pulsed electric field applied to the systemae_shape1 = 'Acos2' specifies the envelope of the pulsed electric field, cos^2 envelope for the vector potential.
epdir_re1 = 0.,0.,1. specify the real part of the unit polarization vector of the pulsed electric field. Specifying
only the real part, it describes a linearly polarized pulse.
laser_int_wcm2_1 = 1d12 specifies the maximum intensity of the applied electric field in unit of W/cm^2.
omega1=0.05696145187d0 specifies the average photon energy (frequency multiplied with hbar).
pulse_tw1=441.195136248d0 specifies the pulse duration. Note that it is not the FWHM but a full duration of
the cos^2 envelope.
See &emfield in Inputs for detail.
&multiscaleThis namelist specifies information necessary for Maxwell - TDDFT multiscale calculations.
&multiscale
fdtddim = '1D'
twod_shape = 'periodic'
nx_m = 4ny_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 thematerial 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.
&atomic_red_coor

68

Chapter 4. Exercises

SALMON document, Release v.1.1.0

Mandatory: atomic_coor or atomic_red_coor (they may be provided as a separate file)&atomic_red_coor
'Si'
.0
.0
'Si'
.25
.25
'Si'
.5
.0
'Si'
.0
.5
'Si'
.5
.5
'Si'
.75
.25
'Si'
.25
.75
'Si'
.75
.75
/

.0
.25
.5
.5
.0
.75
.75
.25

1
1
1
1
1
1
1
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.
Output files
After the calculation, new directory multiscale/ is created, then, following output files are created in the directory,
file nameSi_gs_info.data
Si_eigen.data
Si_k.data
RT_Ac/Si_Ac_xxxxxx.data
RT_Ac/Si_Ac_vac.data
Mxxxxxx/Si_Ac_M.data
Si_gs_rt_multiscale.out

description
results of the ground state as well as input parameters
orbital energies in the ground state calculation
information on k-points
various quantities at a time as functions of macroscopic position
vector potential at vacuum position adjacent to the medium
various quantities at a macroscopic point as functions of timestandard output file

You may download the above files (zipped file) from:https://salmon-tddft.jp/webmanual/v_1_1_0/exercise_zip_files/Si_gs_rt_multiscale_output.zip

Explanations of the output files are described below:
Si_gs_info.data
Results of the ground state as well as input parameters are provided.
#--------------------------------------------------------#grid information----------------------------------------#aL =10.2600000000000
10.2600000000000
10.2600000000000#al(1),al(2),al(3) =10.2600000000000
10.2600000000000
10.
,→2600000000000#aLx,aLy,aLz =10.2600000000000
10.2600000000000
10.2600000000000#bLx,bLy,bLz = 0.612396228769940
0.612396228769940
0.612396228769940#Nd =4#NLx,NLy,NLz=
12
12
12
#NL =
1728
#Hx,Hy,Hz = 0.855000000000000
0.855000000000000
0.855000000000000#(pi/max(Hx,Hy,Hz))**2 =13.5010490764192#(pi/Hx)**2+(pi/Hy)**2+(pi/Hz)**2 =40.5031472292576#Hxyz = 0.625026375000000(continues on next page)

4.4. Maxwell + TDDFT multiscale simulation

69

SALMON document, Release v.1.1.0(continued from previous page)#NKx,NKy,NKz=
222#NKxyz =
8
#Sym=
1
#NK =
8
#NEwald, aEwald =4 0.500000000000000#--------------------------------------------------------#GS calc. option-----------------------------------------#FSset_option =n#Ncg=
5#Nmemory_MB,alpha_MB =8 0.750000000000000#NFSset_start,NFSset_every =75
25#Nscf=
100#Nscf_conv=
100#NI,NE=
8
1#Zatom=14#Lref=
2#i,Kion(ia)(Rion(j,a),j=1,3)#
1
1# 0.000000000000000E+000 0.000000000000000E+000 0.000000000000000E+000#
21#2.56500000000000
2.56500000000000
2.56500000000000#
31#5.13000000000000
0.000000000000000E+000
5.13000000000000#
41# 0.000000000000000E+000
5.13000000000000
5.13000000000000#
51#5.13000000000000
5.13000000000000
0.000000000000000E+000#
61#
7.69500000000000
2.56500000000000
7.69500000000000#
71#2.56500000000000
7.69500000000000
7.69500000000000#
81#7.69500000000000
7.69500000000000
2.56500000000000#--------------------------------------------------------#GS information------------------------------------------#NB,Nelec=
32
32#Eall = -31.2444435912435#ddns(iter = Nscf_conv) 1.054470043491702E-009#ddns_abs_1e(iter = Nscf_conv) 7.414743076744689E-010#esp_var_ave(iter = Nscf_conv) 1.020334316849951E-008#esp_var_max(iter = Nscf_conv) 2.402374610033353E-008#NBoccmax is
16#--------------------------------------------------------#band information----------------------------------------#Bottom of VB -0.171685135011666#Top of VB 0.200444750626413#Bottom of CB 0.279085896060740#Top of CB 0.467391510426397#Fundamental gap 7.864114543432713E-002#Fundamental gap[eV]2.13995139310074#BG between same k-point 7.864114544171730E-002#BG between same k-point[eV]
2.13995139330183#Physicaly upper bound of CB for DOS 0.467391509327423#Physicaly upper bound of CB for eps(omega) 0.639076644315190#--------------------------------------------------------#iter
total-energy
ddns/nelec
esp_var_ave
esp_var_max
1-0.2036656319E+02
0.7386703002E+00
0.1069029083E+00
0.1685663917E+00(continues on next page)

70

Chapter 4. Exercises

SALMON document, Release v.1.1.0(continued from previous page)

2
3
4
5

-0.2528602134E+02-0.2862371415E+02-0.3011102231E+02-0.3087795790E+02

0.4434674022E+00
0.2037034214E+00
0.1582114006E+00
0.1077328223E+00

0.1251761861E+00
0.5065455837E-01
0.4920903464E-01
0.1964285309E-01

0.1947159558E+00
0.8653325118E-01
0.1181905324E+00
0.4585050374E-01

96
97
98
99
100

-0.3124444359E+02-0.3124444359E+02-0.3124444359E+02-0.3124444359E+02-0.3124444359E+02

0.4299999378E-09
0.3271696693E-09
0.2672131350E-09
0.7129545698E-09
0.7414743077E-09

0.1045606891E-07
0.1042233851E-07
0.1041933599E-07
0.1020262421E-07
0.1020334317E-07

0.2402425601E-07
0.2402417900E-07
0.3916492026E-07
0.2402357654E-07
0.2402374610E-07...

Si_eigen.data
Orbital energies in the ground state calculation.
# Ground state eigenenergies# ik: k-point index# ib: Band index# energy: Eigenenergy# occup: Occupation# 1:ik[none] 2:ib[none] 3:energy[a.u.] 4:occup[none]1
1 -1.71685134987767E-001 2.00000000000000E+000
1
2 -9.95580252948176E-002 2.00000000000000E+000
1
3 -9.95580233898604E-002 2.00000000000000E+000
1
4 -9.95580220480095E-002 2.00000000000000E+000
1
5 2.73787456875120E-003 2.00000000000000E+000
...
8
8
8
8
8

28
29
30
31
32

4.34674205363501E-001
4.40615204659137E-001
4.40615205419465E-001
4.40615206907897E-001
4.67391509348806E-001

0.00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000

Si_k.data
Information on k-points. Note that diamond symmetry is used to reduce the k-point in this calculation.
# 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]
1 -2.50000000000000E-001 -2.50000000000000E-001 -2.50000000000000E-001,→00000000000000E+000
2 -2.50000000000000E-001 -2.50000000000000E-001 2.50000000000000E-001,→00000000000000E+000
3 -2.50000000000000E-001 2.50000000000000E-001 -2.50000000000000E-001,→00000000000000E+000
4 -2.50000000000000E-001 2.50000000000000E-001 2.50000000000000E-001,→00000000000000E+000
5 2.50000000000000E-001 -2.50000000000000E-001 -2.50000000000000E-001,→00000000000000E+000
6 2.50000000000000E-001 -2.50000000000000E-001 2.50000000000000E-001,→00000000000000E+000

1.
1.
1.
1.
1.
1.

(continues on next page)

4.4. Maxwell + TDDFT multiscale simulation

71

SALMON document, Release v.1.1.0(continued from previous page)

7 2.50000000000000E-001,→00000000000000E+000
8 2.50000000000000E-001,→00000000000000E+000

2.50000000000000E-001 -2.50000000000000E-001

1.

2.50000000000000E-001

1.

2.50000000000000E-001

RT_Ac/Si_Ac_000000.data
The number in the file name specifies the iteration number. Various quantities at a time are shown as function ofmacroscopic position.
• column 1-3: grid number of macroscopic coordinate in 3D format.
• column 4-6: macroscopic vector potential• column 7-9: macroscopic electric field• column 10-12: macroscopic magnetic field• column 13-15: macroscopic current• column 16: electronic excitation energy per unit cell
• column 17: energy absorbed by electrons per unit cell
• column 18: energy of macroscopic electromagnetic fields per unit cell
# Macroscopic field distribution# IX,IY,IZ: Coordinate# Ac: Vector potential field# E: Electric field# B: Magnetic field# Jm: Matter current density# Eex: Electron excitation energy# Eabs: Absorbed energy# Eemf: Total EM field energy# 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:Jm_x[a.u.] 14:Jm_,→y[a.u.] 15:Jm_z[a.u.] 16:Eex[a.u./unitcell] 17:Eabs[a.u./unitcell] 18:Eemf[a.u./,→unitcell]-2000
1
1 0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000-1999
1
1 0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000-1998
1
1 0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000-1997
1
1 0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0. (continues on next page),→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000

72

Chapter 4. Exercises

SALMON document, Release v.1.1.0(continued from previous page)-1996
1
1 0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
...
252
1
1 0.00000000000000E+000 0.00000000000000E+000 0.
00000000000000E+000 0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
253
1
1 0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
254
1
1 0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
255
1
1 0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
256
1
1 0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000
0.00000000000000E+000 0.00000000000000E+000 0.
,→00000000000000E+000,→

RT_Ac/Si_Ac_vac.data
Vector potentials at vacuum points adjacent to the medium are shown, L for left and R for right adjacent point.
# Ac vacuum region# Data of Ac field at the end of media
# L:
0
1
1
# R:
5
1
1
# 1:Time[a.u.] 2:Ac_x(L)[a.u.] 3:Ac_y(L)[a.u.] 4:Ac_z(L)[a.u.] 5:Ac_x(R)[a.u.] 6:Ac_,→y(R)[a.u.] 7:Ac_z(R)[a.u.]
0.00000000 0.00000000000000E+000
0.00000000000000E+000
0.
,→00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000
0.
,→00000000000000E+000
0.08000000 0.00000000000000E+000
0.00000000000000E+000
0.
,→00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000
0.
,→00000000000000E+000
0.16000000 0.00000000000000E+000
0.00000000000000E+000
0.
,→00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000
0.
(continues on next page),→00000000000000E+000

4.4. Maxwell + TDDFT multiscale simulation

73

SALMON document, Release v.1.1.0(continued from previous page)0.24000000 0.00000000000000E+000
1.02802304891111E-015
3.34045640443765E,→016
0.00000000000000E+000
1.02802304891111E-015
3.34045640443765E-016
0.32000000 0.00000000000000E+000
5.19696825069140E-015
1.73169501167652E,→015
0.00000000000000E+000
5.19696825069140E-015
1.73169724492077E-015...
319.68000000 0.00000000000000E+000 -8.56815797183038E-007 -1.74158413235687E001
0.00000000000000E+000 -8.00468477308030E-007 -1.58038091464266E-001
319.76000000 0.00000000000000E+000 -8.57513903130219E-007 -1.74393964495627E,→001
0.00000000000000E+000 -8.01174071107012E-007 -1.58187516982663E-001
319.84000000 0.00000000000000E+000 -8.58202516138042E-007 -1.74627725814573E,→001
0.00000000000000E+000 -8.01876269144167E-007 -1.58336335855095E-001
319.92000000 0.00000000000000E+000 -8.58881726038604E-007 -1.74859695029779E,→001
0.00000000000000E+000 -8.02575101929425E-007 -1.58484539522173E-001
320.00000000 0.00000000000000E+000 -8.59551627002296E-007 -1.75089870177989E,→001
0.00000000000000E+000 -8.03270602482416E-007 -1.58632119495344E-001,→

M000001/Si_Ac_M.data
The number in the file name specifies the macroscopic grid point in a medium. Various quantities at a macroscopic
point are shown as functions of time.
# Local variable at macro point# Macropoint:111# Jm: Matter current density# Ac: External vector potential field# 1:Time[a.u.] 2:Ac_x[a.u.] 3:Ac_y[a.u.] 4:Ac_z[a.u.] 5:Jm_x[a.u.] 6:Jm_y[a.u.] 7:Jm_,→z[a.u.]
0.00000000 0.00000000000000E+000
0.00000000000000E+000
0.
,→00000000000000E+000
0.00000000000000E+000
0.00000000000000E+000
0.
,→00000000000000E+000
0.08000000 0.00000000000000E+000
0.00000000000000E+000
0.
,→00000000000000E+000-2.75496322261169E-012 -6.64693329538576E-012 -2.
,→15985341184321E-012
0.16000000 2.21567288859314E-013
5.34578094327944E-013
1.73705718053823E,→013-2.44154670033013E-012 -7.05287750131598E-012 -2.56975702246339E-012
0.24000000 6.39495414253759E-013
1.63535423011393E-012
5.53749512919215E,→013-2.13170597168112E-012 -7.46016650418711E-012 -2.97426987823802E-012
0.32000000 1.22886550624652E-012
3.33297163342029E-012
1.17193467844178E,→012-1.81810297340216E-012 -7.87600103950396E-012 -3.35839167619253E-012...
319.68000000 1.23027707032365E-003 -8.70482807641121E-007 -1.71017066989709E001
1.02881666841023E-007
4.92374979404618E-010 -3.32578810347408E-005
319.76000000 1.23227860920852E-003 -8.70992162244069E-007 -1.71172549338950E,→001
9.87865048046008E-008
4.85608114795546E-010 -3.45948031169888E-005
319.84000000 1.23427220321126E-003 -8.71495026996183E-007 -1.71326503499639E,→001
9.45989194632210E-008
4.78870087348624E-010 -3.59262231464884E-005
319.92000000 1.23625818911749E-003 -8.71991570086865E-007 -1.71478932689850E,→001
9.03230551511057E-008
4.72163059159496E-010 -3.72519512786483E-005
320.00000000 1.23823691081260E-003 -8.72481961985393E-007 -1.71629840326064E,→001
8.59631416251532E-008
4.65489301170927E-010 -3.85718005737764E-005,→

Si_gs_rt_multiscale.out
Standard output file.
74

Chapter 4. Exercises

BIBLIOGRAPHY[1] Masashi Noda, Kazuya Ishimura, Katsuyuki Nobusada, Kazuhiro Yabana, and Taisuke Boku. Massively-parallel
electron dynamics calculations in real-time and real-space: toward applications to nanostructures of more than
ten-nanometers in size. Journal of Computational Physics, 265:145–155, 2014.
[2] George F Bertsch, J-I Iwata, Angel Rubio, and Kazuhiro Yabana. Real-space, real-time method for the dielectric
function. Physical Review B, 62(12):7998, 2000.
[3] K. Yabana and G. F. Bertsch. Time-dependent local-density approximation in real time. Phys.
Rev.
B,
54:4484–4487,
Aug
1996.
URL:
https://link.aps.org/doi/10.1103/PhysRevB.54.4484,
doi:10.1103/PhysRevB.54.4484.
[4] Kazuhiro Yabana, T Sugiyama, Y Shinohara, T Otobe, and GF Bertsch. Time-dependent density functional theory
for strong electromagnetic fields in crystalline solids. Physical Review B, 85(4):045134, 2012.
[5] Shunsuke A. Sato and Kazuhiro Yabana. Maxwell + tddft multi-scale simulation for laser-matter interactions.
Journal of Advanced Simulation in Science and Engineering, 1(1):98–110, 2014. doi:10.15748/jasse.1.98.
[6] Yuta Hirokawa, Taisuke Boku, Shunsuke A Sato, and Kazuhiro Yabana. Electron dynamics simulation with timedependent density functional theory on large scale symmetric mode xeon phi cluster. In Parallel and Distributed
Processing Symposium Workshops, 2016 IEEE International, 1202–1211. IEEE, 2016.

75