エクササイス

はじめに

SALMONエクササイスへようこそ！

このエクササイスでは、SALMONの多岐にわたる応用をカバーする いくつかのサンプルを用いて、基本からSALMONの使い方を説明します。 以下では、UNIX/Linux OSの計算環境にあることを前提にします。 最初に、あなたの計算環境にSALMONをダウンロードしインストールすることが必要です。 まだ行っていない場合は、ダウンロードとインストールと実行に従い作業してください。

インストールと実行で述べたように、SALMONを実行するためには少なくとも 入力ファイルと擬ポテンシャルファイルが必要です。 以下では、いくつかのサンプル計算に対する入力ファイルを示し、その入力ファイルに 現れるネームリスト変数の簡単な説明を行います。 その入力ファイルを修正して、あなた自身が行いたい計算を実行することができるでしょう。 サンプルに含まれている元素の擬ポテンシャルも提供されています。 主要な出力ファイルの説明も行います。

以下では６つのエクササイスを紹介します。

最初の３つのエクササイス（エクササイス-1~3）は、孤立したアセチレン分子C2H2に対するものです。 もし孤立した系の電子ダイナミクス計算に興味がある場合は、これらのエクササイスをごらんください。 SALMONでは、通常最初に基底状態計算を行います。 これは、エクササイス-1で説明します。 基底状態計算が終わったのち、２つの電子ダイナミクス計算が用意されています。 エクササイス-2では、分子の分極率と光吸収を得る 実時間での線形光応答計算を示します。 エクササイス-3では、 パルス電場中にある分子の電子ダイナミクス計算を示します。

次の２つのエクササイス(エクササイス-4~5)は、結晶固体シリコンに対するものです。 もし無限周期系における電子ダイナミクス計算を学ぶことに興味があれば、これらのエクササイスを見てください。 小さな単位セルを持つ系の基底状態計算は容易であり、時間発展計算の方がはるかに計算時間がかかるため、 基底状態と時間発展の計算を一つのジョブとして実行することを推奨します。 以下の２つのエクササイスも、そのようになっています。 エクササイス-4では、結晶シリコンの誘電関数を得るための 線形応答性質の計算を示します。 エクササイス5 では、パルス電場により結晶シリコンに誘起される電子ダイナミクス計算を示します。

最後のエクササイス(エクササイス-6)は、バルクシリコンにおけるパルス光の入射と伝播に対して、 パルス光の電磁場に対するマクスウェル方程式と単位セルの電子ダイナミクス計算を結合したものです。 ものです。 これは大きな計算時間を必要とするため、大規模並列スパコンの利用が推奨されます。 エクササイス-6で、 バルクシリコンの表面に垂直に入射する直線偏光パルス光の入射計算を示します。

C2H2 (孤立分子)

エクササイス-1: C2H2分子の基底状態

このエクササイスでは、静的コーン・シャム方程式を解くことにより、アセチレン分子(C2H2)の基底状態計算を学びます。 このエクササイスは、分子やナノ粒子のような孤立した系に対して、SALMONを用いた計算を行う準備をどのように すれば良いかを知るのに有用です。今のところ、SALMONで構造最適化を実行することはできないことに注意して ください。分子の原子位置は入力ファイルて指定され、計算の過程では固定されます。

入力ファイル

コードを実行するために、以下のファイルが必要です。

file name	description
C2H2_gs.inp	ネームリスト変数とそれらの値を含む入力ファイル
C_rps.dat	炭素原子の擬ポテンシャル
H_rps.dat	水素原子の擬ポテンシャル

• 上記の３つのファイル（圧縮ファイル）は、以下からダウンロードできます:

 圧縮された入力ファイルと擬ポテンシャルファイルをダウンロード

• 入力ファイルC2H2_gs.inpでは、ネームリスト変数が指定されています。それらの多くは、

基底状態計算を実行するために必須です。それらの説明を以下に示します:

入力ファイルの説明(C2H2分子の基底状態)

あなたが計算をしたい他の系のための入力ファイルを準備するのに、この情報は有用です。

入力ファイルで用いることのできるネームリスト変数の完全なリストは、ダウンロードファイルのSALMON/manual/input_variables.mdにあります。

出力ファイル

計算を実行した後、あなたがコードを実行したディレクトリに以下の出力ファイルが生成されています。

file name	description
C2H2_info.data	基底状態の解の情報
dns.cube	電子密度のキューブファイル
elf.cube	電子局在関数(ELF)
psi1.cube, psi2.cube, ...	電子軌道
dos.data	状態密度
pdos1.data, pdos2.data, ...	射影された状態密度
C2H2_gs.bin	実時間計算で用いるバイナリ出力ファイル

• 上記のファイル（バイナリファイルC2H2_gs.binを除き、圧縮ファイル)は、以下からダウンロードすることができます:

圧縮された出力ファイルのダウンロード

• 軌道エネルギーのような主要な計算結果はC2H2_info.dataに含まれています。

C2H2_info.dataと他の出力ファイルは、以下で説明されています:

出力ファイル(C2H2分子の基底状態)の説明

Images

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

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

Exercise-2: Polarizability and photoabsorption of C2H2 molecule

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

Input files

To run the code, the input file C2H2_rt_response.inp that contains namelist variables and their values for the linear response calculation is required. The binary file C2H2_gs.bin that is created in the ground state calculation and pseudopotential files are also required. The pseudopotential files should be the same as those used in the ground state calculation.

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

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

 Download zipped input file

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

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

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

Output files

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

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

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

Download zipped output files

• Explanations of the output files are given in:

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

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

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

Input files

To run the code, following files are used. The C2H2.data file is created in the ground state calculation. Pseudopotential files are already used in the ground state calculation. Therefore, C2H2_rt_pulse.inp that specifies namelist variables and their values for the pulsed electric field calculation is the only file that the users need to prepare.

file name	description
C2H2_rt_pulse.inp	input file that contain namelist variables and their values.
C_rps.dat	pseodupotential file for Carbon
H_rps.dat	pseudopotential file for Hydrogen
C2H2.data	binary file created in the ground state calculation

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

 Download zipped input file

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

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

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

Output files

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

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

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

Download zipped output files

• Explanations of the files are described in:

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

Crystalline silicon (periodic solids)

Exercise-4: Dielectric function of crystalline silicon

In this exercise, we learn the linear response calculation of the crystalline silicon of a diamond structure. Calculation is done in a cubic unit cell that contains eight silicon atoms. Since the ground state calculation costs much less computational time than the time evolution calculation, both calculations are successively executed. After finishing the ground state calculation, an impulsive perturbation is applied to all electrons in the unit cell along z direction. Since the dielectric function is isotropic in the diamond structure, calculated dielectric function should not depend on the direction of the perturbation. During the time evolution, electric current averaged over the unit cell volume is calculated. A time-frequency Fourier transformation of the electric current gives us a frequency-dependent conductivity. The dielectric function may be obtained from the conductivity using a standard relation.

Input files

To run the code, following files are used:

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

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

 Download zipped input and pseudopotential files

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

Explanations of input files (dielectric function of crystalline silicon)

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

Output files

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

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

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

Download zipped output files

• Explanations of the output files are described in:

Explanation of output fiels (dielectric function of crystalline silicon)

Exercise-5: Electron dynamics in crystalline silicon under a pulsed electric field

In this exercise, we learn the calculation of electron dynamics in a unit cell of crystalline silicon of a diamond structure. Calculation is done in a cubic unit cell that contains eight silicon atoms. Since the ground state calculation costs much less computational time than the time evolution calculation, both calculations are successively executed. After finishing the ground state calculation, a pulsed electric field that has cos^2 envelope shape is applied. The parameters that characterize the pulsed field such as magnitude, frequency, polarization, and carrier envelope phase are specified in the input file.

Input files

To run the code, following files are used:

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

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

 Download zipped input and pseudopotential files

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

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

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

Output files

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

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

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

Download zipped output files

• Explanations of the output files are described in:

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

Maxwell + TDDFT multiscale simulation

Exercise-6: Pulsed-light propagation through a silicon thin film

In this exercise, we learn the calculation of the propagation of a pulsed light through a thin film of crystalline silicon. We consider a silicon thin film of ?? nm thickness, and an irradiation of a few-cycle, linearly polarized pulsed light normally on the thin film. First, to set up initial orbitals, the ground state calculation is carried out. The pulsed light locates in the vacuum region in front of the thin film. The parameters that characterize the pulsed light such as magnitude and frequency are specified in the input file. The calculation ends when the reflected and transmitted pulses reach the vacuum region.

Input files

To run the code, following files are used:

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

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

 Download zipped input and pseudopotential files

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

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

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

Output files

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

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

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

Download zipped output files

• Explanations of the output files are described in:

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