.. _Exercises: Exercises ==================== Getting started --------------- Welcome to SALMON Exercises! In these exercises, we explain the use of SALMON from the very beginning, taking a few samples that cover applications of SALMON in several directions. We assume that you are in the computational environment of UNIX/Linux OS. First you need to download and install SALMON in your computational environment. If you have not yet done it, do it following the instruction, `download `_ and :any:`install-and-run`. As described in :any:`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 input keywords 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 10 exercises. First 3 exercises (Exercise-1 ~ 3) are for an isolated molecule, acetylene C2H2. If you are interested in learning electron dynamics calculations in isolated systems, please look into these exercises. In SALMON, we usually calculate the ground state solution first using a static density functional theory (DFT). This is illustrated in :any:`Exercise-1 `. After finishing the ground state calculation, two exercises of electron dynamics calculations based on time-dependent density functional theory (TDDFT) are prepared. :any:`Exercise-2 ` illustrates the calculation of linear optical responses in real time, obtaining polarizability and photoabsorption of the molecule. :any:`Exercise-3 ` illustrates the calculation of electron dynamics in the molecule under a pulsed electric field. Next 3 exercises (Exercise-4 ~ 6) are for a crystalline solid, silicon. If you are interested in learning electron dynamics calculations in extended periodic systems, please look into these exercises. :any:`Exercise-4 ` illustrates the ground state calculation of the crystalline silicon based on DFT. :any:`Exercise-5 ` illustrates the calculation of linear response properties of the crystalline silicon based on TDDFT to obtain the dielectric function. :any:`Exercise-6 ` illustrates the calculation of electron dynamics in the crystalline silicon induced by a pulsed electric field. Exercise-7 is for a simultaneous calculation of the propagation of a pulsed light and electronic motion in a bulk silicon, coupling Maxwell equations for the electromagnetic fields of the pulsed light and the electron dynamics in the unit cells based on TDDFT. This calculation is quite time-consuming and is recommended to execute using massively parallel supercomputers. :any:`Exercise-7 ` illustrates the calculation of a linearly polarized pulsed light irradiating normally on a surface of a bulk silicon. Next 2 exercises (Exercise-8 ~ 9) are for geometry optimization based on DFT and Ehrenfest molecular dynamics based on TDDFT for an isolated molecule, acetylene C2H2. :any:`Exercise-8 ` illustrates the geometry optimization in the ground state. :any:`Exercise-9 ` illustrates the Ehrenfest molecular dynamics induced by a pulsed electric field. :any:`Exercise-10 ` is for a macroscopic light propagation through a metallic nanosphere solving Maxwell equations. The optical response of the nanosphere is described by a dielectric function. Finite-Difference Time-Domain (FDTD) method is used to calculated the three-dimensional light propagation. Input files of exercises are included in SALMON, in the directory ``SALMON/samples/exercise_##_/``. C2H2 (isolated molecules) ------------------------- .. _exercise-1: Exercise-1: Ground state of C2H2 molecule ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In this exercise, we learn the calculation of the ground state 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. Acetylene molecule is a linear chain molecule composed of two Carbon atoms and two Hydrogen atoms. .. image:: images/exc1/acetylene.png :scale: 20% In SALMON, we use a three-dimensional (3D) uniform grid system to express physical quantities such as electron orbitals. .. image:: images/exc1/acetylene_grid.png :scale: 20% Input files ^^^^^^^^^^^ To run the code, following files in the directory ``SALMON/samples/exercise_01_C2H2_gs/`` are used: +-----------------------------------+-----------------------------------+ | file name | description | +-----------------------------------+-----------------------------------+ | *C2H2_gs.inp* | input file that contains input | | | keywords and their values | +-----------------------------------+-----------------------------------+ | *C_rps.dat* | pseodupotential file for carbon | | | atom | +-----------------------------------+-----------------------------------+ | *H_rps.dat* | pseudopotential file for hydrogen | | | atom | +-----------------------------------+-----------------------------------+ Pseudopotential files are needed for two elements, Carbon (C) and Hydrogen (H). The pseudopoential depends on the angular momentum, and looks as follows (for Carbon). .. image:: images/exc1/C_rps_pot.png :scale: 40% In the input file *C2H2_gs.inp*, input keywords are specified. Most of them are mandatory to execute the ground state calculation. This will help you to prepare an input file for other systems that you want to calculate. A complete list of the input keywords that can be used in the input file can be found in :any:`List of input keywords `. :: !########################################################################################! ! Excercise 01: Ground state of C2H2 molecule ! !----------------------------------------------------------------------------------------! ! * The detail of this excercise is expained in our manual(see chapter: 'Exercises'). ! ! The manual can be obtained from: https://salmon-tddft.jp/documents.html ! ! * Input format consists of group of keywords like: ! ! &group ! ! input keyword = xxx ! ! / ! ! (see chapter: 'List of input keywords' in the manual) ! !----------------------------------------------------------------------------------------! ! * Conversion from unit_system = 'a.u.' to 'A_eV_fs': ! ! Length: 1 [a.u.] = 0.52917721067 [Angstrom] ! ! Energy: 1 [a.u.] = 27.21138505 [eV] ! ! Time : 1 [a.u.] = 0.02418884326505 [fs] ! !########################################################################################! &calculation !type of theory theory = 'dft' / | :any:`theory ` specifies which theoretical method is used in the calculation. :: &control !common name of output files sysname = 'C2H2' / | :any:`sysname ` is a prefix for filenames of output files. :: &units !units used in input and output files unit_system = 'A_eV_fs' / | :any:`unit_system ` specifies which unit system is used in the input and output files. :: &system !periodic boundary condition yn_periodic = 'n' !number of elements, atoms, electrons and states(orbitals) nelem = 2 natom = 4 nelec = 10 nstate = 6 / | :any:`yn_periodic ` specifies whether or not periodic boundary condition is applied. | :any:`nelem ` is the number of elements in the system. | :any:`natom ` is the number of atoms in the system. | :any:`nelec ` is the number of electrons in the system. | :any:`nstate ` is the number of orbitals that are used in the calculation. :: &pseudo !name of input pseudo potential file file_pseudo(1) = './C_rps.dat' file_pseudo(2) = './H_rps.dat' !atomic number of element izatom(1) = 6 izatom(2) = 1 !angular momentum of pseudopotential that will be treated as local lloc_ps(1) = 1 lloc_ps(2) = 0 !--- Caution ---------------------------------------! ! Indices must correspond to those in &atomic_coor. ! !---------------------------------------------------! / | :any:`file_pseudo(n) ` specifies the filename of the pseudopotential file of the n-th element. | :any:`izatom(n) ` is the atomic number of the n-th element. | :any:`lloc_ps(n) ` specifies which angular momentum component is chosen as the local potential for the n-th element. :: &functional !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).) xc = 'PZ' / | :any:`xc ` specifies the exchange-correlation potential to be used in the calculation. :: &rgrid !spatial grid spacing(x,y,z) dl(1:3) = 0.25d0, 0.25d0, 0.25d0 !number of spatial grids(x,y,z) num_rgrid(1:3) = 64, 64, 64 / | :any:`dl(i) ` specifies the spatial grid spacing in i-th direction. | :any:`num_rgrid(i) ` specifies the number of grid points in i-th direction. :: &scf !maximum number of scf iteration and threshold of convergence nscf = 300 threshold = 1.0d-9 / | :any:`nscf ` specifies the maximum number of SCF iterations. | :any:`threshold ` specifies the threshold to judge the convergence. :: &analysis !output of all orbitals, density, !density of states, projected density of states, !and electron localization function yn_out_psi = 'y' yn_out_dns = 'y' yn_out_dos = 'y' yn_out_pdos = 'y' yn_out_elf = 'y' / | :any:`yn_out_psi `, :any:`yn_out_dns `, :any:`yn_out_dos `, :any:`yn_out_pdos `, :any:`yn_out_elf ` specify output files that are generated after the calculation. :: &atomic_coor !cartesian atomic coodinates '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 !--- Format ---------------------------------------------------! ! 'symbol' x y z index(correspond to that of pseudo potential) ! !--------------------------------------------------------------! / | :any:`&atomic_coor <&atomic_coor>` specifies spatial coordinates of atoms. Execusion ^^^^^^^^^ In a multiprocess environment, calculation will be executed as $ mpiexec -n NPROC salmon < C2H2_gs.inp > C2H2_gs.out where NPROC is the number of MPI processes. A standard output will be stored in the file ``C2H2_gs.out``. .. _output-files-1: Output files ^^^^^^^^^^^^ After the calculation, following output files and a directory are created in the directory that you run the code in addition to the standard output file, +-------------------------------------+-----------------------------------+ | name | description | +-------------------------------------+-----------------------------------+ | *C2H2_info.data* | information on ground state | | | solution | +-------------------------------------+-----------------------------------+ | *C2H2_eigen.data* | orbital energies | +-------------------------------------+-----------------------------------+ | *C2H2_k.data* 　 | k-point distribution | | | (for isolated systems, only | | | gamma point is described) | +-------------------------------------+-----------------------------------+ | *data_for_restart* | directory where files used in | | | the real-time calculation are | | | contained | +-------------------------------------+-----------------------------------+ | *psi_ob1.cube*, *psi_ob2.cube*, ... | electron orbitals | +-------------------------------------+-----------------------------------+ | *dns.cube* | a cube file for electron density | +-------------------------------------+-----------------------------------+ | *dos.data* | density of states | +-------------------------------------+-----------------------------------+ | *pdos1.data*, *pdos2.data*, ... | projected density of states | +-------------------------------------+-----------------------------------+ | *elf.cube* | electron localization function | | | (ELF) | +-------------------------------------+-----------------------------------+ | *PS_C_KY_n.dat* | information on pseodupotential | | | file for carbon atom | +-------------------------------------+-----------------------------------+ | *PS_H_KY_n.dat* | information on pseodupotential | | | file for hydrogen atom | +-------------------------------------+-----------------------------------+ | You may download the above files (zipped file, except for the directory *data_for_restart*) from: | https://salmon-tddft.jp/webmanual/v_2_0_1/exercise_zip_files/01_C2H2_gs.zip We first explain the standard output file. In the beginning of the file, input variables used in the calculation are shown. :: ############################################################################## # SALMON: Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience # # Version 2.0.1 # ############################################################################## Libxc: [disabled] theory= dft use of real value orbitals = T ====== MPI distribution: nproc_k : 1 nproc_ob : 1 nproc_rgrid : 1 1 2 OpenMP parallelization: number of threads : 256 ......... After that, the SCF loop starts. At each iteration step, the total energy as well as orbital energies and some other quantities are displayed. :: ----------------------------------------------- iter= 1 Total Energy= -197.59254070 Gap= -20.17834599 Vh iter= 234 1 -29.9707 2 -28.3380 3 -13.0123 4 5.8457 5 -9.9213 6 -14.3326 iter and int_x|rho_i(x)-rho_i-1(x)|dx/nelec = 1 0.31853198E+00 Ne= 10.0000000000000 ----------------------------------------------- iter= 2 Total Energy= -280.97950515 Gap= -9.59770609 Vh iter= 247 1 -17.4334 2 -24.4941 3 -20.1872 4 0.8020 5 -3.4058 6 -8.7957 iter and int_x|rho_i(x)-rho_i-1(x)|dx/nelec = 2 0.54493263E+00 Ne= 10.0000000000000 ----------------------------------------------- iter= 3 Total Energy= -295.67034640 Gap= -6.90359156 Vh iter= 229 1 -16.0251 2 -19.7759 3 -17.6765 4 -0.9015 5 -2.9323 6 -7.8050 iter and int_x|rho_i(x)-rho_i-1(x)|dx/nelec = 3 0.13010987E+00 Ne= 10.0000000000000 When the convergence criterion is satisfied, the SCF calculation ends. :: ----------------------------------------------- iter= 162 Total Energy= -339.69525272 Gap= 6.78870999 Vh iter= 1 1 -18.4106 2 -13.9966 3 -12.4163 4 -7.3386 5 -7.3386 6 -0.5498 iter and int_x|rho_i(x)-rho_i-1(x)|dx/nelec = 162 0.50237787E-08 Ne= 9.99999999999999 ----------------------------------------------- iter= 163 Total Energy= -339.69525269 Gap= 6.78870999 Vh iter= 1 1 -18.4106 2 -13.9966 3 -12.4163 4 -7.3386 5 -7.3386 6 -0.5498 iter and int_x|rho_i(x)-rho_i-1(x)|dx/nelec = 163 0.69880308E-09 Ne= 9.99999999999999 #GS converged at 164 : 0.69880308E-09 Next, the force acting on ions and some other information related to orbital energies are shown. :: ===== force ===== 1 -0.33652081E-05 0.16854696E-04 -0.59496450E+00 2 -0.59222259E-06 0.24915590E-05 0.57651725E+00 3 -0.37839836E-05 0.20304090E-04 0.59493028E+00 4 -0.86779607E-06 0.39560274E-05 -0.57651738E+00 orbital energy information------------------------------- Lowest occupied orbital -0.676576619015730 Highest occupied orbital (HOMO) -0.269686750876529 Lowest unoccupied orbital (LUMO) -2.020624936948345E-002 Highest unoccupied orbital -2.020624936948345E-002 HOMO-LUMO gap 0.249480501507045 Physicaly upper bound of eps(omega) 0.656370369646246 --------------------------------------------------------- Lowest occupied orbital[eV] -18.4105868958642 Highest occupied orbital (HOMO)[eV] -7.33855002098465 Lowest unoccupied orbital (LUMO)[eV] -0.549840032009334 Highest unoccupied orbital[eV] -0.549840032009334 HOMO-LUMO gap[eV] 6.78870998897532 Physicaly upper bound of eps(omega)[eV] 17.8607468638548 --------------------------------------------------------- writing restart data... writing completed. In the directory ``data_for_restart``, files that will be used in the next-step time evolution calculations are stored. Other output files include following information. **C2H2_info.data** Calculated orbital and total energies as well as parameters specified in the input file are shown. **C2H2_eigen.data** Orbital energies. :: #esp: single-particle energies (eigen energies) #occ: occupation numbers, io: orbital index # 1:io, 2:esp[eV], 3:occ **C2H2_k.data** k-point distribution(for isolated systems, only gamma point is described). :: # 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] # coefficients (2*pi/a [a.u.]) in kx, ky, kz **psi_ob1.cube, psi_ob2.cube, ...** Cube files for electron orbitals. The number in the filename indicates the index of the orbital. Atomic unit is adopted in all cube files. **dns.cube** A cube file for electron density. **dos.data** A file for density of states. The units used in this file are affected by the input parameter, ``unit_system`` in ``&unit``. **elf.cube** A cube file for electron localization function (ELF). We show several image that are created from the output files. * **Highest occupied molecular orbital (HOMO)** The output files *psi_ob1.cube*, *psi_ob2.cube*, ... are used to create the image. .. image:: images/exc1/HOMO.png :scale: 20% * **Electron density** The output files *dns.cube*, ... are used to create the image. .. image:: images/exc1/Dns.png :scale: 20% * **Electron localization function** The output files *elf.cube*, ... are used to create the image. .. image:: images/exc1/Elf.png :scale: 20% .. _exercise-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 distribution of the molecule. This exercise should be carried out after finishing the ground state calculation that was explained in :any:`Exercise-1 `. Polarizability :math:`\alpha_{\mu \nu}(t)` is the basic quantity that characterizes optical responses of molecules and nano-particles, where :math:`\mu, \nu` indicate Cartesian components, :math:`\mu, \nu = x,y,z`. The polarizability :math:`\alpha_{\mu \nu}(t)` relates the :math:`\mu` component of the electric dipole moment at time :math:`t`, :math:`p_{\mu}(t)`, with the :math:`\nu` component of the electric field at time :math:`t'`, :math:`p_{\mu}(t) = \sum_{\nu=x,y,z} \alpha_{\mu \nu}(t-t') E_{\nu}(t').` We introduce a frequency-dependent polarizability by the time-frequency Fourier transformation of the polarizability, :math:`\tilde \alpha_{\mu \nu}(\omega) = \int dt e^{i\omega t} \alpha_{\mu \nu}(t).` The imaginary part of the frequency-dependent polarizability is related to the photoabsorption cross section :math:`\sigma(\omega)` by :math:`\sigma(\omega) = \frac{4\pi \omega}{c} \frac{1}{3} \sum_{\mu=x,y,z} {\rm Im} \tilde \alpha_{\mu \mu}(\omega).` The photoabsorption cross section is also related to the oscillator strength distribution by :math:`\sigma(\omega) = \frac{2\pi^2 e^2}{mc} \frac{df(\omega)}{d\omega}.` In SALMON, the polarizability is calculated in time domain. First the ground state orbital :math:`\phi_i(\mathbf{r})` that satisfies the Kohn-Sham equation, :math:`H_{\rm KS} \phi_i(\mathbf{r}) = \epsilon_i \phi_i(\mathbf{r}),` is prepared. Then an impulsive force given by the potential :math:`V_{\rm ext}(\mathbf{r},t) = I \delta(t) z,` is applied to all electrons in the C2H2 molecule along the molecular axis which we take :math:`z` axis. :math:`I` is the magnitude of the impulse, and :math:`\delta(t)` is the Dirac's delta function. The orbital is distorted by the impulsive force at :math:`t=0`. Immediately after the impulse is applied, the orbital becomes :math:`\psi_i(\mathbf{r},t=0_+) = e^{iIz/\hbar} \phi_i(\mathbf{r}).` After the impulsive force is applied at :math:`t=0`, a time evolution calculation is carried out without any external fields, :math:`i\hbar \frac{\partial}{\partial t} \psi_i(\mathbf{r},t) = H_{\rm KS}(t) \psi_i(\mathbf{r},t).` During the time evolution, the electric dipole moment given by :math:`p_z(t) = \int d\mathbf{r} (-ez) \sum_i \vert \psi_i(\mathbf{r},t) \vert^2,` 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 by :math:`\tilde \alpha_{zz}(\omega) = - \frac{e}{I} \int dt e^{i\omega t} p_z(t).` .. _input-files-1: Input files ^^^^^^^^^^^ To run the code, following files are necessary: +-----------------------------------+---------------------------------------------------------------+ | file name | description | +-----------------------------------+---------------------------------------------------------------+ | *C2H2_rt_response.inp* | input file that contain input | | | keywords and their values. | +-----------------------------------+---------------------------------------------------------------+ | *C_rps.dat* | pseodupotential file for carbon | +-----------------------------------+---------------------------------------------------------------+ | *H_rps.dat* | pseudopotential file for hydrogen | +-----------------------------------+---------------------------------------------------------------+ | *restart* | | directory created in the ground state calculation | | | | (rename the directory from *data_for_restart* to *restart*) | +-----------------------------------+---------------------------------------------------------------+ First three files are prepared in the directory ``SALMON/samples/exercise_02_C2H2_lr/``. The file *C2H2_rt_response.inp* that contains input keywords and their values. The pseudopotential files should be the same as those used in the ground state calculation. In the directory *restart*, those files created in the ground state calculation and stored in the directory *data_for_restart* are included. Therefore, copy the directory as ``cp -R data_for_restart restart`` if you calculate at the same directory as you did the ground state calculation. In the input file *C2H2_rt_response.inp*, input keywords are specified. Most of them are mandatory to execute the 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 input keywords that can be used in the input file can be found in :any:`List of input keywords `. :: !########################################################################################! ! Excercise 02: Polarizability and photoabsorption of C2H2 molecule ! !----------------------------------------------------------------------------------------! ! * The detail of this excercise is expained in our manual(see chapter: 'Exercises'). ! ! The manual can be obtained from: https://salmon-tddft.jp/documents.html ! ! * Input format consists of group of keywords like: ! ! &group ! ! input keyword = xxx ! ! / ! ! (see chapter: 'List of input keywords' in the manual) ! !----------------------------------------------------------------------------------------! ! * Conversion from unit_system = 'a.u.' to 'A_eV_fs': ! ! Length: 1 [a.u.] = 0.52917721067 [Angstrom] ! ! Energy: 1 [a.u.] = 27.21138505 [eV] ! ! Time : 1 [a.u.] = 0.02418884326505 [fs] ! !----------------------------------------------------------------------------------------! ! * Copy the ground state data directory('data_for_restart') (or make symbolic link) ! ! calculated in 'samples/exercise_01_C2H2_gs/' and rename the directory to 'restart/' ! ! in the current directory. ! !########################################################################################! &calculation !type of theory theory = 'tddft_response' / | :any:`theory ` specifies which theoretical method is used in the calculation. :: &control !common name of output files sysname = 'C2H2' / | :any:`sysname ` is a prefix for filenames of output files. :: &units !units used in input and output files unit_system = 'A_eV_fs' / | :any:`unit_system ` specifies which unit system is used in the input and output files. :: &system !periodic boundary condition yn_periodic = 'n' !number of elements, atoms, electrons and states(orbitals) nelem = 2 natom = 4 nelec = 10 nstate = 6 / | :any:`yn_periodic ` specifies whether or not periodic boundary condition is applied. | :any:`nelem ` is the number of elements in the system. | :any:`natom ` is the number of atoms in the system. | :any:`nelec ` is the number of electrons in the system. | :any:`nstate ` is the number of orbitals that are used in the calculation. :: &pseudo !name of input pseudo potential file file_pseudo(1) = './C_rps.dat' file_pseudo(2) = './H_rps.dat' !atomic number of element izatom(1) = 6 izatom(2) = 1 !angular momentum of pseudopotential that will be treated as local lloc_ps(1) = 1 lloc_ps(2) = 0 !--- Caution ---------------------------------------! ! Indices must correspond to those in &atomic_coor. ! !---------------------------------------------------! / | :any:`file_pseudo(n) ` specifies the filename of the pseudopotential file of the n-th element. | :any:`izatom(n) ` is the atomic number of the n-th element. | :any:`lloc_ps(n) ` specifies which angular momentum component is chosen as the local potential for the n-th element. :: &functional !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).) xc = 'PZ' / | :any:`xc ` specifies the exchange-correlation potential to be used in the calculation. :: &rgrid !spatial grid spacing(x,y,z) dl(1:3) = 0.25d0, 0.25d0, 0.25d0 !number of spatial grids(x,y,z) num_rgrid(1:3) = 64, 64, 64 / | :any:`dl(i) ` specifies the spatial grid spacing in i-th direction. | :any:`num_rgrid(i) ` specifies the number of grid points in i-th direction. :: &tgrid !time step size and number of time grids(steps) dt = 1.25d-3 nt = 5000 / | :any:`dt` specifies the time step. | :any:`nt` is the number of time steps for the time propagation. :: &emfield !envelope shape of the incident pulse('impulse': impulsive field) ae_shape1 = 'impulse' !polarization unit vector(real part) for the incident pulse(x,y,z) epdir_re1(1:3) = 0.0d0, 0.0d0, 1.0d0 !--- Caution ---------------------------------------------------------! ! Defenition of the incident pulse is wrriten in: ! ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 ! !---------------------------------------------------------------------! / | :any:`ae_shape1 ` specifies the envelope of the field. For a linear response calculation, ``as_shape1='impulse'`` is used. It indicates that a weak impulsive perturbation is applied at :math:`t=0`. | :any:`epdir_re1(i) ` specifies the i-th component of the real part of the polarization unit vector. :: &analysis !energy grid size and number of energy grids for output files de = 1.0d-2 nenergy = 3000 / | :any:`de` specifies the energy grid size for frequency-domain analysis. | :any:`nenergy` specifies the number of energy grid points for frequency-domain analysis. :: &atomic_coor !cartesian atomic coodinates '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 !--- Format ---------------------------------------------------! ! 'symbol' x y z index(correspond to that of pseudo potential) ! !--------------------------------------------------------------! / | :any:`&atomic_coor <&atomic_coor>` specifies spatial coordinates of atoms. Execusion ^^^^^^^^^ Before execusion, remember to copy the directory *restart* that is created in the ground state calculation as *data_for_restart* in the present directory. In a multiprocess environment, calculation will be executed as $ mpiexec -n NPROC salmon < C2H2_rt_response.inp > C2H2_rt_response.out where NPROC is the number of MPI processes. A standard output will be stored in the file ``C2H2_rt_response.out``. .. _output-files-2: Output files ^^^^^^^^^^^^ After the calculation, following output files are created in the directory that you run the code, +-----------------------------------+-----------------------------------+ | file name | description | +-----------------------------------+-----------------------------------+ | *C2H2_response.data* | polarizability and oscillator | | | strength distribution as | | | functions of energy | +-----------------------------------+-----------------------------------+ | *C2H2_rt.data* | | components of | | | change of dipole moment | | | (electrons/plus definition) | | | | and total dipole moment | | | (electrons/minus + ions/plus) | | | as functions of time | +-----------------------------------+-----------------------------------+ | *C2H2_rt_energy.data* | components of | | | total energy | | | and difference of total energy | | | as functions of time | +-----------------------------------+-----------------------------------+ | *PS_C_KY_n.dat* | information on pseodupotential | | | file for carbon atom | +-----------------------------------+-----------------------------------+ | *PS_H_KY_n.dat* | information on pseodupotential | | | file for hydrogen atom | +-----------------------------------+-----------------------------------+ | You may download the above files (zipped file) from: | https://salmon-tddft.jp/webmanual/v_2_0_1/exercise_zip_files/02_C2H2_lr.zip We first explain the standard output file. In the beginning of the file, input variables used in the calculation are shown. :: ############################################################################## # SALMON: Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience # # Version 2.0.1 ############################################################################## Libxc: [disabled] theory= tddft_response Total time step = 5000 Time step[fs] = 1.250000000000000E-003 Energy range = 3000 Energy resolution[eV]= 1.000000000000000E-002 Field strength[a.u.] = 1.000000000000000E-002 use of real value orbitals = F ====== ......... After that, the time evolution loop starts. At every 10 iteration steps, the time, dipole moments in three Cartesian directions, the total number of electrons, the total energy, and the number of iterations solving the Poisson equation are displayed. :: time-step time[fs] Dipole moment(xyz)[A] electrons Total energy[eV] iterVh #---------------------------------------------------------------------- 10 0.01250000 -0.56521137E-07 -0.28812833E-07 -0.25558983E-01 10.00000000 -339.68150366 34 20 0.02500000 -0.19835467E-06 -0.10147641E-06 -0.45169126E-01 9.99999999 -339.68147442 49 30 0.03750000 -0.37937911E-06 -0.19537418E-06 -0.57843871E-01 9.99999999 -339.68146891 45 40 0.05000000 -0.56465010E-06 -0.29324906E-06 -0.64072126E-01 9.99999999 -339.68146804 38 50 0.06250000 -0.73343753E-06 -0.38431758E-06 -0.65208422E-01 9.99999999 -339.68146679 25 60 0.07500000 -0.87559727E-06 -0.46276791E-06 -0.62464066E-01 9.99999999 -339.68146321 35 70 0.08750000 -0.98769124E-06 -0.52594670E-06 -0.56740338E-01 9.99999998 -339.68145535 20 80 0.10000000 -0.10701350E-05 -0.57309375E-06 -0.48483747E-01 9.99999998 -339.68144840 40 90 0.11250000 -0.11253992E-05 -0.60455485E-06 -0.38296037E-01 9.99999998 -339.68144186 21 Explanations of other output files are given below: **C2H2_rt.data** Results of time evolution calculation for vector potential, electric field, and dipole moment. In the first several lines, explanations of included data are given. :: # 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 # ddm_e: Change of dipole moment (electrons/plus definition) # dm: Total dipole moment (electrons/minus + ions/plus) # 1:Time[fs] 2:Ac_ext_x[fs*V/Angstrom] 3:Ac_ext_y[fs*V/Angstrom] 4:Ac_ext_z[fs*V/Angstrom] 5:E_ext_x[V/Angstrom] 6:E_ext_y[V/Angstrom] 7:E_ext_z[V/Angstrom] 8:Ac_tot_x[fs*V/Angstrom] 9:Ac_tot_y[fs*V/Angstrom] 10:Ac_tot_z[fs*V/Angstrom] 11:E_tot_x[V/Angstrom] 12:E_tot_y[V/Angstrom] 13:E_tot_z[V/Angstrom] 14:ddm_e_x[Angstrom] 15:ddm_e_y[Angstrom] 16:ddm_e_z[Angstrom] 17:dm_x[Angstrom] 18:dm_y[Angstrom] 19:dm_z[Angstrom] Using first column (time in femtosecond) and 19th column (dipole moment in :math:`z` direction), the following graph can be drawn. .. image:: images/exc2/exc2-dipole.png :scale: 40% The dipole moment shows oscillations in femtosecond time scale that reflec electronic excitations. **C2H2_response.data** Time-frequency Fourier transformation of the dipole moment gives the polarizability and the strength function. :: # Fourier-transform spectra: # alpha: Polarizability # df/dE: Strength function # 1:Energy[eV] 2:Re(alpha_x)[Augstrom^2/V] 3:Re(alpha_y)[Augstrom^2/V] 4:Re(alpha_z)[Augstrom^2/V] 5:Im(alpha_x)[Augstrom^2/V] 6:Im(alpha_y)[Augstrom^2/V] 7:Im(alpha_z)[Augstrom^2/V] 8:df_x/dE[none] 9:df_y/dE[none] 10:df_z/dE[none] Using first column (energy in electron-volt) and 10th column (oscillator strength distribution in :math:`z` direction), the following graph can be drawn. .. image:: images/exc2/exc2-response.png :scale: 40% There appears many peaks above the HOMO-LUMO gap energy. The strong excitation appears at around 9.3 eV. **C2H2_rt_energy.data** Energies are stored as functions of time. :: # Real time calculation: # Eall: Total energy # Eall0: Initial energy # 1:Time[fs] 2:Eall[eV] 3:Eall-Eall0[eV] *Eall* and *Eall-Eall0* are total energy and electronic excitation energy, respectively. .. _exercise-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 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 :any:`Exercise-1 `. In the calculation, a pulsed electric field specified by the following vector potential will be used, :math:`A(t) = - \frac{E_0}{\omega} \hat z \cos^2 \frac{\pi}{T} \left( t - \frac{T}{2} \right) \sin \omega \left( t - \frac{T}{2} \right), \hspace{5mm} (0 < t < T).` The electric field is given by :math:`E(t) = -(1/c)(dA(t)/dt)`. The parameters that characterize the pulsed field such as the amplitude :math:`E_0`, frequency :math:`\omega`, pulse duration :math:`T`, polarization direction :math:`\hat z`, are specified in the input file. In the time dependent Kohn-Sham equation, the external field is included as the scalar potential, :math:`V_{\rm ext}(\mathbf{r},t) = eE(t)z`. .. _input-files-2: Input files ^^^^^^^^^^^ To run the code, following files are necessary: +-----------------------------------+---------------------------------------------------------------+ | file name | description | +-----------------------------------+---------------------------------------------------------------+ | *C2H2_rt_pulse.inp* | input file that contain input | | | keywords and their values. | +-----------------------------------+---------------------------------------------------------------+ | *C_rps.dat* | pseodupotential file for carbon | +-----------------------------------+---------------------------------------------------------------+ | *H_rps.dat* | pseudopotential file for hydrogen | +-----------------------------------+---------------------------------------------------------------+ | *restart* | | directory created in the ground state calculation | | | | (rename the directory from *data_for_restart* to *restart*) | +-----------------------------------+---------------------------------------------------------------+ First three files are prepared in the directory ``SALMON/samples/exercise_03_C2H2_rt/``. The file *C2H2_rt_pulse.inp* that contains input keywords and their values. The pseudopotential files should be the same as those used in the ground state calculation. In the directory *restart*, those files created in the ground state calculation and stored in the directory *data_for_restart* are included. Therefore, copy the directory as ``cp -R data_for_restart restart`` if you calculate at the same directory as you did the ground state calculation. In the input file *C2H2_rt_pulse.inp*, input keywords are specified. Most of them are mandatory to execute the calculation of electron dynamics induced by 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 input keywords that can be used in the input file can be found in :any:`List of input keywords `. :: !########################################################################################! ! Excercise 03: Electron dynamics in C2H2 molecule under a pulsed electric field ! !----------------------------------------------------------------------------------------! ! * The detail of this excercise is expained in our manual(see chapter: 'Exercises'). ! ! The manual can be obtained from: https://salmon-tddft.jp/documents.html ! ! * Input format consists of group of keywords like: ! ! &group ! ! input keyword = xxx ! ! / ! ! (see chapter: 'List of input keywords' in the manual) ! !----------------------------------------------------------------------------------------! ! * Conversion from unit_system = 'a.u.' to 'A_eV_fs': ! ! Length: 1 [a.u.] = 0.52917721067 [Angstrom] ! ! Energy: 1 [a.u.] = 27.21138505 [eV] ! ! Time : 1 [a.u.] = 0.02418884326505 [fs] ! !----------------------------------------------------------------------------------------! ! * Copy the ground state data directory('data_for_restart') (or make symbolic link) ! ! calculated in 'samples/exercise_01_C2H2_gs/' and rename the directory to 'restart/' ! ! in the current directory. ! !########################################################################################! &calculation !type of theory theory = 'tddft_pulse' / | :any:`theory ` specifies which theoretical method is used in the calculation. :: &control !common name of output files sysname = 'C2H2' / | :any:`sysname ` is a prefix for filenames of output files. :: &units !units used in input and output files unit_system = 'A_eV_fs' / | :any:`unit_system ` specifies which unit system is used in the input and output files. :: &system !periodic boundary condition yn_periodic = 'n' !number of elements, atoms, electrons and states(orbitals) nelem = 2 natom = 4 nelec = 10 nstate = 6 / | :any:`yn_periodic ` specifies whether or not periodic boundary condition is applied. | :any:`nelem ` is the number of elements in the system. | :any:`natom ` is the number of atoms in the system. | :any:`nelec ` is the number of electrons in the system. | :any:`nstate ` is the number of orbitals that are used in the calculation. :: &pseudo !name of input pseudo potential file file_pseudo(1) = './C_rps.dat' file_pseudo(2) = './H_rps.dat' !atomic number of element izatom(1) = 6 izatom(2) = 1 !angular momentum of pseudopotential that will be treated as local lloc_ps(1) = 1 lloc_ps(2) = 0 !--- Caution ---------------------------------------! ! Indices must correspond to those in &atomic_coor. ! !---------------------------------------------------! / | :any:`file_pseudo(n) ` specifies the filename of the pseudopotential file of the n-th element. | :any:`izatom(n) ` is the atomic number of the n-th element. | :any:`lloc_ps(n) ` specifies which angular momentum component is chosen as the local potential for the n-th element. :: &functional !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).) xc = 'PZ' / | :any:`xc ` specifies the exchange-correlation potential to be used in the calculation. :: &rgrid !spatial grid spacing(x,y,z) dl(1:3) = 0.25d0, 0.25d0, 0.25d0 !number of spatial grids(x,y,z) num_rgrid(1:3) = 64, 64, 64 / | :any:`dl(i) ` specifies the spatial grid spacing in i-th direction. | :any:`num_rgrid(i) ` specifies the number of grid points in i-th direction. :: &tgrid !time step size and number of time grids(steps) dt = 1.25d-3 nt = 5000 / | :any:`dt` specifies the time step. | :any:`nt` is the number of time steps for the time propagation. :: &emfield !envelope shape of the incident pulse('Ecos2': cos^2 type envelope for scalar potential) ae_shape1 = 'Acos2' !peak intensity(W/cm^2) of the incident pulse I_wcm2_1 = 5.00d13 !duration of the incident pulse tw1 = 6.00d0 !mean photon energy(average frequency multiplied by the Planck constant) of the incident pulse omega1 = 3.10d0 !polarization unit vector(real part) for the incident pulse(x,y,z) epdir_re1(1:3) = 0.00d0, 0.00d0, 1.00d0 !--- Caution ---------------------------------------------------------! ! Defenition of the incident pulse is wrriten in: ! ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 ! !---------------------------------------------------------------------! / | :any:`ae_shape1 ` specifies the envelope of the field. | :any:`I_wcm2_1 ` specify the intensity of the pulse in unit of W/cm\ :sup:`2`\. | :any:`tw1 ` specifies the duration of the pulse. | :any:`omega1 ` specifies the mean photon energy of the pulse. | :any:`epdir_re1(i) ` specifies the i-th component of the real part of the polarization unit vector. :: &analysis !energy grid size and number of energy grids for output files de = 1.0d-2 nenergy = 10000 / | :any:`de` specifies the energy grid size for frequency-domain analysis. | :any:`nenergy` specifies the number of energy grid points for frequency-domain analysis. :: &atomic_coor !cartesian atomic coodinates '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 !--- Format ---------------------------------------------------! ! 'symbol' x y z index(correspond to that of pseudo potential) ! !--------------------------------------------------------------! / | :any:`&atomic_coor <&atomic_coor>` specifies spatial coordinates of atoms. Execusion ^^^^^^^^^ Before execusion, remember to copy the directory *restart* that is created in the ground state calculation as *data_for_restart* in the present directory. In a multiprocess environment, calculation will be executed as $ mpiexec -n NPROC salmon < C2H2_rt_pulse.inp > C2H2_rt_pulse.out where NPROC is the number of MPI processes. A standard output will be stored in the file ``C2H2_rt_pulse.out``. .. _output-files-3: Output files ^^^^^^^^^^^^ After the calculation, following output files are created in the directory that you run the code, +-----------------------------------+-----------------------------------+ | file name | description | +-----------------------------------+-----------------------------------+ | *C2H2_pulse.data* | dipole moment as | | | functions of energy | +-----------------------------------+-----------------------------------+ | *C2H2_rt.data* | | components of | | | change of dipole moment | | | (electrons/plus definition) | | | | and total dipole moment | | | (electrons/minus + ions/plus) | | | as functions of time | +-----------------------------------+-----------------------------------+ | *C2H2_rt_energy.data* | components of | | | total energy | | | and difference of total energy | | | as functions of time | +-----------------------------------+-----------------------------------+ | *PS_C_KY_n.dat* | information on pseodupotential | | | file for carbon atom | +-----------------------------------+-----------------------------------+ | *PS_H_KY_n.dat* | information on pseodupotential | | | file for hydrogen atom | +-----------------------------------+-----------------------------------+ | You may download the above files (zipped file) from: | https://salmon-tddft.jp/webmanual/v_2_0_1/exercise_zip_files/03_C2H2_rt.zip We first explain the standard output file. In the beginning of the file, input variables used in the calculation are shown. :: ############################################################################## # SALMON: Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience # # Version 2.0.1 ############################################################################## Libxc: [disabled] theory= tddft_pulse Total time step = 5000 Time step[fs] = 1.250000000000000E-003 Energy range = 10000 Energy resolution[eV]= 1.000000000000000E-002 Laser frequency = 3.10[eV] Pulse width of laser= 6.00000000[fs] Laser intensity = 0.50000000E+14[W/cm^2] use of real value orbitals = F ====== ........ After that, the time evolution loop starts. At every 10 iteration steps, the time, dipole moments in three Cartesian directions, the total number of electrons, the total energy, and the number of iterations solving the Poisson equation are displayed. :: time-step time[fs] Dipole moment(xyz)[A] electrons Total energy[eV] iterVh #---------------------------------------------------------------------- 10 0.01250000 -0.57275542E-07 -0.29197105E-07 -0.74600728E-06 10.00000000 -339.69524047 1 20 0.02500000 -0.20616352E-06 -0.10537273E-06 -0.10256205E-04 10.00000000 -339.69524348 1 30 0.03750000 -0.40063325E-06 -0.20597522E-06 -0.47397133E-04 10.00000000 -339.69524090 3 40 0.05000000 -0.59093535E-06 -0.30630513E-06 -0.13774845E-03 10.00000000 -339.69524287 1 50 0.06250000 -0.75588343E-06 -0.39552925E-06 -0.31097825E-03 10.00000000 -339.69523949 5 60 0.07500000 -0.89221538E-06 -0.47142217E-06 -0.59735355E-03 10.00000000 -339.69523784 11 70 0.08750000 -0.99769538E-06 -0.53192187E-06 -0.10253308E-02 10.00000000 -339.69523285 5 80 0.10000000 -0.10738281E-05 -0.57676878E-06 -0.16195168E-02 9.99999999 -339.69522482 19 90 0.11250000 -0.11250289E-05 -0.60722757E-06 -0.23985719E-02 9.99999999 -339.69521092 2 Explanations of the files are given below: **C2H2_rt.data** Results of time evolution calculation for vector potential, electric field, and dipole moment. In the first several lines, explanations of data included data are given. :: # 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 # ddm_e: Change of dipole moment (electrons/plus definition) # dm: Total dipole moment (electrons/minus + ions/plus) # 1:Time[fs] 2:Ac_ext_x[fs*V/Angstrom] 3:Ac_ext_y[fs*V/Angstrom] 4:Ac_ext_z[fs*V/Angstrom] 5:E_ext_x[V/Angstrom] 6:E_ext_y[V/Angstrom] 7:E_ext_z[V/Angstrom] 8:Ac_tot_x[fs*V/Angstrom] 9:Ac_tot_y[fs*V/Angstrom] 10:Ac_tot_z[fs*V/Angstrom] 11:E_tot_x[V/Angstrom] 12:E_tot_y[V/Angstrom] 13:E_tot_z[V/Angstrom] 14:ddm_e_x[Angstrom] 15:ddm_e_y[Angstrom] 16:ddm_e_z[Angstrom] 17:dm_x[Angstrom] 18:dm_y[Angstrom] 19:dm_z[Angstrom] The applied electric field is drawn using the first column (time in femtosecond) and the 7th column (electric field in :math:`z` direction in Volt per Angstrom). .. image:: images/exc3/exc3-Efield.png :scale: 40% The induced dipole moment is drawn using the first column (time in femtosecond) and 19th column (dipole moment in :math:`z` direction). It shows an oscillation similar to the applied electric field. However, the response is not linear since the applied electric field is rather strong. .. image:: images/exc3/exc3-dipole.png :scale: 40% **C2H2_pulse.data** Time-frequency Fourier transformation of the dipole moment. In the first several lines, explanations of data included data are given. :: # Fourier-transform spectra: # energy: Frequency # dm: Dopile moment # 1:energy[eV] 2:Re(dm_x)[fs*Angstrom] 3:Re(dm_y)[fs*Angstrom] 4:Re(dm_z)[fs*Angstrom] 5:Im(dm_x)[fs*Angstrom] 6:Im(dm_y)[fs*Angstrom] 7:Im(dm_z)[fs*Angstrom] 8:|dm_x|^2[fs^2*Angstrom^2] 9:|dm_y|^2[fs^2*Angstrom^2] 10:|dm_z|^2[fs^2*Angstrom^2] The spectrum of the induced dipole moment, :math:`|d(\omega)|^2` is shown in logarithmic scale as a function of the energy, :math:`\hbar \omega`. High harmonic generations are visible in the spectrum. .. image:: images/exc3/exc3-spectrum.png :scale: 40% **C2H2_rt_energy.data** Energies are stored as functions of time. In the first several lines, explanations of data included data are given. :: # Real time calculation: # Eall: Total energy # Eall0: Initial energy # 1:Time[fs] 2:Eall[eV] 3:Eall-Eall0[eV] *Eall* and *Eall-Eall0* are total energy and electronic excitation energy, respectively. The figure below shows the electronic excitation energy as a function of time, using the first column (time in femtosecond) and the 3rd column (*Eall-Eall0*). Although the frequency is below the HOMO-LUMO gap energy, electronic excitations take place because of nonlinear absorption process. .. image:: images/exc3/exc3-Eex.png :scale: 40% Additional exercise ^^^^^^^^^^^^^^^^^^^ If we change parameters of the applied electric field, we find a drastic change in the electronic excitations. In the example below, we increase the intensity from ``I_wcm2_1 = 5.00d13`` to ``I_wcm2_1 = 1.00d12`` and changes the frequency from ``omega1 = 3.10d0`` to ``omega1 = 9.28d0``. The new frequency corresponds to the resonant excitation energy seen in the linear response analysis shown in in :any:`Exercise-2 `. The change in the input file is shown below. :: &emfield !envelope shape of the incident pulse('Ecos2': cos^2 type envelope for scalar potential) ae_shape1 = 'Acos2' !peak intensity(W/cm^2) of the incident pulse I_wcm2_1 = 1.00d12 !duration of the incident pulse tw1 = 6.00d0 !mean photon energy(average frequency multiplied by the Planck constant) of the incident pulse omega1 = 9.28d0 !polarization unit vector(real part) for the incident pulse(x,y,z) epdir_re1(1:3) = 0.00d0, 0.00d0, 1.00d0 The applied electric field shows a rapid oscillation. .. image:: images/exc3a/exc3a-Efield.png :scale: 40% The induced dipole moment also shows a rapid oscillation and does not decrease even though the electric field decreases. This is because the frequency of the applied electric field coincides with the excitation energy of the molecule. .. image:: images/exc3a/exc3a-dipole.png :scale: 40% The electronic excitation energy also shows a monotonic increase. Although the strength of the applied electric field is much smaller than the previous case, the amount of the excitation energy is larger, again due to the resonant excitation. .. image:: images/exc3a/exc3a-Eex.png :scale: 40% Crystalline silicon (periodic solids) ------------------------------------- .. _exercise-4: Exercise-4: Ground state of crystalline silicon ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In this exercise, we learn the the ground state calculation of the crystalline silicon of a diamond structure. Calculation is done in a cubic unit cell that contains eight silicon atoms. This exercise will be useful to learn how to set up calculations in SALMON for any periodic systems such as crystalline solid. Input files ^^^^^^^^^^^ To run the code, following files in samples are used: +-----------------------------------+-----------------------------------+ | file name | description | +-----------------------------------+-----------------------------------+ | *Si_gs.inp* | input file that contains input | | | keywords and their values | +-----------------------------------+-----------------------------------+ | *Si_rps.dat* | pseodupotential file for silicon | | | atom | +-----------------------------------+-----------------------------------+ In the input file *Si_gs.inp*, input keywords are specified. Most of them are mandatory to execute the ground state calculation. This will help you to prepare an input file for other systems that you want to calculate. A complete list of the input keywords that can be used in the input file can be found in :any:`List of input keywords `. :: !########################################################################################! ! Excercise 04: Ground state of crystalline silicon(periodic solids) ! !----------------------------------------------------------------------------------------! ! * The detail of this excercise is expained in our manual(see chapter: 'Exercises'). ! ! The manual can be obtained from: https://salmon-tddft.jp/documents.html ! ! * Input format consists of group of keywords like: ! ! &group ! ! input keyword = xxx ! ! / ! ! (see chapter: 'List of input keywords' in the manual) ! !----------------------------------------------------------------------------------------! ! * Conversion from unit_system = 'a.u.' to 'A_eV_fs': ! ! Length: 1 [a.u.] = 0.52917721067 [Angstrom] ! ! Energy: 1 [a.u.] = 27.21138505 [eV] ! ! Time : 1 [a.u.] = 0.02418884326505 [fs] ! !########################################################################################! &calculation !type of theory theory = 'dft' / | :any:`theory ` specifies which theoretical method is used in the calculation. :: &control !common name of output files sysname = 'Si' / | :any:`sysname ` is a prefix for filenames of output files. :: &units !units used in input and output files unit_system = 'a.u.' / | :any:`unit_system ` specifies which unit system is used in the input and output files. :: &system !periodic boundary condition yn_periodic = 'y' !grid box size(x,y,z) al(1:3) = 10.26d0, 10.26d0, 10.26d0 !number of elements, atoms, electrons and states(bands) nelem = 1 natom = 8 nelec = 32 nstate = 32 / | :any:`yn_periodic ` specifies whether or not periodic boundary condition is applied. | :any:`al(i) ` specifies the side length of the unit cell. | :any:`nelem ` is the number of elements in the system. | :any:`natom ` is the number of atoms in the system. | :any:`nelec ` is the number of electrons in the system. | :any:`nstate ` is the number of orbitals that are used in the calculation. :: &pseudo !name of input pseudo potential file file_pseudo(1) = './Si_rps.dat' !atomic number of element izatom(1) = 14 !angular momentum of pseudopotential that will be treated as local lloc_ps(1) = 2 !--- Caution -------------------------------------------! ! Index must correspond to those in &atomic_red_coor. ! !-------------------------------------------------------! / | :any:`file_pseudo(n) ` specifies the filename of the pseudopotential file of the n-th element. | :any:`izatom(n) ` is the atomic number of the n-th element. | :any:`lloc_ps(n) ` specifies which angular momentum component is chosen as the local potential for the n-th element. :: &functional !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).) xc = 'PZ' / | :any:`xc ` specifies the exchange-correlation potential to be used in the calculation. :: &rgrid !number of spatial grids(x,y,z) num_rgrid(1:3) = 12, 12, 12 / | :any:`num_rgrid(i) ` specifies the number of real-space grid point in i-th direction. :: &kgrid !number of k-points(x,y,z) num_kgrid(1:3) = 4, 4, 4 / | :any:`num_kgrid(i) ` specifies the number of k-points for i-th direction discretizing the Brillouin zone. :: &scf !maximum number of scf iteration and threshold of convergence nscf = 300 threshold = 1.0d-9 / | :any:`nscf ` specifies the maximum number of SCF iterations. | :any:`threshold ` specifies the threshold to judge the convergence. :: &atomic_red_coor !cartesian atomic reduced coodinates 'Si' .0 .0 .0 1 'Si' .25 .25 .25 1 'Si' .5 .0 .5 1 'Si' .0 .5 .5 1 'Si' .5 .5 .0 1 'Si' .75 .25 .75 1 'Si' .25 .75 .75 1 'Si' .75 .75 .25 1 !--- Format ---------------------------------------------------! ! 'symbol' x y z index(correspond to that of pseudo potential) ! !--------------------------------------------------------------! / | :any:`&atomic_red_coor <&atomic_red_coor>` specifies spatial coordinates of atoms in reduced coordinate system. .. _output-files-4: Output files ^^^^^^^^^^^^ After the calculation, following output files and a directory are created in the directory that you run the code, +-----------------------------------+-----------------------------------+ | name | description | +-----------------------------------+-----------------------------------+ | *Si_info.data* 　 | information on ground state | | | solution | +-----------------------------------+-----------------------------------+ | *Si_eigen.data* 　 | energy eigenvalues of orbitals | +-----------------------------------+-----------------------------------+ | *Si_k.data* 　 | k-point distribution | +-----------------------------------+-----------------------------------+ | *PS_Si_KY_n.dat* | information on pseodupotential | | | file for silicon atom | +-----------------------------------+-----------------------------------+ | *data_for_restart* | directory where files used in | | | the real-time calculation are | | | contained | +-----------------------------------+-----------------------------------+ | You may download the above files (zipped file, except for the directory *data_for_restart*) from: | https://salmon-tddft.jp/webmanual/v_2_0_1/exercise_zip_files/04_bulkSi_gs.zip Main results of the calculation such as orbital energies are included in *Si_info.data*. Explanations of the *Si_info.data* and other output files are below: **Si_info.data** Calculated orbital and total energies as well as parameters specified in the input file are shown in this file. **Si_eigen.data** 1 particle energies. :: #esp: single-particle energies (eigen energies) #occ: occupation numbers, io: orbital index # 1:io, 2:esp[a.u.], 3:occ **Si_k.data** 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] # coefficients (2*pi/a [a.u.]) in kx, ky, kz .. _exercise-5: Exercise-5: 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. This exercise should be carried out after finishing the ground state calculation that was explained in :any:`Exercise-4 `. 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-3: Input files ^^^^^^^^^^^ To run the code, following files in samples are used: +-----------------------------------+-------------------------------------+ | file name | description | +-----------------------------------+-------------------------------------+ | *Si_rt_response.inp* | input file that contain input | | | keywords and their values | +-----------------------------------+-------------------------------------+ | *Si_rps.dat* | pseodupotential file of silicon | +-----------------------------------+-------------------------------------+ | *restart* | | directory created in the ground | | | state calculation | | | | (rename the | | | directory from | | | *data_for_restart* to *restart*) | +-----------------------------------+-------------------------------------+ In the input file *Si_rt_response.inp*, input keywords 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 input keywords can be found in :any:`List of input keywords `. :: !########################################################################################! ! Excercise 05: Dielectric function of crystalline silicon ! !----------------------------------------------------------------------------------------! ! * The detail of this excercise is expained in our manual(see chapter: 'Exercises'). ! ! The manual can be obtained from: https://salmon-tddft.jp/documents.html ! ! * Input format consists of group of keywords like: ! ! &group ! ! input keyword = xxx ! ! / ! ! (see chapter: 'List of input keywords' in the manual) ! !----------------------------------------------------------------------------------------! ! * Conversion from unit_system = 'a.u.' to 'A_eV_fs': ! ! Length: 1 [a.u.] = 0.52917721067 [Angstrom] ! ! Energy: 1 [a.u.] = 27.21138505 [eV] ! ! Time : 1 [a.u.] = 0.02418884326505 [fs] ! !----------------------------------------------------------------------------------------! ! * Copy the ground state data directory('data_for_restart') (or make symbolic link) ! ! calculated in 'samples/exercise_04_bulkSi_gs/' and rename the directory to 'restart/'! ! in the current directory. ! !########################################################################################! &calculation !type of theory theory = 'tddft_response' / | :any:`theory ` specifies which theoretical method is used in the calculation. :: &control !common name of output files sysname = 'Si' / | :any:`sysname ` is a prefix for filenames of output files. :: &units !units used in input and output files unit_system = 'a.u.' / | :any:`unit_system ` specifies which unit system is used in the input and output files. :: &system !periodic boundary condition yn_periodic = 'y' !grid box size(x,y,z) al(1:3) = 10.26d0, 10.26d0, 10.26d0 !number of elements, atoms, electrons and states(bands) nelem = 1 natom = 8 nelec = 32 nstate = 32 / | :any:`yn_periodic ` specifies whether or not periodic boundary condition is applied. | :any:`al(i) ` specifies the side length of the unit cell. | :any:`nelem ` is the number of elements in the system. | :any:`natom ` is the number of atoms in the system. | :any:`nelec ` is the number of electrons in the system. | :any:`nstate ` is the number of orbitals that are used in the calculation. :: &pseudo !name of input pseudo potential file file_pseudo(1) = './Si_rps.dat' !atomic number of element izatom(1) = 14 !angular momentum of pseudopotential that will be treated as local lloc_ps(1) = 2 !--- Caution -------------------------------------------! ! Index must correspond to those in &atomic_red_coor. ! !-------------------------------------------------------! / | :any:`file_pseudo(n) ` specifies the filename of the pseudopotential file of the n-th element. | :any:`izatom(n) ` is the atomic number of the n-th element. | :any:`lloc_ps(n) ` specifies which angular momentum component is chosen as the local potential for the n-th element. :: &functional !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).) xc = 'PZ' / | :any:`xc ` specifies the exchange-correlation potential to be used in the calculation. :: &rgrid !number of spatial grids(x,y,z) num_rgrid(1:3) = 12, 12, 12 / | :any:`num_rgrid(i) ` specifies the number of real-space grid point in i-th direction. :: &kgrid !number of k-points(x,y,z) num_kgrid(1:3) = 4, 4, 4 / | :any:`num_kgrid(i) ` specifies the number of k-points for i-th direction discretizing the Brillouin zone. :: &tgrid !time step size and number of time grids(steps) dt = 0.08d0 nt = 6000 / | :any:`dt` specifies the time step. | :any:`nt` is the number of time steps for the time propagation. :: &emfield !envelope shape of the incident pulse('impulse': impulsive field) ae_shape1 = 'impulse' !polarization unit vector(real part) for the incident pulse(x,y,z) epdir_re1(1:3) = 0.00d0, 0.00d0, 1.00d0 !--- Caution ---------------------------------------------------------! ! Defenition of the incident pulse is wrriten in: ! ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 ! !---------------------------------------------------------------------! / | :any:`ae_shape1 ` specifies the envelope of the field. For a linear response calculation, ``as_shape1='impulse'`` is used. It indicates that a weak impulsive perturbation is applied at :math:`t=0`. | :any:`epdir_re1(i) ` specifies the i-th component of the real part of the polarization unit vector. :: &analysis !energy grid size and number of energy grids for output files de = 4.0d-4 nenergy = 5000 / | :any:`de` specifies the energy grid size for frequency-domain analysis. | :any:`nenergy` specifies the number of energy grid points for frequency-domain analysis. :: &atomic_red_coor !cartesian atomic reduced coodinates 'Si' .0 .0 .0 1 'Si' .25 .25 .25 1 'Si' .5 .0 .5 1 'Si' .0 .5 .5 1 'Si' .5 .5 .0 1 'Si' .75 .25 .75 1 'Si' .25 .75 .75 1 'Si' .75 .75 .25 1 !--- Format ---------------------------------------------------! ! 'symbol' x y z index(correspond to that of pseudo potential) ! !--------------------------------------------------------------! / | :any:`&atomic_red_coor <&atomic_red_coor>` specifies spatial coordinates of atoms in reduced coordinate system. .. _output-files-5: Output files ^^^^^^^^^^^^ After the calculation, following output files are created in the directory that you run the code, +-----------------------------------+------------------------------------------+ | file name | description | +-----------------------------------+------------------------------------------+ | *Si_response.data* | Fourier spectra of the conductivity | | | and dielectric functions | +-----------------------------------+------------------------------------------+ | *Si_rt.data* | vector potential, electric field, | | | and matter current as functions of time | +-----------------------------------+------------------------------------------+ | *Si_rt_energy* | components of total energy and | | | difference of total energy | | | as functions of time | +-----------------------------------+------------------------------------------+ | *PS_Si_KY_n.dat* | information on pseodupotential | | | file for silicon atom | +-----------------------------------+------------------------------------------+ | You may download the above files (zipped file) from: | https://salmon-tddft.jp/webmanual/v_2_0_1/exercise_zip_files/05_bulkSi_lr.zip Explanations of the output files are described below: **Si_response.data** 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:Energy[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] **Si_rt.data** Results of time evolution calculation for vector potential, electric field, and matter current density. :: # 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 (electrons) # 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.] **Si_rt_energy** *Eall* and *Eall-Eall0* are total energy and electronic excitation energy, respectively. :: # Real time calculation: # Eall: Total energy # Eall0: Initial energy # 1:Time[a.u.] 2:Eall[a.u.] 3:Eall-Eall0[a.u.] .. _exercise-6: Exercise-6: 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. This exercise should be carried out after finishing the ground state calculation that was explained in :any:`Exercise-4 `. 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-4: Input files ^^^^^^^^^^^ To run the code, following files in samples are used: +-----------------------------------+-------------------------------------+ | file name | description | +-----------------------------------+-------------------------------------+ | *Si_rt_pulse.inp* | input file that contain input | | | keywords and their values. | +-----------------------------------+-------------------------------------+ | *Si_rps.dat* | pseodupotential file for Carbon | +-----------------------------------+-------------------------------------+ | *restart* | | directory created in the ground | | | state calculation | | | | (rename the directory from | | | *data_for_restart* to *restart*) | +-----------------------------------+-------------------------------------+ In the input file *Si_rt_pulse.inp*, input keywords 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 input keywords can be found in :any:`List of input keywords `. :: !########################################################################################! ! Excercise 06: Electron dynamics in crystalline silicon under a pulsed electric field ! !----------------------------------------------------------------------------------------! ! * The detail of this excercise is expained in our manual(see chapter: 'Exercises'). ! ! The manual can be obtained from: https://salmon-tddft.jp/documents.html ! ! * Input format consists of group of keywords like: ! ! &group ! ! input keyword = xxx ! ! / ! ! (see chapter: 'List of input keywords' in the manual) ! !----------------------------------------------------------------------------------------! ! * Conversion from unit_system = 'a.u.' to 'A_eV_fs': ! ! Length: 1 [a.u.] = 0.52917721067 [Angstrom] ! ! Energy: 1 [a.u.] = 27.21138505 [eV] ! ! Time : 1 [a.u.] = 0.02418884326505 [fs] ! !----------------------------------------------------------------------------------------! ! * Copy the ground state data directory('data_for_restart') (or make symbolic link) ! ! calculated in 'samples/exercise_04_bulkSi_gs/' and rename the directory to 'restart/'! ! in the current directory. ! !########################################################################################! &calculation !type of theory theory = 'tddft_pulse' / | :any:`theory ` specifies which theoretical method is used in the calculation. :: &control !common name of output files sysname = 'Si' / | :any:`sysname ` is a prefix for filenames of output files. :: &units !units used in input and output files unit_system = 'a.u.' / | :any:`unit_system ` specifies which unit system is used in the input and output files. :: &system !periodic boundary condition yn_periodic = 'y' !grid box size(x,y,z) al(1:3) = 10.26d0, 10.26d0, 10.26d0 !number of elements, atoms, electrons and states(bands) nelem = 1 natom = 8 nelec = 32 nstate = 32 / | :any:`yn_periodic ` specifies whether or not periodic boundary condition is applied. | :any:`al(i) ` specifies the side length of the unit cell. | :any:`nelem ` is the number of elements in the system. | :any:`natom ` is the number of atoms in the system. | :any:`nelec ` is the number of electrons in the system. | :any:`nstate ` is the number of orbitals that are used in the calculation. :: &pseudo !name of input pseudo potential file file_pseudo(1) = './Si_rps.dat' !atomic number of element izatom(1) = 14 !angular momentum of pseudopotential that will be treated as local lloc_ps(1) = 2 !--- Caution -------------------------------------------! ! Index must correspond to those in &atomic_red_coor. ! !-------------------------------------------------------! / | :any:`file_pseudo(n) ` specifies the filename of the pseudopotential file of the n-th element. | :any:`izatom(n) ` is the atomic number of the n-th element. | :any:`lloc_ps(n) ` specifies which angular momentum component is chosen as the local potential for the n-th element. :: &functional !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).) xc = 'PZ' / | :any:`xc ` specifies the exchange-correlation potential to be used in the calculation. :: &rgrid !number of spatial grids(x,y,z) num_rgrid(1:3) = 12, 12, 12 / | :any:`num_rgrid(i) ` specifies the number of real-space grid point in i-th direction. :: &kgrid !number of k-points(x,y,z) num_kgrid(1:3) = 4, 4, 4 / | :any:`num_kgrid(i) ` specifies the number of k-points for i-th direction discretizing the Brillouin zone. :: &tgrid !time step size and number of time grids(steps) dt = 0.08d0 nt = 6000 / | :any:`dt` specifies the time step. | :any:`nt` is the number of time steps for the time propagation. :: &emfield !envelope shape of the incident pulse('Acos2': cos^2 type envelope for vector potential) ae_shape1 = 'Acos2' !peak intensity(W/cm^2) of the incident pulse I_wcm2_1 = 5.0d11 !duration of the incident pulse tw1 = 441.195136248d0 !mean photon energy(average frequency multiplied by the Planck constant) of the incident pulse omega1 = 0.05696145187d0 !polarization unit vector(real part) for the incident pulse(x,y,z) epdir_re1(1:3) = 0.0d0, 0.0d0, 1.0d0 !--- Caution ---------------------------------------------------------! ! Defenition of the incident pulse is wrriten in: ! ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 ! !---------------------------------------------------------------------! / | :any:`ae_shape1 ` specifies the envelope of the field. | :any:`I_wcm2_1 ` specify the intensity of the pulse in unit of W/cm\ :sup:`2`\. | :any:`tw1 ` specifies the duration of the pulse. | :any:`omega1 ` specifies the mean photon energy of the pulse. | :any:`epdir_re1(i) ` specifies the i-th component of the real part of the polarization unit vector. :: &atomic_red_coor !cartesian atomic reduced coodinates 'Si' .0 .0 .0 1 'Si' .25 .25 .25 1 'Si' .5 .0 .5 1 'Si' .0 .5 .5 1 'Si' .5 .5 .0 1 'Si' .75 .25 .75 1 'Si' .25 .75 .75 1 'Si' .75 .75 .25 1 !--- Format ---------------------------------------------------! ! 'symbol' x y z index(correspond to that of pseudo potential) ! !--------------------------------------------------------------! / | :any:`&atomic_red_coor <&atomic_red_coor>` specifies spatial coordinates of atoms in reduced coordinate system. .. _output-files-6: Output files ^^^^^^^^^^^^ After the calculation, following output files are created in the directory that you run the code, +-----------------------------------+------------------------------------------+ | file name | description | +-----------------------------------+------------------------------------------+ | *Si_pulse.data* | matter current and electric field | | | as functions of energy | +-----------------------------------+------------------------------------------+ | *Si_rt.data* | vector potential, electric field, | | | and matter current as functions of time | +-----------------------------------+------------------------------------------+ | *Si_rt_energy* | components of total energy and | | | difference of total energy | | | as functions of time | +-----------------------------------+------------------------------------------+ | *PS_Si_KY_n.dat* | information on pseodupotential | | | file for silicon atom | +-----------------------------------+------------------------------------------+ | You may download the above files (zipped file) from: | https://salmon-tddft.jp/webmanual/v_2_0_1/exercise_zip_files/06_bulkSi_rt.zip Explanations of the output files are described below: **Si_pulse.data** Time-frequency Fourier transformation of the matter current and electric field. :: # Fourier-transform spectra: # energy: Frequency # Jm: Matter current # E_ext: External electric field # E_tot: Total electric field # 1:energy[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:|Jm_x|^2[a.u.] 9:|Jm_y|^2[a.u.] 10:|Jm_z|^2[a.u.] 11:Re(E_ext_x)[a.u.] 12:Re(E_ext_y)[a.u.] 13:Re(E_ext_z)[a.u.] 14:Im(E_ext_x)[a.u.] 15:Im(E_ext_y)[a.u.] 16:Im(E_ext_z)[a.u.] 17:|E_ext_x|^2[a.u.] 18:|E_ext_y|^2[a.u.] 19:|E_ext_z|^2[a.u.] 20:Re(E_ext_x)[a.u.] 21:Re(E_ext_y)[a.u.] 22:Re(E_ext_z)[a.u.] 23:Im(E_ext_x)[a.u.] 24:Im(E_ext_y)[a.u.] 25:Im(E_ext_z)[a.u.] 26:|E_ext_x|^2[a.u.] 27:|E_ext_y|^2[a.u.] 28:|E_ext_z|^2[a.u.] **Si_rt.data** Results of time evolution calculation for vector potential, electric field, and matter current density. :: # 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 (electrons) # 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.] **Si_rt_energy** *Eall* and *Eall-Eall0* are total energy and electronic excitation energy, respectively. :: # Real time calculation: # Eall: Total energy # Eall0: Initial energy # 1:Time[a.u.] 2:Eall[a.u.] 3:Eall-Eall0[a.u.] Maxwell + TDDFT multiscale simulation ------------------------------------- .. _exercise-7: Exercise-7: 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 42 nm thickness, and an irradiation of a few-cycle, linearly polarized pulsed light normally on the thin film. This exercise should be carried out after finishing the ground state calculation that was explained in :any:`Exercise-4 `. 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. .. _input-files-5: Input files ^^^^^^^^^^^ To run the code, following files in samples are used: +-----------------------------------+-------------------------------------+ | file name | description | +-----------------------------------+-------------------------------------+ | *Si_rt_multiscale.inp* | input file that contain input | | | keywords and their values. | +-----------------------------------+-------------------------------------+ | *Si_rps.dat* | pseodupotential file for silicon | +-----------------------------------+-------------------------------------+ | *restart* | | directory created in the ground | | | state calculation | | | | (rename the directory from | | | *data_for_restart* to *restart*) | +-----------------------------------+-------------------------------------+ In the input file *Si_rt_multiscale.inp*, input keywords 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 input keywords can be found in :any:`List of input keywords `. :: !########################################################################################! ! Excercise 07: Maxwell+TDDFT multiscale simulation ! ! (Pulsed-light propagation through a silicon thin film) ! !----------------------------------------------------------------------------------------! ! * The detail of this excercise is expained in our manual(see chapter: 'Exercises'). ! ! The manual can be obtained from: https://salmon-tddft.jp/documents.html ! ! * Input format consists of group of keywords like: ! ! &group ! ! input keyword = xxx ! ! / ! ! (see chapter: 'List of input keywords' in the manual) ! !----------------------------------------------------------------------------------------! ! * Conversion from unit_system = 'a.u.' to 'A_eV_fs': ! ! Length: 1 [a.u.] = 0.52917721067 [Angstrom] ! ! Energy: 1 [a.u.] = 27.21138505 [eV] ! ! Time : 1 [a.u.] = 0.02418884326505 [fs] ! !----------------------------------------------------------------------------------------! ! * Copy the ground state data directory('data_for_restart') (or make symbolic link) ! ! calculated in 'samples/exercise_04_bulkSi_gs/' and rename the directory to 'restart/'! ! in the current directory. ! !########################################################################################! &calculation !type of theory theory = 'multi_scale_maxwell_tddft' / | :any:`theory ` specifies which theoretical method is used in the calculation. :: &control !common name of output files sysname = 'Si' / | :any:`sysname ` is a prefix for filenames of output files. :: &units !units used in input and output files unit_system = 'a.u.' / | :any:`unit_system ` specifies which unit system is used in the input and output files. :: &system !periodic boundary condition yn_periodic = 'y' !grid box size(x,y,z) al(1:3) = 10.26d0, 10.26d0, 10.26d0 !number of elements, atoms, electrons and states(bands) nelem = 1 natom = 8 nelec = 32 nstate = 32 / | :any:`yn_periodic ` specifies whether or not periodic boundary condition is applied. | :any:`al(i) ` specifies the side length of the unit cell. | :any:`nelem ` is the number of elements in the system. | :any:`natom ` is the number of atoms in the system. | :any:`nelec ` is the number of electrons in the system. | :any:`nstate ` is the number of orbitals that are used in the calculation. :: &pseudo !name of input pseudo potential file file_pseudo(1) = './Si_rps.dat' !atomic number of element izatom(1) = 14 !angular momentum of pseudopotential that will be treated as local lloc_ps(1) = 2 !--- Caution -------------------------------------------! ! Index must correspond to those in &atomic_red_coor. ! !-------------------------------------------------------! / | :any:`file_pseudo(n) ` specifies the filename of the pseudopotential file of the n-th element. | :any:`izatom(n) ` is the atomic number of the n-th element. | :any:`lloc_ps(n) ` specifies which angular momentum component is chosen as the local potential for the n-th element. :: &functional !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).) xc = 'PZ' / | :any:`xc ` specifies the exchange-correlation potential to be used in the calculation. :: &rgrid !number of spatial grids(x,y,z) num_rgrid(1:3) = 12, 12, 12 / | :any:`num_rgrid(i) ` specifies the number of real-space grid point in i-th direction. :: &kgrid !number of k-points(x,y,z) num_kgrid(1:3) = 4, 4, 4 / | :any:`num_kgrid(i) ` specifies the number of k-points for i-th direction discretizing the Brillouin zone. :: &tgrid !time step size and number of time grids(steps) dt = 0.08d0 nt = 6000 / | :any:`dt` specifies the time step. | :any:`nt` is the number of time steps for the time propagation. :: &emfield !envelope shape of the incident pulse('Acos2': cos^2 type envelope for vector potential) ae_shape1 = 'Acos2' !peak intensity(W/cm^2) of the incident pulse I_wcm2_1 = 1.0d12 !duration of the incident pulse tw1 = 441.195136248d0 !mean photon energy(average frequency multiplied by the Planck constant) of the incident pulse omega1 = 0.05696145187d0 !polarization unit vector(real part) for the incident pulse(x,y,z) epdir_re1(1:3) = 0.0d0, 0.0d0, 1.0d0 !--- Caution ---------------------------------------------------------! ! Defenition of the incident pulse is wrriten in: ! ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 ! !---------------------------------------------------------------------! / | :any:`ae_shape1 ` specifies the envelope of the field. | :any:`I_wcm2_1 ` specify the intensity of the pulse in unit of W/cm\ :sup:`2`\. | :any:`tw1 ` specifies the duration of the pulse. | :any:`omega1 ` specifies the mean photon energy of the pulse. | :any:`epdir_re1(i) ` specifies the i-th component of the real part of the polarization unit vector. :: &multiscale !number of macro grids in electromagnetic analysis for x, y, and z directions nx_m = 8 ny_m = 1 nz_m = 1 !macro grid spacing for x, y, and z directions hx_m = 100.0d0 hy_m = 100.0d0 hz_m = 100.0d0 !number of macroscopic grids for vacumm region !(nxvacl_m is for negative x-direction in front of material) !(nxvacr_m is for positive x-direction behind material) nxvacl_m = 1000 nxvacr_m = 1000 / | :any:`nx_m `, :any:`ny_m `, :any:`nz_m ` specify the number of macroscopic grid points inside the material. | :any:`hx_m `, :any:`hy_m `, :any:`hz_m ` specify the grid spacing of macroscopic coordinates. | :any:`nxvacl_m ` / :any:`nxvacr_m ` specifies the number of grid points in the vacuum region in the left / right side of the material. :: &maxwell !boundary condition of electromagnetic analysis !first index(1-3 rows) corresponds to x, y, and z directions !second index(1-2 columns) corresponds to bottom and top of the directions !('abc' is absorbing boundary condition) boundary_em(1,1) = 'abc' boundary_em(1,2) = 'abc' / | :any:`boundary_em(i,n) ` specifies the boundary condition for the electromagnetic analysis. The first index i corresponds to the x,y, and z direction. The second index n specifies left or right side of the material. :: &atomic_red_coor !cartesian atomic reduced coodinates 'Si' .0 .0 .0 1 'Si' .25 .25 .25 1 'Si' .5 .0 .5 1 'Si' .0 .5 .5 1 'Si' .5 .5 .0 1 'Si' .75 .25 .75 1 'Si' .25 .75 .75 1 'Si' .75 .75 .25 1 !--- Format ---------------------------------------------------! ! 'symbol' x y z index(correspond to that of pseudo potential) ! !--------------------------------------------------------------! / | :any:`&atomic_red_coor <&atomic_red_coor>` specifies spatial coordinates of atoms in reduced coordinate system. .. _output-files-7: Output files ^^^^^^^^^^^^ After the calculation, new directory *multiscale/* is created, then, following output files are created in the directory, +-----------------------------------+------------------------------------+ | file name | description | +-----------------------------------+------------------------------------+ | *Si_m/mxxxxxx/Si_rt.data* | | vector potential, electric field,| | | and matter current | | | | at macroscopic position *xxxxxx* | | | as functions of time | +-----------------------------------+------------------------------------+ | *Si_m/mxxxxxx/Si_rt_energy.data* | | components of total energy and | | | difference of total energy | | | | at macroscopic position *xxxxxx* | | | as functions of time | +-----------------------------------+------------------------------------+ | *Si_m/mxxxxxx/PS_Si_KY_n.dat* | | information on pseodupotential | | | file for silicon atom | | | | at macroscopic position *xxxxxx* | +-----------------------------------+------------------------------------+ | *Si_RT_Ac/Si_Ac_yyyyyy.data* | | vector potential, | | | electric field, | | | magnetic field, | | | | electromagnetic current density | | | at time step *yyyyyy* | | | | as function of space | +-----------------------------------+------------------------------------+ | *Si_wave.data* | amplitudes of incident, reflected, | | | and transmitted wave | +-----------------------------------+------------------------------------+ | You may download the above files (zipped file) from: | https://salmon-tddft.jp/webmanual/v_2_0_1/exercise_zip_files/07_bulkSi_ms.zip Explanations of the output files are described below: **Si_m/mxxxxxx/Si_rt.data** The number in the file name specifies the macroscopic position. Results of time evolution calculation for vector potential, electric field, and matter current density. :: # 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 (electrons) # 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.] **Si_m/mxxxxxx/Si_rt_energy.data** The number in the file name specifies the macroscopic position. *Eall* and *Eall-Eall0* are total energy and electronic excitation energy, respectively. :: # Real time calculation: # Eall: Total energy # Eall0: Initial energy # 1:Time[a.u.] 2:Eall[a.u.] 3:Eall-Eall0[a.u.] **Si_RT_Ac/Si_Ac_yyyyyy.data** The number in the file name specifies the iteration number. Various quantities at a time are shown as function of macroscopic position. :: # Multiscale TDDFT calculation # IX, IY, IZ: FDTD Grid index # x, y, z: Coordinates # Ac: Vector potential field # E: Electric field # J_em: Electromagnetic current density # 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:Jem_x[a.u.] 14:Jem_y[a.u.] 15:Jem_z[a.u.] 16:E_em[a.u./vol] 17:E_abs[a.u./vol] **Si_wave.data** Amplitudes of incident, reflected, and transmitted wave. :: # 1D multiscale calculation: # E_inc: E-field amplitude of incident wave # E_ref: E-field amplitude of reflected wave # E_tra: E-field amplitude of transmitted wave # 1:Time[a.u.] 2:E_inc_x[a.u.] 3:E_inc_y[a.u.] 4:E_inc_z[a.u.] 5:E_ref_x[a.u.] 6:E_ref_y[a.u.] 7:E_ref_z[a.u.] 8:E_tra_x[a.u.] 9:E_tra_y[a.u.] 10:E_tra_z[a.u.] Geometry optimization and Ehrenfest molecular dynamics ------------------------------------------------------ .. _exercise-8: Exercise-8: Geometry optimization of C2H2 molecule ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In this exercise, we learn the calculation of geometry optimization 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. Input files ^^^^^^^^^^^ To run the code, following files in samples are used: +-----------------------------------+-----------------------------------+ | file name | description | +-----------------------------------+-----------------------------------+ | *C2H2_opt.inp* | input file that contains input | | | keywords and their values | +-----------------------------------+-----------------------------------+ | *C_rps.dat* | pseodupotential file for carbon | | | atom | +-----------------------------------+-----------------------------------+ | *H_rps.dat* | pseudopotential file for hydrogen | | | atom | +-----------------------------------+-----------------------------------+ In the input file *C2H2_opt.inp*, input keywords are specified. Most of them are mandatory to execute the geometry optimization. This will help you to prepare an input file for other systems that you want to calculate. A complete list of the input keywords that can be used in the input file can be found in :any:`List of input keywords `. :: !########################################################################################! ! Excercise 08: Geometry optimization of C2H2 molecule ! !----------------------------------------------------------------------------------------! ! * The detail of this excercise is expained in our manual(see chapter: 'Exercises'). ! ! The manual can be obtained from: https://salmon-tddft.jp/documents.html ! ! * Input format consists of group of keywords like: ! ! &group ! ! input keyword = xxx ! ! / ! ! (see chapter: 'List of input keywords' in the manual) ! !----------------------------------------------------------------------------------------! ! * Conversion from unit_system = 'a.u.' to 'A_eV_fs': ! ! Length: 1 [a.u.] = 0.52917721067 [Angstrom] ! ! Energy: 1 [a.u.] = 27.21138505 [eV] ! ! Time : 1 [a.u.] = 0.02418884326505 [fs] ! !########################################################################################! &calculation !type of theory theory = 'dft' !geometry optimization option yn_opt = 'y' / | :any:`theory ` specifies which theoretical method is used in the calculation. | :any:`yn_opt ` is a switch to carry out the structure optimization. :: &control !common name of output files sysname = 'C2H2' / | :any:`sysname ` is a prefix for filenames of output files. :: &units !units used in input and output files unit_system = 'A_eV_fs' / | :any:`unit_system ` specifies which unit system is used in the input and output files. :: &system !periodic boundary condition yn_periodic = 'n' !grid box size(x,y,z) al(1:3) = 12.0d0, 12.0d0, 16.0d0 !number of elements, atoms, electrons and states(orbitals) nelem = 2 natom = 4 nelec = 10 nstate = 6 / | :any:`yn_periodic ` specifies whether or not periodic boundary condition is applied. | :any:`al(i) ` specifies the spatial box size of the cubiod cell. | :any:`nelem ` is the number of elements in the system. | :any:`natom ` is the number of atoms in the system. | :any:`nelec ` is the number of electrons in the system. | :any:`nstate ` is the number of orbitals that are used in the calculation. :: &pseudo !name of input pseudo potential file file_pseudo(1) = './C_rps.dat' file_pseudo(2) = './H_rps.dat' !atomic number of element izatom(1) = 6 izatom(2) = 1 !angular momentum of pseudopotential that will be treated as local lloc_ps(1) = 1 lloc_ps(2) = 0 !--- Caution ---------------------------------------! ! Indices must correspond to those in &atomic_coor. ! !---------------------------------------------------! / | :any:`file_pseudo(n) ` specifies the filename of the pseudopotential file of the n-th element. | :any:`izatom(n) ` is the atomic number of the n-th element. | :any:`lloc_ps(n) ` specifies which angular momentum component is chosen as the local potential for the n-th element. :: &functional !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).) xc = 'PZ' / | :any:`xc ` specifies the exchange-correlation potential to be used in the calculation. :: &rgrid !spatial grid spacing(x,y,z) dl(1:3) = 0.20d0, 0.20d, 0.20d0 / | :any:`dl(i) ` specifies the spatial grid spacing in i-th direction. :: &scf !maximum number of scf iteration and threshold of convergence for ground state calculation nscf = 300 threshold = 1.0d-9 / | :any:`nscf ` specifies the maximum number of SCF iterations. | :any:`threshold ` specifies the threshold to judge the convergence. :: &opt !threshold(maximum force on atom) of convergence for geometry optimization convrg_opt_fmax = 1.0d-3 / &atomic_coor !cartesian atomic coodinates 'C' 0.0 0.0 0.6 1 y 'H' 0.0 0.0 1.7 2 y 'C' 0.0 0.0 -0.6 1 y 'H' 0.0 0.0 -1.7 2 y !--- Format -------------------------------------------------------! ! 'symbol' x y z index(correspond to that of pseudo potential) y/n ! !--- Caution ------------------------------------------------------! ! final index(y/n) determines free/fix for the atom coordinate. ! !------------------------------------------------------------------! / | :any:`&atomic_coor <&atomic_coor>` specifies spatial coordinates of atoms. .. _output-files-8: Output files ^^^^^^^^^^^^ After the calculation, following output files and a directory are created in the directory that you run the code, +-------------------------------------+------------------------------------+ | name | description | +-------------------------------------+------------------------------------+ | *C2H2_info.data* | information on ground state | | | solution | +-------------------------------------+------------------------------------+ | *C2H2_eigen.data* | 1 particle energies | +-------------------------------------+------------------------------------+ | *C2H2_trj.xyz* | atomic coordinates during the | | | geometry optimization | +-------------------------------------+------------------------------------+ | *C2H2_k.data* 　 | k-point distribution | | | (for isolated systems, only | | | gamma point is described) | +-------------------------------------+------------------------------------+ | *data_for_restart* | directory where files used in | | | the real-time calculation are | | | contained | +-------------------------------------+------------------------------------+ | *PS_C_KY_n.dat* | information on pseodupotential | | | file for carbon atom | +-------------------------------------+------------------------------------+ | *PS_H_KY_n.dat* | information on pseodupotential | | | file for hydrogen atom | +-------------------------------------+------------------------------------+ | You may download the above files (zipped file, except for the directory *data_for_restart*) from: | https://salmon-tddft.jp/webmanual/v_2_0_1/exercise_zip_files/08_C2H2_opt.zip Main results of the calculation such as orbital energies are included in *C2H2_info.data*. Explanations of the *C2H2_info.data* and other output files are below: **C2H2_info.data** Calculated orbital and total energies as well as parameters specified in the input file are shown in this file. **C2H2_eigen.data** 1 particle energies. :: #esp: single-particle energies (eigen energies) #occ: occupation numbers, io: orbital index # 1:io, 2:esp[eV], 3:occ **C2H2_trj.xyz** The atomic coordinates during the geometry optimization in xyz format. **C2H2_k.data** k-point distribution(for isolated systems, only gamma point is described). :: # 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] # coefficients (2*pi/a [a.u.]) in kx, ky, kz .. _exercise-9: Exercise-9: Ehrenfest molecular dynamics of C2H2 molecule ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In this exercise, we learn the calculation of the molecular dynamics in the acetylene (C2H2) molecule under a pulsed electric field, solving the time-dependent Kohn-Sham equation and the Newtonian equation. As outputs of the calculation, time-evolution of the electron density as well as molecular structures and associated quantities such as the electron and ion kinetic energies, the electric dipole moment of the system and temperature as functions of time are calculated.. This tutorial should be carried out after finishing the geometry optimization that was explained in :any:`Exercise-8 `. 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 in samples are used. The directory *restart* is created in the ground state calculation as *data_for_restart*. Pseudopotential files are already used in the geometry optimization. Therefore, *C2H2_md.inp* that specifies input keywords and their values for the pulsed electric field and molecular dynamics calculations is the only file that the users need to prepare. +-----------------------------------+-------------------------------------+ | file name | description | +-----------------------------------+-------------------------------------+ | *C2H2_md.inp* | input file that contain input | | | keywords and their values. | +-----------------------------------+-------------------------------------+ | *C_rps.dat* | pseodupotential file for carbon | +-----------------------------------+-------------------------------------+ | *H_rps.dat* | pseudopotential file for hydrogen | +-----------------------------------+-------------------------------------+ | *restart* | | directory created in the geometry | | | optimization | | | | (rename the directory from | | | *data_for_restart* to *restart*) | +-----------------------------------+-------------------------------------+ In the input file *C2H2_md.inp*, input keywords are specified. Most of them are mandatory to execute the calculation of electron dynamics induced by a pulsed electric field. This will help you to prepare the input file for other systems and other pulsed electric fields with molecular dynamics calculation that you want to calculate. A complete list of the input keywords that can be used in the input file can be found in :any:`List of input keywords `. :: !########################################################################################! ! Excercise 09: Ehrenfest molecular dynamics of C2H2 molecule ! !----------------------------------------------------------------------------------------! ! * The detail of this excercise is expained in our manual(see chapter: 'Exercises'). ! ! The manual can be obtained from: https://salmon-tddft.jp/documents.html ! ! * Input format consists of group of keywords like: ! ! &group ! ! input keyword = xxx ! ! / ! ! (see chapter: 'List of input keywords' in the manual) ! !----------------------------------------------------------------------------------------! ! * Conversion from unit_system = 'a.u.' to 'A_eV_fs': ! ! Length: 1 [a.u.] = 0.52917721067 [Angstrom] ! ! Energy: 1 [a.u.] = 27.21138505 [eV] ! ! Time : 1 [a.u.] = 0.02418884326505 [fs] ! !----------------------------------------------------------------------------------------! ! * Ehrenfest-MD option is still trial. ! ! * Copy the ground state data directory ('data_for_restart') (or make symbolic link) ! ! calculated in 'samples/exercise_08_C2H2_opt/' and rename the directory to 'restart/' ! ! in the current directory. ! !########################################################################################! &calculation !type of theory theory = 'tddft_pulse' !molecular dynamics option yn_md = 'y' / | :any:`theory ` specifies which theoretical method is used in the calculation. | :any:`yn_md ` is a switch for Ehrenfest molecular dynamics. :: &control !common name of output files sysname = 'C2H2' / | :any:`sysname ` is a prefix for filenames of output files. :: &units !units used in input and output files unit_system = 'A_eV_fs' / | :any:`unit_system ` specifies which unit system is used in the input and output files. :: &system !periodic boundary condition yn_periodic = 'n' !grid box size(x,y,z) al(1:3) = 12.0d0, 12.0d0, 16.0d0 !number of elements, atoms, electrons and states(orbitals) nelem = 2 natom = 4 nelec = 10 nstate = 6 / | :any:`yn_periodic ` specifies whether or not periodic boundary condition is applied. | :any:`al(i) ` specifies the spatial box size of the cubiod cell. | :any:`nelem ` is the number of elements in the system. | :any:`natom ` is the number of atoms in the system. | :any:`nelec ` is the number of electrons in the system. | :any:`nstate ` is the number of orbitals that are used in the calculation. :: &pseudo !name of input pseudo potential file file_pseudo(1) = './C_rps.dat' file_pseudo(2) = './H_rps.dat' !atomic number of element izatom(1) = 6 izatom(2) = 1 !angular momentum of pseudopotential that will be treated as local lloc_ps(1) = 1 lloc_ps(2) = 0 !--- Caution ---------------------------------------! ! Indices must correspond to those in &atomic_coor. ! !---------------------------------------------------! / | :any:`file_pseudo(n) ` specifies the filename of the pseudopotential file of the n-th element. | :any:`izatom(n) ` is the atomic number of the n-th element. | :any:`lloc_ps(n) ` specifies which angular momentum component is chosen as the local potential for the n-th element. :: &functional !functional('PZ' is Perdew-Zunger LDA: Phys. Rev. B 23, 5048 (1981).) xc = 'PZ' / | :any:`xc ` specifies the exchange-correlation potential to be used in the calculation. :: &rgrid !spatial grid spacing(x,y,z) dl(1:3) = 0.20d0, 0.20d0, 0.20d0 / | :any:`dl(i) ` specifies the spatial grid spacing in i-th direction. :: &tgrid !time step size and number of time grids(steps) dt = 1.00d-3 nt = 5000 / | :any:`dt` specifies the time step. | :any:`nt` is the number of time steps for the time propagation. :: &emfield !envelope shape of the incident pulse('Ecos2': cos^2 type envelope for scalar potential) ae_shape1 = 'Ecos2' !peak intensity(W/cm^2) of the incident pulse I_wcm2_1 = 1.00d8 !duration of the incident pulse tw1 = 6.00d0 !mean photon energy(average frequency multiplied by the Planck constant) of the incident pulse omega1 = 9.28d0 !polarization unit vector(real part) for the incident pulse(x,y,z) epdir_re1(1:3) = 0.00d0, 0.00d0, 1.00d0 !carrier emvelope phase of the incident pulse !(phi_cep1 must be 0.25 + 0.5 * n(integer) when ae_shape1 = 'Ecos2') phi_cep1 = 0.75d0 !--- Caution ---------------------------------------------------------! ! Defenition of the incident pulse is wrriten in: ! ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 ! !---------------------------------------------------------------------! / | :any:`ae_shape1 ` specifies the envelope of the field. | :any:`I_wcm2_1 ` specify the intensity of the pulse in unit of W/cm\ :sup:`2`\. | :any:`tw1 ` specifies the duration of the pulse. | :any:`omega1 ` specifies the mean photon energy of the pulse. | :any:`epdir_re1(i) ` specifies the i-th component of the real part of the polarization unit vector. | :any:`phi_cep1 ` specifies the carrier-envelope phase of the pulse. :: &md !ensemble ensemble = 'NVE' !set of initial velocities yn_set_ini_velocity = 'y' !setting temperature [K] for NVT ensemble, velocity scaling, !and generating initial velocities temperature0_ion_k = 300.0d0 !time step interval for updating pseudopotential step_update_ps = 20 / | :any:`ensemble ` specifies the choice of the ensemble. | :any:`yn_set_ini_velocity ` is a switch to prepare initial velocity for atoms. | :any:`temperature0_ion_k ` specifies the temperature that is used to generate initial velocity of ions. | :any:`step_update_ps ` specifies the time step interval to update projector for the nonlocal pseudopotential. .. _output-files-9: Output files ^^^^^^^^^^^^ After the calculation, following output files are created in the directory that you run the code, +-------------------------------------+------------------------------------+ | file name | description | +-------------------------------------+------------------------------------+ | *C2H2_pulse.data* | dipole moment as | | | functions of energy | +-------------------------------------+------------------------------------+ | *C2H2_rt.data* | | components of | | | change of dipole moment | | | (electrons/plus definition) | | | | and total dipole moment | | | (electrons/minus + ions/plus) | | | as functions of time | +-------------------------------------+------------------------------------+ | *C2H2_rt_energy.data* | components of | | | total energy | | | and difference of total energy | | | as functions of time | +-------------------------------------+------------------------------------+ | *C2H2_trj.xyz* | Trajectory of atoms(ions): | | | Atomic coordinates, velocities, | | | and forces are printed | +-------------------------------------+------------------------------------+ | *PS_C_KY_n.dat* | information on pseodupotential | | | file for carbon atom | +-------------------------------------+------------------------------------+ | *PS_H_KY_n.dat* | information on pseodupotential | | | file for hydrogen atom | +-------------------------------------+------------------------------------+ | You may download the above files (zipped file) from: | https://salmon-tddft.jp/webmanual/v_2_0_1/exercise_zip_files/09_C2H2_md.zip Explanations of the files are described below: **C2H2_pulse.data** Time-frequency Fourier transformation of the dipole moment. :: # Fourier-transform spectra: # energy: Frequency # dm: Dopile moment # 1:energy[eV] 2:Re(dm_x)[fs*Angstrom] 3:Re(dm_y)[fs*Angstrom] 4:Re(dm_z)[fs*Angstrom] 5:Im(dm_x)[fs*Angstrom] 6:Im(dm_y)[fs*Angstrom] 7:Im(dm_z)[fs*Angstrom] 8:|dm_x|^2[fs^2*Angstrom^2] 9:|dm_y|^2[fs^2*Angstrom^2] 10:|dm_z|^2[fs^2*Angstrom^2] **C2H2_rt.data** Results of time evolution calculation for vector potential, electric field, and dipole moment. :: # 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 # ddm_e: Change of dipole moment (electrons/plus definition) # dm: Total dipole moment (electrons/minus + ions/plus) # 1:Time[fs] 2:Ac_ext_x[fs*V/Angstrom] 3:Ac_ext_y[fs*V/Angstrom] 4:Ac_ext_z[fs*V/Angstrom] 5:E_ext_x[V/Angstrom] 6:E_ext_y[V/Angstrom] 7:E_ext_z[V/Angstrom] 8:Ac_tot_x[fs*V/Angstrom] 9:Ac_tot_y[fs*V/Angstrom] 10:Ac_tot_z[fs*V/Angstrom] 11:E_tot_x[V/Angstrom] 12:E_tot_y[V/Angstrom] 13:E_tot_z[V/Angstrom] 14:ddm_e_x[Angstrom] 15:ddm_e_y[Angstrom] 16:ddm_e_z[Angstrom] 17:dm_x[Angstrom] 18:dm_y[Angstrom] 19:dm_z[Angstrom] **C2H2_rt_energy.data** *Eall* and *Eall-Eall0* are total energy and electronic excitation energy, respectively. :: # Real time calculation: # Eall: Total energy # Eall0: Initial energy # Tion: Kinetic energy of ions # Temperature_ion: Temperature of ions # E_work: Work energy of ions(sum f*dr) # 1:Time[fs] 2:Eall[eV] 3:Eall-Eall0[eV] # 4:Tion[eV] 5:Temperature_ion[K] 6:E_work[eV] **C2H2_trj.xyz** Atomic coordinates [Angstrom], velocities [a.u.] and forces [a.u.] are printed along the time evolution in xyz format. FDTD simulation(electromagnetic analysis) ----------------------------------------- .. _exercise-10: Exercise-10: Pulsed electric field response of a metallic nanosphere in classical electromagnetism(FDTD simulation) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In this exercise, we learn the pulsed electric field response in the metallic nanosphere, solving the time-dependent Maxwell equations. As outputs of the calculation, the time response of the electromagnetic field is calculated. 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, the input file *classicEM_rt_pulse.inp* that contains input keywords and their values for the pulsed electric field calculation is required. The shape file of the metallic nanosphere *shape.cube* is also required. The shape file can be generated by program ``FDTD_make_shape`` in SALMON utilities: https://salmon-tddft.jp/utilities.html 'shape.inp' is an input file for 'FDTD_make_shape' to generate 'shape.cube'. The input files are in samples +-----------------------------------+------------------------------------+ | file name | description | +-----------------------------------+------------------------------------+ | *classicEM_rt_pulse.inp* | input file that contain input | | | keywords and their values. | +-----------------------------------+------------------------------------+ | *shape.cube* | shape file for fdtd | +-----------------------------------+------------------------------------+ | *shape.inp* | input file for ``FDTD_make_shape`` | +-----------------------------------+------------------------------------+ In the input file *classicEM_rt_pulse.inp*, input keywords are specified. Most of them are mandatory to execute the 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 input keywords that can be used in the input file can be found in :any:`List of input keywords `. :: !########################################################################################! ! Excercise 10: Pulsed electric field response of a metallic nanosphere ! ! in classical electromagnetism(FDTD simulation) ! !----------------------------------------------------------------------------------------! ! * The detail of this excercise is expained in our manual(see chapter: 'Exercises'). ! ! The manual can be obtained from: https://salmon-tddft.jp/documents.html ! ! * Input format consists of group of keywords like: ! ! &group ! ! input keyword = xxx ! ! / ! ! (see chapter: 'List of input keywords' in the manual) ! !----------------------------------------------------------------------------------------! ! * Conversion from unit_system = 'a.u.' to 'A_eV_fs': ! ! Length: 1 [a.u.] = 0.52917721067 [Angstrom] ! ! Energy: 1 [a.u.] = 27.21138505 [eV] ! ! Time : 1 [a.u.] = 0.02418884326505 [fs] ! !----------------------------------------------------------------------------------------! ! * The read-in file 'shape_file' in &maxwell category can be generated by program ! ! 'FDTD_make_shape' in SALMON utilities(https://salmon-tddft.jp/utilities.html). ! ! 'shape.inp' is an input file for 'FDTD_make_shape' to generate 'shape.cube'. ! ! * Results can be visualized by program 'FDTD_make_figani' in SALMON utilities. ! !########################################################################################! &calculation !type of theory theory = 'maxwell' / | :any:`theory ` specifies which theoretical method is used in the calculation. :: &control !name of directory where output files are contained base_directory = 'result' / | :any:`base_directory ` specifies the directory name where output files are generated. :: &units !units used in input and output files unit_system = 'A_eV_fs' / | :any:`unit_system ` specifies which unit system is used in the input and output files. :: &system !periodic boundary condition yn_periodic = 'n' / | :any:`yn_periodic ` specifies whether or not periodic boundary condition is applied. :: &emfield !envelope shape of the incident pulse('Ecos2': cos^2 type envelope for scalar potential) ae_shape1 = 'Ecos2' !peak intensity(W/cm^2) of the incident pulse I_wcm2_1 = 1.00d8 !duration of the incident pulse tw1 = 4.60d0 !mean photon energy(average frequency multiplied by the Planck constant) of the incident pulse omega1 = 5.49d0 !polarization unit vector(real part) for the incident pulse(x,y,z) epdir_re1(1:3) = 0.00d0, 0.00d0, 1.00d0 !carrier emvelope phase of the incident pulse !(phi_cep1 must be 0.25 + 0.5 * n(integer) when ae_shape1 = 'Ecos2') phi_cep1 = 0.75d0 !--- Caution ---------------------------------------------------------! ! Defenition of the incident pulse is wrriten in: ! ! https://www.sciencedirect.com/science/article/pii/S0010465518303412 ! !---------------------------------------------------------------------! / | :any:`ae_shape1 ` specifies the envelope of the field. | :any:`I_wcm2_1 ` specify the intensity of the pulse in unit of W/cm\ :sup:`2`\. | :any:`tw1 ` specifies the duration of the pulse. | :any:`omega1 ` specifies the mean photon energy of the pulse. | :any:`epdir_re1(i) ` specifies the i-th component of the real part of the polarization unit vector. | :any:`phi_cep1 ` specifies the carrier-envelope phase of the pulse. :: &maxwell !box size and spacing of spatial grid(x,y,z) al_em(1:3) = 120d0, 120d0, 120d0 dl_em(1:3) = 1.2d0, 1.2d0, 1.2d0 !time step size and number of time grids(steps) dt_em = 2.30d-4 nt_em = 20000 !name of input shape file and number of media in the file shape_file = './shape.cube' media_num = 1 !*** MEDIA INFORMATION(START) **************************************! !type of media(media ID) media_type(1) = 'lorentz-drude' !--- Au described by Lorentz-Drude model ---------------------------! ! The parameters are determined from: ! ! (https://www.osapublishing.org/ao/abstract.cfm?uri=ao-37-22-5271) ! !-------------------------------------------------------------------! !number of poles and plasma frequency of media(media ID) pole_num_ld(1) = 6 omega_p_ld(1) = 9.030d0 !oscillator strength, collision frequency, !and oscillator frequency of media(media ID,pole ID) f_ld(1,1:6) = 0.760d0, 0.024d0, 0.010d0, 0.071d0, 0.601d0, 4.384d0 gamma_ld(1,1:6) = 0.053d0, 0.241d0, 0.345d0, 0.870d0, 2.494d0, 2.214d0 omega_ld(1,1:6) = 0.000d0, 0.415d0, 0.830d0, 2.969d0, 4.304d0, 13.32d0 !*** MEDIA INFORMATION(END) ****************************************! !*** SOURCE INFORMATION(START) *************************************! !type of method to generate the incident pulse !('source': incident current source) wave_input = 'source' !location of source(x,y,z) source_loc1(1:3) = -37.8d0, 0.0d0, 0.0d0 !propagation direction of the incident pulse(x,y,z) ek_dir1(1:3) = 1.0d0, 0.0d0, 0.0d0 !*** SOURCE INFORMATION(END) ***************************************! !*** OBSERVATION INFORMATION(START) ********************************! !number of observation points obs_num_em = 1 !time step interval for sampling obs_samp_em = 20 !location of observation point(observation ID,x,y,z) obs_loc_em(1,1:3) = 0.0d0, 0.0d0, 0.0d0 !output flag for electrmagnetic field distribution(observation ID) yn_obs_plane_em(1) = 'n' !--- Make of animation file ----------------------------------------! ! When yn_obs_plane_em(1) = 'y', animation file can be made ! ! by program 'FDTD_make_figani' in SALMON utilities. ! ! The animation file visualizes electromagnetic field distributions ! ! on the cross-section including the observation point ! ! whose location is determined by obs_loc_em. ! !-------------------------------------------------------------------! !*** OBSERVATION INFORMATION(END) **********************************! / | :any:`al_em(i) ` specifies the lengths of three sides of the cuboid where the grid points are prepared. | :any:`dl_em(i) ` specifies the grid spacings in three Cartesian directions. | :any:`dt_em ` specifies the time step of the time evolution calculation. | :any:`nt_em ` specifies the number of time steps in the calculation. | :any:`shape_file ` specifies the filename of the shape file. | :any:`media_num ` specifies the number of the types of media that is provided in the shape file. | :any:`media_type(n) ` specifies the type of the n-th media. | :any:`pole_num_ld(n) ` and :any:`omega_p_ld(n) ` specify the number of poles and the plasmal frequency of the n-th media, respectively. | :any:`f_ld(n,m) `, :any:`omega_ld(n,m) `, :any:`gamma_ld(n,m) ` specify the oscillator strength, oscillator frequency, and collision frequency of the m-th pole of the n-th media, respectively. | :any:`wave_input ` specifies an electric current source that is used for the generation of the pulse. | :any:`source_loc1(i) ` specifies the coordinate of the current source. | :any:`ek_dir1(i) ` specifies the propagation direction of the pulse. | :any:`obs_num_em ` specifies the number of the observing point. | :any:`obs_samp_em ` specifies the sampling interval. | :any:`obs_loc_em(n,i) ` specifies the coordinate of n-th observing point. | :any:`yn_obs_plane_em(n) ` is a switch to output the electromagnetic fields on the xy, yz, and xz planes that include the n-th observation point. .. _output-files-10: Output files ^^^^^^^^^^^^ After the calculation, following output files are created in the directory ``'result'``, +-------------------------------------+-----------------------------------+ | file name | description | +-------------------------------------+-----------------------------------+ | *obs0_info.data* | information to generate animation | +-------------------------------------+-----------------------------------+ | *obs1_at_point_rt.data* | components of | | | electric and magnetic fields | | | as functions of time | +-------------------------------------+-----------------------------------+ | You may download the above files (zipped file) from: | https://salmon-tddft.jp/webmanual/v_2_0_1/exercise_zip_files/10_classicEM_rt.zip Explanations of the files are described below: **obs0_info.data** This file is used to generate animation files by using SALMON utilities: https://salmon-tddft.jp/utilities.html **obs1_at_point_rt.data** Results of time evolution calculation for electric and magnetic fields at observation point 1. :: # Real time calculation: # E: Electric field # H: Magnetic field # 1:Time[fs] 2:E_x[V/Angstrom] 3:E_y[V/Angstrom] 4:E_z[V/Angstrom] 5:H_x[A/Angstrom] 6:H_y[A/Angstrom] 7:H_z[A/Angstrom]