SALMON TUTORIAL, TSUKUBA, 2018 (modified for SALMON-v.1.2.0)

How to Use SALMON:
Periodic Systems
Exercise-3

Atsushi Yamada
Center for Computational Sciences, University of Tsukuba
Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/1

Introduction and Exercise Menu
Option for crystal system(periodic boundary condition):“iperiodic = 3”

Menu of the exercise(Input file)....
sysname = 'Si'/&system
iperiodic = 3
al = 10.26d0,10.26d0,10.26d0
isym = 1
nstate = 32....

Calculations of silicon (Si) :1. Ground State
2. Dielectric Function
3. Real-Time TDDFT Simulation with Incident Laser Pulse
Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/
SALMON TUTORIAL, TSUKUBA, 20182

1. Ground State Calculation(Job Submission)

Prepare files 

Submit job %> ls
Si_rps.dat

Si_sc_gs.inp%> (job submit command)

Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/
SALMON TUTORIAL, TSUKUBA, 20173

1. Ground State Calculation(input file)&functional (Functional)
xc ='BJ_PW'
Functional/

Si_sc_gs.inp(Calculation Type)&calculation
calc_mode = 'GS'/
&control (Control)
sysname = 'Si'/

It specifies ground statecalculation only

Body name of output file names.
e.x. “Si_GS.out”(one of output file names)(space grid)&rgridnum_rgrid = 12,12,12/

Atomic unit [a.u.] is used as default.
To use Å/fs/eV unit system, give&units
unit_system='A_eV_fs'/(but W/cm2 for electric field(laser) strength)(multiples of ４ only）
division number ofunit cell length(# of ｋ-points) （Even number only. User&kgrid
specific k-points is available with
num_kgrid = 4,4,4
reading option of external file）/&system (System)
Unit cell length
iperiodic = 3(cuboid only)(Parameters of Ground State SCF)
&scf
al = 10.26d0,10.26d0,10.26d0
nscf = 120
Maximum iteration number
isym = 1
no symmetry
threshold=1.0d-7
nstate = 32
# of bands used in the calculation
SCF convergence threshold:/nelec = 32
（In the case, 16 occupied# of electrons
electron density difference per one electronand 16 unoccupiednelem = 1# of atomic species
orbitals are used）&atomic_red_coor(atomic coordinates)
natom = 8
# of atoms'Si'.0.0.0
1/'Si' .25 .25 .25 1'Si' .5 .0 .5 1
(Pseudopotential) Atomic number of the 1-th&pseudo[species, x,y,z, species-ID]'Si' .0 .5 .5 1
iZatom(1)=14
atomic species'Si' .5 .5 .0 1
Here is reduced coordinate (unitpseudo_file(1) = './Si_rps.dat'
File name of pseudopotential'Si' .75 .25 .75 1 cell length unit).
Lloc_ps(1)=2
Number of the Reference
Use ”&atomic_coor” for a.u.(or'Si'.25.75.75
1angularmomentum/Å) unit,
Scalable Ab-initio Light-Matter simulator 'Si'for Optics.75 and.75Nanosciences.25 1（given in the pseudo4
http://salmon-tddft.jp/
SALMONTUTORIAL,TSUKUBA,2018
potential data file）/

1. Ground State Calculation(Output files)
List of Output Files:•variables.log --- List of inputted variables(keywords) in the calculation•out.log--- Standard output log（Here, this is just example name. The file name is given in your job script file）•

Si_gs_info.data --- Information of GS SCF calculation etc•

Si_k.data•

Si_eigen.data --- Orbital eigen energy values in GS ( band structure)•gs_wfn_k/--- k-points information--- GS wave function(This can be used as read-in data in the next calculation)•

PS_Si_KY_n.dat--- Temporary data of pseudopotential•

stdout.log--- Standard output of system（file name given in job.sh）•stderr.log--- Standard error of system （file name given in job.sh）

Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/
SALMON TUTORIAL, TSUKUBA, 20185

1. Ground State Calculation(Check of results)
Followings are useful to check the calculation results.

1. Convergence of SCF calculation（next page）• Standard output (out.log).
• Si_gs_info.out (this file is generated after SCF finished)

2. Band gap•

Si_gs_info.out
Band gaps are printed in the lines of ”Fundamental gap”(indirecttransition) and ”BG between same k-point”(direct transition).

Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/
SALMON TUTORIAL, TSUKUBA, 20186

1. Ground State Calculation(Check of Convergence of SCF)%> less out.log…. (omit) …..
Iteration number----------------------------------------------iter =62
Total Energy = -31.2252432282157 -2.500217455292386E-007
Total energy, total energy difference from the last stepjav(1),jav(2),jav(3)= 0.551402E-12 -0.197001E-10 0.131539E-10(orbital eigen energies)
1 -0.150535 2 -0.122854 3 -0.122854 4 -0.122854
Eigen orbital energy of the first k-point
5 -0.027750 6 -0.027750 7 -0.027750 8 0.001569
9 0.129800 10 0.129800 11 0.129800 12 0.151207
13 0.151207 14 0.151207 15 0.168080 16 0.168080
17 0.300588 18 0.304820 19 0.304820 20 0.304820
21 0.338168 22 0.338168 23 0.349556 24 0.349556（Information of GS convergence is also
25 0.349556 26 0.360471 27 0.360471 28 0.360471
printed in Si_GS.out after the SCF finished）
29 0.487072 30 0.487079 31 0.487096 32 0.515053(forces on atoms)
1 -0.000000 -0.000000
0.000000
Forces on each atom
2 -0.000000 -0.000000 -0.000000
30.000000
0.000000
0.000000
4 -0.000000
0.000000
0.000000
50.000000
0.000000 -0.000000
60.000000
0.000000 -0.000000
Average and Maximum of Eigen energy difference
7 -0.000000 -0.000000 -0.000000
80.000000
0.000000 -0.000000
Total electron density difference (square root of diff.),e_var_ave,e_var_max= 2.807887450831825E-009 6.335738233753371E-008
Electron density difference per one electrondiff-dns,ddns/nelec= 1.019596987160528E-007 7.949054588372419E-008----------------------------------------------(absolute value of the diff.)
GS converged at 62
Convergence(The red one is used to judge convergence by default)…. (omit) …..

Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/
SALMON TUTORIAL, TSUKUBA, 20187

2. Calculation of Dielectric Function(Job Submission)

Prepare files Copy the pre-calculated ground state data(or link)
Submit job %> ls
Si_rps.dat

Si_sc_dielec.inp%> cp -r (directory of the step 1)/gs_wfn_k/./%> (job submit command)

Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/
SALMON TUTORIAL, TSUKUBA, 20178

2. Calculation of Dielectric Function(Input File)
2.Input file for dielectric function calculation:
Si_sc_dielec.inp&calculation
calc_mode = 'RT'/
Real-Time:i.e. RS-TDDFT&controlsysname = 'Si'/&system
iperiodic = 3
al = 10.26d0,10.26d0,10.26d0
isym = 1
nstate = 32
nelec = 32
nelem = 1
natom = 8/
&pseudoiZatom(1)=14
pseudo_file(1) = './Si_rps.dat'
Lloc_ps(1)=2/&functional
xc ='BJ_PW'/&rgridnum_rgrid = 12,12,12/&kgridnum_kgrid = 4,4,4/(time grid)&tgrid# of time steps
nt=3000
dt=0.16
Time step size [a.u.]/(Laser/External field)&emfield
Type of Laser
ae_shape1 = 'impulse'(or electric field)
Direction of
epdir_re1 = 0.,0.,1.
electric field vector/&atomic_red_coor'Si' .0 .0 .0 1
'Si' .25 .25 .25 1….. (omit) ….
/&propagation (time integration)
propagator='etrs'
Algorithm of/time integration

Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/
SALMON TUTORIAL, TSUKUBA, 20189

2. Calculation of Dielectric Function(Output Files)
List of Output Files:•variables.log ---•out.log---•

Si_rt.data---Same as the example 1 (see example 1)vector potential, electric fields, current densities (at eachtime step)•Si_rt_energy.data--

energies (every 10 steps)•Si_lr.data

data from linear response calculation including dielectric---function ε(ω) (in the case of ”impulse” keyword)•

PS_Si_KY_n.dat ---•stdout.log---•

stderr.log---•

sc_performance_20171027_155208.log

Log from system (see example 1)--- measured calculation time

Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/
SALMON TUTORIAL, TSUKUBA, 201810

2. Calculation of Dielectric Function(Check of results)
 Output file format of Si_lr.data
1: Frequency (or Energy) [au]2: Re(σ_x), 3: Re(σ_y), 4: Re(σ_z), 5: Im(σ_x), 6: Im(σ_y), 7: Im(σ_z),
8: Re(ε_x), 9: Re(ε_y), 10: Re(ε_z), 11: Im(ε_x), 12: Im(ε_y), 13: Im(ε_z)
Imaginary part of Dielectric function,
which can be converted to absorption spectrum%> gnuplot

gnuplot> p “Si_lr.data” u ($1*27.2114):13 w l

1au(Hartree)=27.2114eV

 Imaginary part of dielectric function (z-component)
as a function of energyIm[ ε(ω) ]※Tips to get beautiful ε(ω):

Energy[eV]See K.Yabana, et.al., Phys.Rev.B 85,045134 (2012) for the treatment in the small ω.

Relatively short simulation time (not long simulation time, not very short time) is good to get smooth ε（ω）
curve due to the discrete k-points.

Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/SALMON TUTORIAL, TSUKUBA, 201811

3. Real-Time TDDFT Simulation
with Incident Laser pulse (Job Submission)

Prepare files Submit job %> ls
Si_rps.dat

Si_sc_pulse.inp%> (job submit command)

In this calculation, it’s not necessary tocopy the pre-calculated ground state data like the previous case(see the next slide)

Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/
SALMON TUTORIAL, TSUKUBA, 201712

3. Real-Time TDDFT Simulation
with Incident Laser pulse (Input File)(Although you can use option to read the ground state wave function as the last example,
Altanative option including both of GS calculation & Real-Time TDDFT simulation is used here. )Input File: Si_sc_pulse.inp&calculation
calc_mode = 'GS_RT'/&controlsysname = 'Si'/&functional
xc ='TBmBJ'/

GS + RT(i.e. Ground State calc.
+ Real-Time TDDFT)&system
iperiodic = 3
al = 10.26d0,10.26d0,10.26d0
isym = 1
nstate = 32
nelec = 32
nelem = 1
natom = 8/
&pseudoiZatom(1)=14
pseudo_file(1) = './Si_rps.dat'
Lloc_ps(1)=2/&rgridnum_rgrid = 12,12,12/&kgridnum_kgrid = 4,4,4/&tgridnt=3000
dt=0.16/&propagation
propagator='etrs'/&scf
nscf = 120
threshold=1.0d-7/

Function Type of Electric Field.
Vector potential with cos2type envelop&emfield
ae_shape1 = 'Acos2'
rlaser_int_wcm2_1 = 1d14
pulse_tw1 = 441.195136248d0
omega1 = 0.05696145187d0
epdir_re1 = 0.,0.,1.
/

Pulse Intensity atmaximum [W/cm2]
Time width of pulse
Pulse frequency(photon energy)&atomic_red_coor'Si' .0 .0 .0 1
'Si' .25 .25 .25 1….. (omit) …..
/

Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/
SALMON TUTORIAL, TSUKUBA, 201813

3. Real-Time TDDFT Simulation
with Incident Laser pulse (Input File)
Other analysis options are available.
( use &analysis block in input file)For examples: Print DOS

 Use keyword like “out_dos=‘y’” Print projection analysis

 Use keyword like “projection_option=‘gs’”( number of excited electrons and holes)
 Print electron density (cube format etc)
 ……
……

 use keywords like
out_dns_rt = 'y'out_dns_rt_step = 3000
format3d = 'cube'

Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/SALMON TUTORIAL, TSUKUBA, 201814

3. Real-Time TDDFT Simulation
with Incident Laser pulse (Output File)
List of Output Files:（※Other output files can be generated with analysis options in input file)•variables.log---•

out.log•

Si_gs_info.data•

Si_eigen.data•

Si_k.data•

Si_rt.data•

Si_rt_energy.data•

Si_lr.data•

PS_Si_KY_n.dat•

stdout.log•

stderr.log•

sc_performance_20171027_155208.log

Same as the example 1,2 (see example 1,2)---Output for ground state calculation (see example 1)

Output for RT-TDDFT calculation (see example 2)

Log from system (see example 1,2)

Scalable Ab-initio Light-Matter simulator for Optics and Nanosciences
http://salmon-tddft.jp/
SALMON TUTORIAL, TSUKUBA, 201815

3. Real-Time TDDFT Simulation
with Incident Laser pulse (Check of Results)
units are all [a.u.] Format of output file: Si_rt.datac = light speed
1: 𝑡External Vector Potential
2:𝐴𝑒𝑥𝑡𝑡 /c, 3:𝐴𝑒𝑥𝑡𝑡 /c,
4:𝐴𝑒𝑥𝑡𝑡 /c𝑥𝑦𝑧
External Electric Field
5:𝐸𝑥𝑒𝑥𝑡 𝑡
6:𝐸𝑦𝑒𝑥𝑡 𝑡
7:𝐸𝑧𝑒𝑥𝑡 𝑡
8:𝐴𝑡𝑜𝑡𝑡 /c 9:𝐴𝑡𝑜𝑡
10:𝐴𝑡𝑜𝑡𝑡 /c
Total (External+Induced) Vector Potential
𝑥𝑦 𝑡 /c𝑧
11:𝐸𝑥𝑡𝑜𝑡 𝑡
12:𝐸𝑦𝑡𝑜𝑡 𝑡
13:𝐸𝑧𝑡𝑜𝑡 𝑡
Total (External+Induced) Electric Field𝑚𝑚𝑚
14:𝐽𝑥 𝑡15:𝐽𝑦 𝑡16:𝐽𝑧 𝑡Current Density of Matter Format of output file: Si_rt_energy.data
1: 𝑡
2:𝐸𝑡𝑜𝑡 (𝑡)3:𝐸𝑡𝑜𝑡 𝑡 − 𝐸𝑡𝑜𝑡 (0)%> gnuplot

Total Energy

Excitation Energy

gnuplot> p “Si_rt.data” u 1:7 w l Incident Electric Field (z-component)

gnuplot> p “Si_rt.data” u 1:16 w l

 Current Density as a function of t (z-component)

gnuplot> p “Si_rt_energy.data” u 1:($3*27.2114) w l

 Excitation Energy
as a function of time𝑚 and Nanosciences
𝐸𝑧𝑒𝑥𝑡Scalable𝑡 Ab-initio Light-Matter simulator for𝐽Optics
𝑧 𝑡
http://salmon-tddft.jp/SALMON TUTORIAL, TSUKUBA, 2018

𝐸𝑡𝑜𝑡 𝑡 − 𝐸𝑡𝑜𝑡16(0)