ABCAP : advanced — qsub sh —August 21, 20193

Band Structure Calculation

3.1

Ferromagnetic Fe

Prepare a directory for the calculation:

Purpose:----------------------------cd ~/abc
mkdir Fe
cd Fe../Setnew.sh-----------------------------(1) Study the symmetry of crystal (symmetry operations).
(2) Study the symmetry of wavefunction (irreduciblerepresentations).
(3) Study the optical transition between valence andconduction bands (dipole allowed).

Enter a command, H, which shows a procedure of thecalculation.
The procedure consists of(4) Calculate the optical absorption spectrum.

• Edit a file, ???.data.

(5) Treat magnetic materials.

• Execute a shell-script file, ???.sh.

(6) Use the +U method.

[1] Edit the file, ab_prp.data by using the following

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information:Environment variables>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Fe
a=2.87A (229, Oh9, Im-3m)
body-centered (il=3) cubic latticegenerators
5 (0, 0, 0)
19 (0, 0, 0)
25 (0, 0, 0)
atomic position (0.0, 0.0, 0.0)
magnetic (jmag=2)>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Let’s use bash.
In order to set some environment variables, executethe following commands:---------------------------------------------cat /home/CMD/teac02/Bash_envs >> ~/.bash_profile
source ~/.bash_profile----------------------------------------------

The content of this Bash_envs file is######### Bash_envs ###########
export ABCAP=’/home/CMD/teac02/abcap1707’----------------------------(ab_prp.data)
ab_prp.qsub-----------------------------

export FC_TYPE=’gen’
export
FC=’ifort’
exportFO=export
MPIFC=’mpif90’
exportMPIFO=

Execute ab_prp.qsub: This is used for executing
ab_prp.sh.
It makes a file, ab_input.data, which is a real input file for the ABCAP calculation.
The file, ab_input.data, is made from the informations of ab_prp.data and atom.data. Theatom.data file is a data base for atoms from H toU.

export PATH=.:$HOME/bin:$PATH
export HOSTNAME=‘hostname‘######### Bash_envs ###########

2[2] Calculate the initial charge density:Preparation----------------------------(ab_input.data) ab_in.qsub-----------------------------

Make a directory, e.g., abc, for the ABCAP calculation.
Copy a shell-script file, Setnew.sh, as follows.
----------------------------cd ~mkdir abc
cp $ABCAP/samples/Setnew.sh abc/-----------------------------In ab_in.qsub, the following programs run.
• ab_in.exe checks the crystal structure, andmakes totally-symmetric basis functions.
• ab_inch.exe makes the initial charge density
as the superposition of atomic charge densities.

The shell-script file, Setnew.sh, is used on starting a
new calculation: Files needed for ABCAP calculation
are copied from the directory,$ABCAP/samples/LaMnO3c_f_6/.

• ab_kpgn.exe generates the k points used in
the calculation.
1• ab_size.exe estimates the size of calculation.

• plot.ps is obtained, which shows he k-spacepath in the e-k curve.

• ab_ospw.exe calculates the overlap integral
among the totally symmetric basis functions.

[7] Drawing of the density of states (DOS)• fl_dm00.exe sets the initial value of the local
density matrix. (diagonal elements are 1/2)

• Edit bn_pdos.data. Give the energy region
to be drawn.

[3] Iteration for the selfconsistent calculation. Edit

• Run bn_pdos.sh.

fl06.sh and set the number of iteration at the parameter, ITER_MAIN.

• Edit p2_dos.data. Select the total DOS, thes, p, d, and f partial DOS.
• Run p2_dos.sh----------------------------(ab_input.data) fl06.qsub-----------------------------•

In fl06.qsub, the following programs run:•fl_pot.exe makes the potential from thecharge densty.

3.2• fl_potuj.exe makes the +U potential fromthe local density matrix.

• fl_chg.exe determines the Fermi energy andcalculate the charge desity from the eigen functions.
• fl_dmmx.exe calculates the local density matrix.
• fl_pot.exe calculates the total energy.

In ’magnetic state’ section in the ab_prp.data file,the jmag0 parameter should be 0, namely,

fl_mx5.exe calculates the next input ofcharge density.

magnetic state-2----*----3----*----4----*2!jmag0 !noSO:(0(N),1(AF),2(M))----------------------------------------------

Here, fl_ptuj.exe works only with lda+u> 0.
A summary on each cycle of the iterative calculation is written in the file, iter.log. The summaryis shown on the display by the commnad,3.3

Antiferromagnetic Cr>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Cr andiferromagnetic (221, Oh1, Pm-3m)
a=2.88A (bcc)
simple (il=1) cubic lattice for AFM
generators
5 (0, 0, 0)
19 (0, 0, 0)
25 (0, 0, 0)
atomic positions (0.0, 0.0, 0.0)
(0.5, 0.5, 0.5)
antiferromagnetic (jmag=1)
operation 1 (1/2, 1/2, 1/2)>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>----------------------------check.sh-----------------------------[4] Drawing of the crystal structure• Edit bn_atps.data. Give the region of drawing in the file.
• Run bn_atps.sh and p3_atps.sh.
• A postscript file, plot.ps, is obtained.

[5] Drawing of the band structure (e-k curve)

In ’magnetic state’ section in the ab_prp.data file,the jmag0 parameter should be 1, followed by the antiferromagnetic operation code, namely• Edit bnpl.data. Give paths in the k space tobe drawn.
• Run bnpl.sh.
•Nonmagnetic Si>>>>>>>>> ab_prp.data >>>>>>>>>>>
Si (227, Oh7, Fd-3m)
a=5.4296 A
face-centered (il=2) cubic latticegenerators
5 (0/1, 0/1, 0/1)
19 (1/4, 1/4, 1/4)
25 (1/4, 1/4, 1/4)
atomic position (0.0, 0.0, 0.0)
nonmagnetic (jmag=0)>>>>>>>>> ab_prp.data >>>>>>>>>>>• fl_bnd.exe calculates eigen functions
through a standard diagonalization.

•plot.ps is obtained for the nonmagnetic
case (jmag=0) or the antiferromagnetic case(jmag=1); plot1.ps and plot2.ps are obtained for the magnetic case (jmag=2).

magnetic state-2----*----3----*----4----*1!jmag0 !noSO:(0(N),1(AF),2(M))
1
1 2 1 2 1 2 !igen,jgen(2,3) for AF----------------------------------------------

plot.ps is obtained for the nonmagnetic
case (jmag=0) or the antiferromagnetic case(jmag=1); plot1.ps and plot2.ps are obtained for the magnetic case (jmag=2).

Here, the antiferromagnetic operation means the symmetry operation which shows the relation between theup-spin state and the down-spin state.

[6] Drawing of the k-space path
• Run brzone.sh.
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4The k group• Nonmagnetic NiO• Ferromagnetic NiO[1] Irreducible representations for the k group• Edit ab_irep.data: Give k points to be calculated.

• Type II AFM NiO

5.1>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
abcap-ab_irep.data1! the number of k
0 0 0 1
! k point>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
NiO
a=4.17A,NaCl structureface-centered (il=2) cubic lattie
generators
5 (0, 0, 0)
19 (0, 0, 0)
25 (0, 0, 0)
atomic positions (0.0, 0.0, 0.0) Ni(0.5, 0.5, 0.5) O
nonmagnetic(jmag=0)
ferromagnetic (jmag=2)>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>• Run ab_irep.sh.
• See ab_irep.log.

[2] Compatibility in k space•

Edit ab_compat.data: Give a series of kpoints for which you want to know the compatibility between the successive k points.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
abcap-ab_compat.data2! the number of k points
0 0 0 1
! k point
1 0 0 8! k point>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

5.2

Antiferromagnetic NiO• Type I AFM>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
NiO [a(cubic)=4.17A]
a=2.948635A, c=4.17A
simple (il=1) tetragonal latticegenerators
2 (0, 0, 0)
21 (0, 0, 0)
25 (0, 0, 0)
atomic positions (0.0, 0.0, 0.0) Ni-up(0.5, 0.5, 0.5) Ni-down(0.5, 0.5, 0.0) O(0.0, 0.0, 0.5) O
antiferromagnetic (jmag=1)
1 (1/2, 1/2, 1/2)>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>• Run ab_compat.sh.
• See ab_compat.log.

[3] Optical transition (dipole allowed)• Edit optsel.data: Give k points to be calculated.
>>>>>>>>>> optsel.data >>>>>>>>>>>>>
0! jpr (std output control)
0! idoub (0: noSOi or 1: SOi)
0 0 0 1 ! k-point
6! irrep. of vector (r or p)>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>• Run optsel.sh.

• Type II AFM NiO• See optsel.txt.

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Nonmagnetic andferromagnetic NiO>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
NiO [a(cubic)=4.17A]
a=2.948635A, c=14.445304A
Rhombohedral (il=-1) lattie
generators
3 (0, 0, 0)
10 (0, 0, 0)
13 (0, 0, 0)
atomic positions (0.0, 0.0, 0.0) Ni-up(0.0, 0.0, 0.5) Ni-down(2/3, 1/3, 1/12) O
antiferromagnetic (jmag=1)
1 (0, 0, 1/2)>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>LDA+U method

The LDA+U calculation is done by the input
data in the ’exchange-correlation potential’ section of
ab_input.data file, namely,exchange-correlation potential --------------vwn
11.000000
lda+u, amix_u
13
10.7
0.7 kind, l, U[eV], J[eV]---------------------------------------------This is an example for the calculation of LaMnO3 , inwhich kind=1 means La, and U-J=10eV, J=0.7eV.
Typical values of U are 2eV – 5eV for the 3d (l=2)
orbital, and 5eV – 10eV for the 4f (l=3) orbital.

6Optical property• Calculate the dielctric function within the dipole
interband transition.

For example, please check the value of the band gap
and the feature of valence band top for NiO.
3• Calculate the optical constants.

----------------------------(p2_dielec.data) p2_dielec.sh(p2_optnk.data)
p2_optnk.sh(p2_absorb.data) p2_absorb.sh-----------------------------• Calculate the optical property of thin film.

[1] Preparation
Use a command, Setopt.sh, to prepare a directory
for the optical-spectrum calculation. We assume
that the band structure calculation has been doneat the directory, NiOr_a2_u6.

[8] Drawing of optical property of the thin film----------------------------(optra.data)
optra.sh(p2_optra.data) p2_optra.sh---------------------------------------------------------cd ~/abc
cp $ABCAP/samples/Setopt.sh .
Setopt.sh NiOr_a2_u6-----------------------------

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Space group information• generators:
File: generator.data

This makes a directory, NiOr_a2_u6_s, and copies
some files from $ABCAP/samples/ZnO_5_s0 and
NiOr_a2_u6 to this directory.

• Wycoﬀ positions:File: wycoff.data[2] Initial check----------------------------cd ~/abc/NiOr_a2_u6_sH
bnpl.sh ; gs plot.ps
bngap.sh ; cat bngap.log; cat bngap.txt-----------------------------• To make ab_prp.data,
there is a tool, ab_crystal.sh.

[3] Adjustment of the band gap

8Some other materials

8.1

AlP>>>>>>>>> ab_prp.data >>>>>>>>>>>AlP (216, Td2, F-43m) zinc blendea=5.45 A
face-centered (il=2) cubic latticegenerators
5 (0, 0, 0)
43 (0, 0, 0)
atomic positions(0.0, 0.0, 0.0 ) Al(0.25, 0.25, 0.25) P
nonmagnetic (jmag=0)>>>>>>>>> ab_prp.data >>>>>>>>>>>----------------------------(bn_scis.data) bn_scis.shbngap.sh ; cat bngap.log----------------------------bn_scis.sh makes a scissors operation.

[4] Carrier doping----------------------------(bn_dope.data) bn_dope.sh(bnpl.data)
bnpl.sh-----------------------------

8.2

Al>>>>>>>>> ab_prp.data >>>>>>>>>>>Al (225, Oh5, Fm-3m) fcc
a=4.05 A
face-centered (il=2) cubic latticegenerators
5 (0, 0, 0)
19 (0, 0, 0)
25 (0, 0, 0)
atomic position (0.0, 0.0, 0.0)
nonmagnetic (jmag=0)>>>>>>>>> ab_prp.data >>>>>>>>>>>[5] Calculation of the dielectric function----------------------------(df01.data) df01.qsub-----------------------------[6] Contribution of plasma oscillation----------------------------(wpw.data) wpw.shbn_efp2.sh(df_total.data) df_total.sh-----------------------------

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Crystal structures

NIMS database:
http://crystdb.nims.go.jp/crystdb/
search-materials[7] Drawing of optical constants4• Search ’nims’ and ’atomwork’ by using internet.
• Click ”Enter AtomWork”• login.
• Input elements of the compound(example: Al P)
Click ”Search materials”.
• Choose a structure.
• Choose a paper from the refernce list.
• See crystal structure (standardized).

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