* Hydrogen terminated Au(111) surface [#a734259b]
This tutorial explains how to analyze the electronic structure of a surface by using Au(111) slab with the bottom surface terminated by hydrogen.~
#ref(http://www-cp.prec.eng.osaka-u.ac.jp/puki_state/graph/structure_Au111-H.png,center,nolink,30%)
** SCF calculation [#tb8cd26e]
To obtain the self-consistent charge density, electronic optimization is performed.
- Input file (nfinp_scf)
0 0 0 0 0 0 : I_CTROL (DUMMY)
6.00 20.00 2 6 6 : GMAX GMAXP NTYP NATM NATM2
1 0 : NUM_SPAC_GROUP BRAVIS_LATTICE_TYPE
Cartesian
5.498778336527 0.000000000000 0.000000000000
-2.749389168264 4.762081729212 0.000000000000
0.000000000000 0.000000000000 85.304940510023
12 12 1 1 1 1 : NK1 NK2 NK3 MK1 MK2 MK3
1 0 : NCORD NINV : IWEI IMDTYP ITYP
0.000000000000 0.000000000000 8.979467422108 1 0 1
0.000000000000 3.174721152808 4.489733711054 1 0 1
0.000000000000 -3.174721152808 0.000000000000 1 0 1
0.000000000000 0.000000000000 -4.489733711054 1 0 1
0.000000000000 3.174721152808 -8.979467422108 1 0 1
0.000000026956 -3.174721183174 -10.610158124432 1 1 2
79.00 0.50 12.0107 1 1 0.0 : IATOMN ALFA AMION ILOC IVAN ZETA1
1.00 0.50 12.0107 1 1 0.0 : IATOMN ALFA AMION ILOC IVAN ZETA1
0 0 0 0 0 : ICOND INIPOS INIVEL ININOS INIACC
0 1 : IPRE IPRI
200 200 0 80000.00 0 : NMD1 NMD2 LAST_ITER CPUMAX IFSTOP
6 1 : WAY_MIX MIX_WHAT
0 20 0.60 : ITER_START KBXMIX MIX_ALPHA
0.20 0.30 0.20 0.20 0.20 : DTIM1 DTIM2 DTIM3 DTIM4 DTIM
200.00 2 1 1.0D-12 : DTIO IMDALG IEXPL EDELTA
-0.0010 1.00D-03 0 : WIDTH FORCCR ISTRESS
rev-vdW-DF2 1 : XCTYPE KSPIN
2.00 : DESTM
101 : NBZTYP
4 4 4 : DUMMY
4 4 4 : DUMMY
48 : KEG
1 : NEXTST
0 : DUMMY
2 : IMSD
0 : EVALUATE_EKO_DIFF
0 : NPDOSAO
0 0.000 : SM_N DOPING
- Execution~
In the command line or in the job script, execute
> mpirun -np 24 < nfinp_scf > nfout_scf
** PDOS (AOLDOS) calculation [#jb76cbfe]
Then densities of state projected onto the atomic orbitals (PDOS/AOLDOS) are calculated by using the following input file:
- Input file (nfinp_aoldos)
0 0 0 0 0 0 : I_CTROL (DUMMY)
6.00 20.00 2 6 6 : GMAX GMAXP NTYP NATM NATM2
1 0 : NUM_SPAC_GROUP BRAVIS_LATTICE_TYPE
Cartesian
5.498778336527 0.000000000000 0.000000000000
-2.749389168264 4.762081729212 0.000000000000
0.000000000000 0.000000000000 85.304940510023
12 12 1 1 1 1 : NK1 NK2 NK3 MK1 MK2 MK3
1 0 : NCORD NINV : IWEI IMDTYP ITYP
0.000000000000 0.000000000000 8.979467422108 1 0 1
0.000000000000 3.174721152808 4.489733711054 1 0 1
0.000000000000 -3.174721152808 0.000000000000 1 0 1
0.000000000000 0.000000000000 -4.489733711054 1 0 1
0.000000000000 3.174721152808 -8.979467422108 1 0 1
0.000000026956 -3.174721183174 -10.610158124432 1 1 2
79.00 0.50 12.0107 1 1 0.0 : IATOMN ALFA AMION ILOC IVAN ZETA1
1.00 0.50 12.0107 1 1 0.0 : IATOMN ALFA AMION ILOC IVAN ZETA1
14 0 0 0 0 : ICOND INIPOS INIVEL ININOS INIACC
0 1 : IPRE IPRI
200 200 0 80000.00 0 : NMD1 NMD2 LAST_ITER CPUMAX IFSTOP
6 1 : WAY_MIX MIX_WHAT
0 20 0.60 : ITER_START KBXMIX MIX_ALPHA
0.20 0.30 0.20 0.20 0.20 : DTIM1 DTIM2 DTIM3 DTIM4 DTIM
200.00 2 1 1.0D-12 : DTIO IMDALG IEXPL EDELTA
-0.0010 1.00D-03 0 : WIDTH FORCCR ISTRESS
rev-vdW-DF2 1 : XCTYPE KSPIN
2.00 : DESTM
101 : NBZTYP
4 4 4 : DUMMY
4 4 4 : DUMMY
48 : KEG
1 : NEXTST
0 : DUMMY
2 : IMSD
0 : EVALUATE_EKO_DIFF
6 : NPDOSAO
1
2
3
4
5
6
-15.00 5.00 0.20 501 : EPDOS(1) EPDOS(2) EPDOS(3) NPDOSE
2.2 0.3 : RAD WIDTH FOR TYPE 1
0.7 0.3 : RAD WIDTH FOR TYPE 2
0.2 12 : DR NR
0 0.000 : SM_N DOPING
Here to calculate PDOS/AOLDOS by a postprocessing, ICOND is set to 14
14 0 0 0 0 : ICOND INIPOS INIVEL ININOS INIACC
NPDOSAO (Number of Atomic orbitals for PDOS) > 0
6 : NPDOSAO
followed by the atomic indices for which PDOS are calculated
1
2
3
4
5
6
Then minimum energy (EPDOS(1)), maximum energy (EPDOS(2)), width for Gaussian broadening (EPDOS(3)) (in eV), and energy mesh
-15.00 5.00 0.20 501 : EPDOS(1) EPDOS(2) EPDOS(3) NPDOSE
Cutoff radii (RAD) for the atomic orbitals and smearing width (WIDTH) in the Bohr radius
2.2 0.3 : RAD WIDTH FOR TYPE 1
0.7 0.3 : RAD WIDTH FOR TYPE 2
Width (DR) and number of grids (NR) for the radial integration
0.2 12 : DR NR
Note that EPSDOS(3) is used only when
&OTHERS
GAUSSDOS
&END
is written in the input file for the calculation of density of states with the Gaussian smearing.
- Execution
> mpirun -np 24 < nfinp_aoldos > nfout_aoldos
- Analysis
PDOS/AOLDOS is printed by the keyword "AO_LDOS" in the output file as
AO_LDOS: atm spn energy s px py pz dzz dxx-yy dxy dyz dzx s+p+d eg t2g
AO_LDOS: 1 1 -15.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
AO_LDOS: 1 1 -14.96 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
AO_LDOS: 1 1 -14.92 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
...
PDOS/AOLDOS can be extracted by using the state2pdos.pl script as
state2pdos.pl nfout_aoldos
then the following messages are printed
make dos data file :: 0001
make dos data file :: 0002
make dos data file :: 0003
make dos data file :: 0004
make dos data file :: 0005
make dos data file :: 0006
meaning that the dos data are printed to files 0001, 0002, ... 0006.
NOTE: with the latest version of the code, they will be pdos_0001.dat, pdos_0002.data, ...
The data are given in the above files in the following order (column-wise):
Energy s px py pz dzz dxx-yy dxy dyz dzx s p d
Finally plot the data using for e.g., gnuplot or xmgrace.
Alternatively, you can perform SCF and AOLDOS calculation in the same run, simply setting NPDOSAO > 0 and other AOLDOS related parameters in the SCF calculations by using the following input file (nfinp_scf+aoldos)
0 0 0 0 0 0 : I_CTROL (DUMMY)
6.00 20.00 2 6 6 : GMAX GMAXP NTYP NATM NATM2
1 0 : NUM_SPAC_GROUP BRAVIS_LATTICE_TYPE
Cartesian
5.498778336527 0.000000000000 0.000000000000
-2.749389168264 4.762081729212 0.000000000000
0.000000000000 0.000000000000 85.304940510023
12 12 1 1 1 1 : NK1 NK2 NK3 MK1 MK2 MK3
1 0 : NCORD NINV : IWEI IMDTYP ITYP
0.000000000000 0.000000000000 8.979467422108 1 0 1
0.000000000000 3.174721152808 4.489733711054 1 0 1
0.000000000000 -3.174721152808 0.000000000000 1 0 1
0.000000000000 0.000000000000 -4.489733711054 1 0 1
0.000000000000 3.174721152808 -8.979467422108 1 0 1
0.000000026956 -3.174721183174 -10.610158124432 1 1 2
79.00 0.50 12.0107 1 1 0.0 : IATOMN ALFA AMION ILOC IVAN ZETA1
1.00 0.50 12.0107 1 1 0.0 : IATOMN ALFA AMION ILOC IVAN ZETA1
0 0 0 0 0 : ICOND INIPOS INIVEL ININOS INIACC
0 1 : IPRE IPRI
200 200 0 80000.00 0 : NMD1 NMD2 LAST_ITER CPUMAX IFSTOP
6 1 : WAY_MIX MIX_WHAT
0 20 0.60 : ITER_START KBXMIX MIX_ALPHA
0.20 0.30 0.20 0.20 0.20 : DTIM1 DTIM2 DTIM3 DTIM4 DTIM
200.00 2 1 1.0D-12 : DTIO IMDALG IEXPL EDELTA
-0.0010 1.00D-03 0 : WIDTH FORCCR ISTRESS
rev-vdW-DF2 1 : XCTYPE KSPIN
2.00 : DESTM
101 : NBZTYP
4 4 4 : DUMMY
4 4 4 : DUMMY
48 : KEG
1 : NEXTST
0 : DUMMY
2 : IMSD
0 : EVALUATE_EKO_DIFF
6 : NPDOSAO
1
2
3
4
5
6
-15.00 5.00 0.20 501 : EPDOS(1) EPDOS(2) EPDOS(3) NPDOSE
2.2 0.3 : RAD WIDTH FOR TYPE 1
0.7 0.3 : RAD WIDTH FOR TYPE 2
0.2 12 : DR NR
0 0.000 : SM_N DOPING
-Visualization
Let us visualize PDOSs for the bottom Au and H atoms using gnuplot.
Here is an example gnuplot script to generate an eps file (pdos.gp)
set terminal postscript eps color 'Helvetica' 20
set output 'pdos.eps'
xmin=-11.0
xmax=4.0
ymin=0.0
ymax=2.0
set xrange [xmin:xmax]
set yrange [ymin:ymax]
set yzeroaxis
set xlabel '{/Helvetica-Oblique E}-{/Helvetica-Oblique E}_F (eV)'
set ylabel 'PDOS (Arb. unit)'
plot 'pdos_0005.dat' using ($1):($11) title 'Au#5 s' with lines lw 3, \
'pdos_0005.dat' using ($1):($12) title 'Au#5 p' with lines lw 3, \
'pdos_0005.dat' using ($1):($13) title 'Au#5 d' with lines lw 3, \
'pdos_0006.dat' using ($1):($2) title 'H s' with lines lw 2
Type
> gnuplot pdos.gp
to generate the eps file called "pdos.eps" as shown below
#ref(http://www-cp.prec.eng.osaka-u.ac.jp/puki_state/graph/pdos_au111_5L-H.png,center,nolink,30%)
#ref(http://www-cp.prec.eng.osaka-u.ac.jp/puki_state/graph/pdos_au111_5L-H.png,center,nolink,20%)
** Band structure calculation [#l6de7d56]
The band structure calculation can be performed after the self-consistent charge and potential are obtained. Here's an example of the input file for the band structure calculation:
- Input file (nfinp_band)
0 0 0 0 0 0 : I_CTROL (DUMMY)
6.00 20.00 2 6 6 : GMAX GMAXP NTYP NATM NATM2
1 0 : NUM_SPAC_GROUP BRAVIS_LATTICE_TYPE
Cartesian
5.498778336527 0.000000000000 0.000000000000
-2.749389168264 4.762081729212 0.000000000000
0.000000000000 0.000000000000 85.304940510023
12 12 1 1 1 1 : NK1 NK2 NK3 MK1 MK2 MK3
1 0 : NCORD NINV : IWEI IMDTYP ITYP
0.000000000000 0.000000000000 8.979467422108 1 0 1
0.000000000000 3.174721152808 4.489733711054 1 0 1
0.000000000000 -3.174721152808 0.000000000000 1 0 1
0.000000000000 0.000000000000 -4.489733711054 1 0 1
0.000000000000 3.174721152808 -8.979467422108 1 0 1
0.000000026956 -3.174721183174 -10.610158124432 1 1 2
79.00 0.50 12.0107 1 1 0.0 : IATOMN ALFA AMION ILOC IVAN ZETA1
1.00 0.50 12.0107 1 1 0.0 : IATOMN ALFA AMION ILOC IVAN ZETA1
22 0 0 0 0 : ICOND INIPOS INIVEL ININOS INIACC
0 1 : IPRE IPRI
200 200 0 80000.00 0 : NMD1 NMD2 LAST_ITER CPUMAX IFSTOP
6 1 : WAY_MIX MIX_WHAT
0 20 0.60 : ITER_START KBXMIX MIX_ALPHA
0.20 0.30 0.20 0.20 0.20 : DTIM1 DTIM2 DTIM3 DTIM4 DTIM
200.00 2 1 1.0D-12 : DTIO IMDALG IEXPL EDELTA
-0.0010 1.00D-03 0 : WIDTH FORCCR ISTRESS
rev-vdW-DF2 1 : XCTYPE KSPIN
2.00 : DESTM
101 : NBZTYP
4 4 4 : DUMMY
4 4 4 : DUMMY
48 : KEG
1 : NEXTST
0 : DUMMY
2 : IMSD
0 : EVALUATE_EKO_DIFF
0 : NPDOSAO
0 0.000 : SM_N DOPING
!
&KPOINTS_BAND
NKSEG 3
KMESH 40 20 40
KPOINTS
0.0 0.0 0.0
0.5 0.0 0.0
0.33333333 0.33333333 0.0
0.0 0.0 0.0
&END
For the band structure calculation, ICOND is set to 22, and the following options are added in the input file
&KPOINTS_BAND
NKSEG 3
KMESH 40 20 40
KPOINTS
0.0 0.0 0.0
0.5 0.0 0.0
0.33333333 0.33333333 0.0
0.0 0.0 0.0
&END
where the variables in the &KPOINTS_BAND ... &END block are
- the number of k-point segment (NKSEG)
- the k-point mesh for each segment (KMESH)
- the k-points which define the symmetry k-points (# of k-points should be NKSEG+1)
K-points are given in the unit of the reciprocal lattice vectors.~
After the band structure run, the file "energy.data" is generated.
To convert the "energy.data" into plottable one, "energy2band" utility is used.
Type
> energy2band
and input number of bands, number of bands to be plotted, number of k-points, and Fermi level, one gets "band.data", which can be plotted using gnuplot or xmgrace.
Here is an example script to run energy2band:
#!/bin/sh
E2B=energy2band
scfout_file='nfout_scf'
bandout_file='nfout_band'
ef=`grep 'FERMI' ${scfout_file} | awk '{print $4}'`
nb=`grep 'NUMBER OF BANDS CONSIDERED' ${bandout_file} | awk '{print $6}'`
nk=`grep 'NUMBER OF K-POINTS' ${bandout_file} | grep -v '=' | awk '{print $5}'`
${E2B} << EOF
${nb}
${nb}
${nk}
${ef}
EOF
By using the following gnuplot script, the band structure can be visualized as follows:
#ref(http://www-cp.prec.eng.osaka-u.ac.jp/puki_state/graph/band_au111_5L-H.png,center,nolink,30%)
#ref(http://www-cp.prec.eng.osaka-u.ac.jp/puki_state/graph/band_au111_5L-H.png,center,nolink,20%)
The following gnuplot script can be used to generate the band structure plot:
emin=-12
emax=4
xmin=0.0000
xmax=1.80236106
G=0.00000000
M=0.65970994
K=1.04059365
G2=1.80236106
offset=-0.5
set xrange [xmin:xmax]
set yrange [emin:emax]
set arrow from M,emin to M,emax nohead lt 1
set arrow from K,emin to K,emax nohead lt 1
set xzeroaxis
unset xtics
unset key
set ylabel '{/Helvetica-Oblique E-E}_F (eV)'
set label '{/Symbol G}' at G,emin+offset center
set label 'M' at M,emin+offset center
set label 'K' at K,emin+offset center
set label '{/Symbol G}' at G2,emin+offset center
#set terminal postscript eps 'Helvetica' 20
#set output 'band.eps'
plot 'band.data' with lines lw 3
pause -1
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