#author("2025-04-25T08:30:22+09:00","default:StatE","StatE")
#author("2025-04-25T15:14:52+09:00","default:StatE","StatE")
* Pyrite (FeS2) [#jeb2297a]
In this section, how to perform the electronic structure analysis is described using pyrite (FeS2) as an example.
** SCF calculation [#v9916338]
First of all, let us perform an SCF calculation using ''pw.x'' to get wave functions and charge density. If necessary, let us perform the geometry optimization.
Below is the input file used for the SCF calculation
- ''scf.in''
&CONTROL
calculation = 'scf'
etot_conv_thr = 1.2000000000d-04
forc_conv_thr = 1.0000000000d-04
outdir = './out/'
prefix = 'fes2'
pseudo_dir = '../pseudo/'
tprnfor = .true.
tstress = .true.
verbosity = 'high'
/
&SYSTEM
degauss = 2.0000000000d-02
ecutrho = 1.0800000000d+03
ecutwfc = 9.0000000000d+01
ibrav = 0
nat = 12
nosym = .false.
!nspin = 2
nbnd = 80
ntyp = 2
occupations = 'smearing'
smearing = 'cold'
!starting_magnetization(1) = 3.1250000000d-01
!starting_magnetization(2) = 1.0000000000d-01
/
&ELECTRONS
conv_thr = 2.4000000000d-09
electron_maxstep = 80
mixing_beta = 4.0000000000d-01
/
ATOMIC_SPECIES
Fe 55.845 Fe.pbe-spn-kjpaw_psl.0.2.1.UPF
S 32.065 s_pbe_v1.4.uspp.F.UPF
ATOMIC_POSITIONS crystal
Fe 0.0000000000 0.0000000000 0.0000000000
Fe 0.5000000000 0.0000000000 0.5000000000
Fe 0.0000000000 0.5000000000 0.5000000000
Fe 0.5000000000 0.5000000000 0.0000000000
S 0.3850400000 0.3850400000 0.3850400000
S 0.6149600000 0.6149600000 0.6149600000
S 0.1149600000 0.6149600000 0.8850400000
S 0.8850400000 0.3850400000 0.1149600000
S 0.6149600000 0.8850400000 0.1149600000
S 0.3850400000 0.1149600000 0.8850400000
S 0.8850400000 0.1149600000 0.6149600000
S 0.1149600000 0.8850400000 0.3850400000
K_POINTS automatic
4 4 4 0 0 0
CELL_PARAMETERS angstrom
5.4281000000 0.0000000000 0.0000000000
0.0000000000 5.4281000000 0.0000000000
0.0000000000 0.0000000000 5.4281000000
** Density of states calculation [#d2b48dcd]
After confirming the convergence of SCF, let us perform density of states (DOS) calculation using ''dos.x''.
Below is the input file for the DOS calculation.
- ''dos.in''
&DOS
outdir ='./out/'
prefix ='fes2'
fildos ='fes2.dos'
bz_sum = 'tetrahedra'
Emin = -85.0
Emax = 25.0
DeltaE = 0.01
/
In this exercise, the SCF calculation was performed with the smearing method, while DOS is calculated using the tetrahedron method.
** Refined Density of states calculation [#f83b2359]
To get more precise, let us perform a non-SCF (NSCF) calculation.
This is not always necessary, but if necessary, perform a NSCF with a finer k-point mesh.
Remember this NSCF calculation can take longer than SCF calculation, depending on the number of k-point.~
For this purpose set ''calculation'' ''nscf'' in the &CONTROL namelist as
calculation = 'nscf'
and finer k-point grid in the K_POINTS card, for example:
K_POINTS automatic
9 9 9 0 0 0
then the nscf calculation is done, perform the DOS calculation using dos.x.
** Projected DOS calculation [#f5e17a06]
To get DOS projected onto the atomic orbitals (PDOS), let us use ''projwfc.x''.
It is important to remember that unlike the DOS calculation, to get "accurate" PDOS, the preceding SCF or NSCF calculation should be done using the tetrahedron method, otherwise PDOS are calculated using the smearing method with the Gaussian function to approximate the delta function.
Below is an input file for the PDOS calculation
- ''projwfc.in''
&PROJWFC
outdir = './out/'
prefix = 'fes2'
Emin = -25.00
Emax = 25.00
DeltaE = 0.01
/
For a better characterization of PDOS, it is useful to use rotated atomic orbitals in such a way that the occupation matrix is diagonalized.
This can be done by setting ''diag_basis'' .true. as
diag_basis = .true.
Furthermore, Lowdin population analysis is performed during the PDOS calculation.
See the output file and search the word ''Lowdin Charges'', which looks like:
Lowdin Charges:
Atom # 1: total charge = 16.8478, s = 2.4992,
Atom # 1: total charge = 16.8478, p = 7.3552, p1= 2.4500, p2= 2.4720, p3= 2.4332,
Atom # 1: total charge = 16.8478, d = 6.9934, d1= 0.9573, d2= 0.8688, d3= 1.7250, d4= 1.6888, d5= 1.7535,
Atom # 2: total charge = 16.8460, s = 2.4917,
Atom # 2: total charge = 16.8460, p = 7.3512, p1= 2.4353, p2= 2.4631, p3= 2.4528,
Atom # 2: total charge = 16.8460, d = 7.0031, d1= 0.9289, d2= 0.8879, d3= 1.7192, d4= 1.6805, d5= 1.7866,
Atom # 3: total charge = 16.8204, s = 2.4916,
Atom # 3: total charge = 16.8204, p = 7.3495, p1= 2.4327, p2= 2.4857, p3= 2.4311,
Atom # 3: total charge = 16.8204, d = 6.9793, d1= 0.9570, d2= 0.8475, d3= 1.7116, d4= 1.6795, d5= 1.7836,
Atom # 4: total charge = 16.8502, s = 2.4957,
Atom # 4: total charge = 16.8502, p = 7.3523, p1= 2.4398, p2= 2.4296, p3= 2.4828,
Atom # 4: total charge = 16.8502, d = 7.0022, d1= 0.9437, d2= 0.8749, d3= 1.7397, d4= 1.6725, d5= 1.7714,
Atom # 5: total charge = 5.4643, s = 1.4831,
Atom # 5: total charge = 5.4643, p = 3.9813, p1= 1.1366, p2= 1.4327, p3= 1.4119,
Atom # 5: total charge = 5.4643, d = 0.0000, d1= 0.0000, d2= 0.0000, d3= 0.0000, d4= 0.0000, d5= 0.0000,
Atom # 6: total charge = 5.4643, s = 1.4831,
Atom # 6: total charge = 5.4643, p = 3.9813, p1= 1.1366, p2= 1.4320, p3= 1.4126,
Atom # 6: total charge = 5.4643, d = 0.0000, d1= 0.0000, d2= 0.0000, d3= 0.0000, d4= 0.0000, d5= 0.0000,
Atom # 7: total charge = 5.4600, s = 1.4921,
Atom # 7: total charge = 5.4600, p = 3.9679, p1= 1.1348, p2= 1.4123, p3= 1.4208,
Atom # 7: total charge = 5.4600, d = 0.0000, d1= 0.0000, d2= 0.0000, d3= 0.0000, d4= 0.0000, d5= 0.0000,
Atom # 8: total charge = 5.4600, s = 1.4921,
Atom # 8: total charge = 5.4600, p = 3.9679, p1= 1.1348, p2= 1.4122, p3= 1.4210,
Atom # 8: total charge = 5.4600, d = 0.0000, d1= 0.0000, d2= 0.0000, d3= 0.0000, d4= 0.0000, d5= 0.0000,
Atom # 9: total charge = 5.4591, s = 1.4921,
Atom # 9: total charge = 5.4591, p = 3.9670, p1= 1.1314, p2= 1.4170, p3= 1.4186,
Atom # 9: total charge = 5.4591, d = 0.0000, d1= 0.0000, d2= 0.0000, d3= 0.0000, d4= 0.0000, d5= 0.0000,
Atom # 10: total charge = 5.4591, s = 1.4921,
Atom # 10: total charge = 5.4591, p = 3.9670, p1= 1.1314, p2= 1.4188, p3= 1.4168,
Atom # 10: total charge = 5.4591, d = 0.0000, d1= 0.0000, d2= 0.0000, d3= 0.0000, d4= 0.0000, d5= 0.0000,
Atom # 11: total charge = 5.4606, s = 1.4873,
Atom # 11: total charge = 5.4606, p = 3.9732, p1= 1.1304, p2= 1.3943, p3= 1.4486,
Atom # 11: total charge = 5.4606, d = 0.0000, d1= 0.0000, d2= 0.0000, d3= 0.0000, d4= 0.0000, d5= 0.0000,
Atom # 12: total charge = 5.4606, s = 1.4873,
Atom # 12: total charge = 5.4606, p = 3.9732, p1= 1.1304, p2= 1.3957, p3= 1.4471,
Atom # 12: total charge = 5.4606, d = 0.0000, d1= 0.0000, d2= 0.0000, d3= 0.0000, d4= 0.0000, d5= 0.0000,
Spilling Parameter: 0.0085
This may be helpful to get an insight into the charge (state). However, the extreme care is required to make a conclusion on the atomic charge, as one can may see from the above result.
** Bader charge analysis [#lde073e7]
To further gain an insight into the charge state/atomic charge, let us perform the Bader charge analysis.
*** Preparation [#h9f6de65]
To perform the Bader charge analysis, the charge density of the system in the Gaussian cube formate is required.
To do this, one needs to use ''pp.x''.
Below is an example for ''pp.x'' to generate a charge density file.
- ''pp.in''
&INPUTPP
prefix = 'fes2'
outdir = './out/'
filplot = 'fes2'
plot_num = 0
/
&PLOT
iflag = 3
output_format = 6
fileout = 'fes2_val.cube'
/
''plot_num'' is used to output the charge density in real space, ''iflag'' is used to specify that the dimension of the charge density, and ''output_format'' is used to specify the file format.
*** Execution [#u4b77208]
Supposing the path to the program ''bader'' is set, one can simply execute the following command
bader fes2_val.cube
Output may look like:
GRID BASED BADER ANALYSIS (Version 1.03 11/13/17)
OPEN ... fes2_val.cube
GAUSSIAN-STYLE INPUT FILE
DENSITY-GRID: 108 x 108 x 108
CLOSE ... fes2_val.cube
RUN TIME: 0.27 SECONDS
CALCULATING BADER CHARGE DISTRIBUTION
0 10 25 50 75 100
PERCENT DONE: **********************
REFINING AUTOMATICALLY
ITERATION: 1
EDGE POINTS: 428375
REASSIGNED POINTS: 28371
RUN TIME: 2.29 SECONDS
CALCULATING MINIMUM DISTANCES TO ATOMS
0 10 25 50 75 100
PERCENT DONE: **********************
RUN TIME: 0.22 SECONDS
WRITING BADER ATOMIC CHARGES TO ACF.dat
WRITING BADER VOLUME CHARGES TO BCF.dat
NUMBER OF BADER MAXIMA FOUND: 72
SIGNIFICANT MAXIMA FOUND: 72
VACUUM CHARGE: 0.0000
NUMBER OF ELECTRONS: 112.00003
The calculated Bader charges are written to ''ACF.dat'' as
# X Y Z CHARGE MIN DIST ATOMIC VOL
--------------------------------------------------------------------------------
1 10.257622 10.257622 10.257622 15.308219 1.792039 65.277172
2 5.128811 10.257622 5.128811 15.308219 1.792040 65.277172
3 10.257622 5.128811 5.128811 15.308219 1.792040 65.277172
4 5.128811 5.128811 10.257622 15.308219 1.792040 65.277172
5 3.949595 3.949595 3.949595 6.354199 1.892313 102.381722
6 6.308027 6.308027 6.308027 6.337589 1.877954 102.164956
7 1.179216 6.308027 9.078406 6.337589 1.877956 102.164956
8 9.078406 3.949595 1.179216 6.354199 1.892313 102.381722
9 6.308027 9.078406 1.179216 6.337589 1.877956 102.164956
10 3.949595 1.179216 9.078406 6.354199 1.892313 102.381722
11 9.078406 1.179216 6.308027 6.354199 1.892311 102.381722
12 1.179216 9.078406 3.949595 6.337589 1.877957 102.164956
--------------------------------------------------------------------------------
VACUUM CHARGE: 0.0000
VACUUM VOLUME: 0.0000
NUMBER OF ELECTRONS: 112.0000
Note the charge is based on the valence charge defined by the pseudopotentials used.
In this example, we use the following pseudopotentials:
- ''Fe.pbe-spn-kjpaw_psl.0.2.1.UPF''
- ''s_pbe_v1.4.uspp.F.UPF''
More specifically, the respective valence configurations can be found in the header of these potential files as
- ''Fe.pbe-spn-kjpaw_psl.0.2.1.UPF''
nl pn l occ Rcut Rcut US E pseu
3S 1 0 2.00 1.100 1.300 -6.910119
4S 2 0 2.00 0.800 1.400 -0.388933
3P 2 1 6.00 1.000 1.300 -4.413015
4P 3 1 0.00 1.000 1.600 -0.097407
3D 3 2 6.00 1.400 2.000 -0.551558
- ''s_pbe_v1.4.uspp.F.UPF''
nl pn l occ Rcut Rcut US E pseu
3S 3 0 2.00 0.00000000000 1.50000000000 -1.26833444300
3P 3 1 4.00 0.00000000000 1.50000000000 -0.51513600900
It can be seen that the numbers of valence electros for Fe and S are 16 and 6, respectively.
Based on simple mathematics, it seems Fe is positively charged, whereas S, negatively charged.
Compare with the Lowdin charges.
For more precise discussion on the actual charge state, one may need further analysis of PDOS (and others).
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