Pyrite (FeS2) †

In this section, how to perform the electronic structure analysis is described using pyrite (FeS2) as an example.

↑

SCF calculation †

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 †

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 †

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 †

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. However, the extreme care is required to make a conclusion on the atomic charge, as one can may see from the above result.

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