Crystalline Si

In this example, silicon in the diamond structure (space group number of 227) with the lattice constant of 10.30 Bohr, cutoff energy of 16 Ry (GMAX=4, GMAXP=8), and nonshifted 8 x 8 x 8 k-point, is used as an example of the SCF calculation of solid with the band gap.

SCF calculation

  • Input file (nfinp_1)
         0     0     0     0     0     0 : I_CTRL(1:6) (DUMMY)
      4.00  8.00     1     2     2       : GMAX, GMAXP, NTYP, NATM, NATM2
       227     2                         : NUM_SPACE_GROUP TYPE_BRAVIS_LATTICE
     10.30 10.30 10.30 90.00 90.00 90.00 : A B C ALPHA BETA GAMMA
        08    08    08     1     1     1 : N1 N2 N3 M1 M2 M3
         0     0                         : NCORD NINV : IWEI IMDTYP ITYP
    0.00d0      0.00d0      0.00d0    1    1    1
    0.25d0      0.25d0      0.25d0    1    1    1
        14  0.50 28.09     6     1   0.2 : TYPE 1IATOMN,ALFA,AMION,ILOC,IVAN
         0     0     0     0     0       : ICOND INIPOS INIVEL ININOS INIACC
         0     1                         : IPRE IPRI 
        20    20     0    84200.00     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
       300.00  4     1    0.50D-09       : DTIO IMDALG IEXPL EDELTA   
    0.0002    0.50D+03     0             : WIDTH FORCCR ISTRESS
    ggapbe     1                         : XCTYPE KSPIN
      2.00                               : DESTM
       102                               : NBZTYP
         4     4     4                   : DUMMY
         4     4     4                   : DUMMY
         8                               : KEG
         1                               : NEXTST    
         0                               : DUMMY
         2                               : IMSD
         0                               : EVALUATE_EKO_DIFF
         2                               : NPDOSAO
         1 
         2 
    -15.00  5.00  0.20   501
     2.400  0.20
            0.20    14
         0  0.00                         : SM_N DOPPING
  • Execution (interactive mode)
    $ mpirun -np 6 ./STATE < nfinp_1 > nfout_1
  • Execution (batch job)
    $ qsub qsub.sh
    • Job script (qsub.sh)
      #$ -S /bin/sh
      #$ -cwd
      #$ -pe fillup 6
      #$ -N Si
      
      #disable OPENMP parallelism
      OMP_NUM_THREADS=1
      
      # execuable of the STATE code
      ln -fs ../../src/STATE
      
      # pseudopotential data
      ln -fs ${HOME}/STATE/gncpp/pot.Si_pbe1 fort.37
       
      # launch STATE
      mpirun -np $NSLOTS ./STATE < nfinp_1 > nfout_1
  • Output file (nfout_1)
    Convergence of the total energy can be monitored by using grep as
    $ grep ETOT: nfout_1
    The result is:
    ETOT:   1     -6.05513096  0.6055E+01  0.3203E-02
    ETOT:   2     -7.84016187  0.1785E+01  0.5187E-02
    ETOT:   3     -7.87270490  0.3254E-01  0.2825E-02
    ETOT:   4     -7.87351715  0.8123E-03  0.6089E-03
    ETOT:   5     -7.87355245  0.3530E-04  0.1887E-03
    ETOT:   6     -7.87355822  0.5769E-05  0.2560E-04
    ETOT:   7     -7.87355833  0.1069E-06  0.1066E-04
    ETOT:   8     -7.87355833  0.4548E-08  0.1730E-05
    ETOT:   9     -7.87355833  0.1916E-09  0.4194E-06
    ETOT:  10     -7.87355833  0.2984E-10  0.1669E-07
    ETOT:  11     -7.87355833  0.1951E-11  0.9524E-08
    Converged total energy and its components
                         TOTAL ENERGY AND ITS COMPONENTS 
                      TOTAL ENERGY     =          -7.87355833 A.U.
                       FREE ENERGY     =          -7.87355833 A.U.
                    KINETIC ENERGY     =           3.01922457 A.U.
                    HARTREE ENERGY     =           0.55014222 A.U.
                         XC ENERGY     =          -2.40098662 A.U.
                      LOCAL ENERGY     =          -0.84294976 A.U.
                   NONLOCAL ENERGY     =           0.16885288 A.U.
                      EWALD ENERGY     =          -8.36784162 A.U.
                         PC ENERGY     =           0.00000000 A.U.
                   ENTROPIC ENERGY     =           0.00000000 A.U.

Band structure calculation

To calculate the band structure, an SCF calculation is performed to obtain a converged charge density, and the non-SCF calculation along the symmetry lines is performed.

  • Input file (nfinp_scf)
     0  0  0  0  0  0                      : INPUT_CTRL(1:6) (DUMMY)
     6.00  12.00 1  2  2                   : GMAX GMAXP NTYP NATM NATM2
     227   2                               : num_space_group, type
    10.2347 10.2347 10.2347 90.0 90.0 90.0 : A B C ALPHA BETA GAMMA
     4  4  4  2  2  2                      : N1 N2 N3 M1 M2 M3
     0  0                                  : NCORD, NINV
     0.00  0.00  0.00  1  1  1             : CPS(1,1:3) IWEI IMDTYP ITYP
     0.25  0.25  0.25  1  1  1             : CPS(2,1:3) IWEI IMDTYP ITYP
     14 0.5000 28.09 6 1 0.0               : ATOMN ALFA AMION ILOC IVAN ZETA1
     0     0     0     0     0             : ICOND INIPOS INIVEL ININOS INIACC
     0     1                               : IPRE IPRI
     200   200   0     84200.00    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
     300.00      4     1     0.50D-09      : DTIO IMDALG IEXPL EDELTA
    -0.0020      0.50D+03    0             : WIDTH FORCCR ISTRESS
    ggapbe     1                           : xctype,kspin
     2.00                                  : DETSTM
     101                                   : NBZTYP
     0     0     0                         : NKX NKY NKZ (DUMMY)
     0     0     0                         : NKX2 NKY2 NKZ2 (DUMMY)
     8                                     : KEG
     1                                     : NEXTST
     0                                     : (DUMMY)
     2                                     : IMSD
     0                                     : EVALUATE_EKO_DIFF
     0                                     : NPDOSAO
     0        0.00                         : SM_N DOPING
  • Input file (nfinp_band) 0 0 0 0 0 0 : INPUT_CTRL(1:6) (DUMMY)
     6.00  12.00 1  2  2                   : GMAX GMAXP NTYP NATM NATM2
     227   2                               : num_space_group, type
    10.2347 10.2347 10.2347 90.0 90.0 90.0 : A B C ALPHA BETA GAMMA
     4  4  4  2  2  2                      : N1 N2 N3 M1 M2 M3
     0  0                                  : NCORD, NINV
     0.00  0.00  0.00  1  1  1             : CPS(1,1:3) IWEI IMDTYP ITYP
     0.25  0.25  0.25  1  1  1             : CPS(2,1:3) IWEI IMDTYP ITYP
     14 0.5000 28.09 6 1 0.0               : ATOMN ALFA AMION ILOC IVAN ZETA1
    22     0     0     0     0             : ICOND INIPOS INIVEL ININOS INIACC
     0     1                               : IPRE IPRI
     200   200   0     84200.00    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
     300.00      4     1     0.50D-09      : DTIO IMDALG IEXPL EDELTA
    -0.0100      0.50D+03    0             : WIDTH FORCCR ISTRESS
    ggapbe     1                           : xctype,kspin
     2.00                                  : DETSTM
     101                                   : NBZTYP
     0     0     0                         : NKX NKY NKZ (DUMMY)
     0     0     0                         : NKX2 NKY2 NKZ2 (DUMMY)
    16                                     : KEG 
     1                                     : NEXTST
     0                                     : (DUMMY)
     2                                     : IMSD
     0                                     : EVALUATE_EKO_DIFF
     0                                     : NPDOSAO
     0        0.00                         : SM_N DOPING  
    &KPOINTS_BAND
     NKSEG 6
     KMESH 40 20 20 20 40 20
     KPOINTS
     0.000 0.000 0.000
     0.000 0.500 0.500
     0.250 0.500 0.750
     0.500 0.500 0.500
     0.000 0.000 0.000
     0.375 0.375 0.750
     0.500 0.500 1.000
    &END
    When the non-SCF calculation is performed, k-points and Kohn-Sham eigenvalues are printed in "energy.data." However, "energy.data" alone cannot be used to plot the band structure. For this purpose, "energy2band" included in the "util" directory is used. Here a sample bash script, which generate the band structure is shown.
    #!/bin/sh
    #
    # Fermi level obtained in the SCF calculation
    ef=0.0790726449
    # Number of k-points
    nk=161
    # Number of bands
    nb=16
    # Divisions for each segment (in this case we have 6 segments)
    ik1=40
    ik2=60
    ik3=80
    ik4=100
    ik5=140
    ik6=160
    # Maximum energy
    emin=-12.5
    # Minimum energy
    emax=7.5
    #
    nk1=`expr $ik1 + 2`
    nk2=`expr $ik2 + 2`
    nk3=`expr $ik3 + 2`
    nk4=`expr $ik4 + 2`
    nk5=`expr $ik5 + 2`
    nk6=`expr $ik6 + 2`
    #
    e2b=~/STATE/util/bandutil/src/energy2band
    #
    ${e2b} << EOF
    ${nb}
    ${nb}
    ${nk}
    ${ef}
    EOF
    #
    k1=`head -${nk1} band.data | tail -1 | awk '{print $1}'`
    k2=`head -${nk2} band.data | tail -1 | awk '{print $1}'`
    k3=`head -${nk3} band.data | tail -1 | awk '{print $1}'`
    k4=`head -${nk4} band.data | tail -1 | awk '{print $1}'`
    k5=`head -${nk5} band.data | tail -1 | awk '{print $1}'`
    k6=`head -${nk6} band.data | tail -1 | awk '{print $1}'`
    #
    xmin=0.0
    xmax=${k6}
    offset=-0.5
    #
    pos=`echo "scale=2; $emin + $offset" | bc`
    #
    gnuplot<<EOF
    set xrange [$xmin:$xmax]
    set yrange [$emin:$emax]
    set arrow from ${k1},${emin} to ${k1},${emax} nohead lt 0
    set arrow from ${k2},${emin} to ${k2},${emax} nohead lt 0
    set arrow from ${k3},${emin} to ${k3},${emax} nohead lt 0
    set arrow from ${k4},${emin} to ${k4},${emax} nohead lt 0
    set arrow from ${k5},${emin} to ${k5},${emax} nohead lt 0
    unset xtics
    set mytics
    set ylabel 'Energy (eV)'
    set label '{/Symbol G}' at 0.0, ${pos}
    set label 'X' at ${k1}, ${pos}
    set label 'W' at ${k2}, ${pos}
    set label 'L' at ${k3}, ${pos}
    set label '{/Symbol G}' at ${k4}, ${pos}
    set label 'K' at ${k5}, ${pos}
    set label 'X' at ${k6}, ${pos}
    plot 'band.data' with lines
    EOF
    Note that the energy origin is set to the valence band maximum, which is located at the Gamma point.
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Last-modified: 2019-11-28 (木) 21:48:05 (12d)