How to calculate the Band Structure of Silicon

To download and install the Abinit code click on the following link:

To do the band calculation we need 2 input files and a pseudopotential

algerien1970@linux-ml0a:~/abinitio/abinit-tutorials/Si_band> ls
Si_bands.files  Si_bands.in si_h.cpi

Si_bands.in

# Crystalline silicon
# computation of the bandstructure

# Definition of the unit cell: fcc
acell 3*10.27           # theoretical lattice constant
                       # Angstrom          
rprim  0.0  0.5  0.5   # FCC primitive vectors (to be scaled by acell)
       0.5  0.0  0.5   
       0.5  0.5  0.0

# Definition of the atom types
ntypat 1         # There is only one type of atom
znucl 14        # The keyword "znucl" refers to the atomic number of the 
                 # possible type(s) of atom. The pseudopotential(s) 
                 # mentioned in the "files" file must correspond
                 # to the type(s) of atom. Here, the only type is Silicon.

# Definition of the atoms
natom 2             # There are two atoms
typat 1 1           # They both are of type 1
xred                # The location of the atoms will follow
  0.0  0.0  0.0     # Triplet giving the REDUCED coordinate of atom 1.
  0.25 0.25 0.25    # Triplet giving the REDUCED coordinate of atom 2.

ndtset 2

# Definition of the k-point grids
kptopt1 1          # Option for the automatic generation of k points,
                  # taking into account the symmetry
nshiftk1 4
shiftk1  0.5 0.5 0.5  # These shifts will be the same for all grids
        0.5 0.0 0.0  # FCC Monkhorst-Pack (MP) grids
        0.0 0.5 0.0
        0.0 0.0 0.5
ngkpt1  4 4 4         # parameters that define the MP grid


# Definition of the planewave basis set 
ecut 2.5          # Maximal kinetic energy cut-off, in Hartree

ixc  2           # XC potential Perdew-Zunger

# Definition of the SCF procedure
nstep 10          # Maximal number of SCF cycles
toldfe1  1.0d-7    # Will stop when this tolerance is achieved on total energy
diemac 12.0       # Although this is not mandatory, it is worth to
                  # precondition the SCF cycle. The model dielectric
                  # function used as the standard preconditioner
                  # is described in the "dielng" input variable section.
                  # Here, we follow the prescription for bulk silicon.

# Calculation of the band structure
iscf2    -2           # non self consistent calculation
getden2  -1           # read the charge density
kptopt2  -7           # 7 segments
ndivk2    4 21 16 8 18 11 21 # number of divisions of the segments
kptbounds2             # limits of the segments
 0.25  0.625 0.625    # U
 0.25  0.5   0.75     # W
 0     0     0        # Gamma
 0     0.5   0.5      # X
 0.25  0.5   0.75     # W
 0     0.5   0        # L
 0     0     0        # Gamma
 0.375 0.375 0.75     # K

tolwfr2  1.0d-12      # tolerance on wavefunction squared residual
nband2   5           # number of bands 
enunit2  1            # Will output the eigenenergies in eV
prtvol2  2            # output printing option

Si_bands.files

Si_bands.in
Si_bands.out
Si_i  
Si_o
Si_t 
si_h.cpi

Pseudopotential

/Copper_SCF> curl -O http://www.pseudo-dojo.org/pseudos/nc-sr-04_pbe_standard/Cu.psp8.gz

SCF + BAND calculations

/Si_band> abinit < Si_bands.files |tee Si_bands.log

Plotting using the AbinitBandStructureMaker.py script

To learn how to use the script check the following:

How to use the program

STEP 1 : produce a .dbs ﬁle

/Si_band> python /home/../abinit-7.10.5/scripts/post_processing/AbinitBandStructureMaker.py Si_bands.out

=========================================
 AbinitBandStructureMaker.py version 1.3
=========================================

2 dataset(s) detected

Which dataset(s) do you want to use (1 to 2) ? 2
"Si_bands.out.dbs" file created successfully

STEP 2 : edit the .dbs ﬁle

GRAPH TITLE:
Band Structure from Si_bands.out

NUMBER OF VALENCE BANDS:
4

FERMI ENERGY (eV):
automatic

SPECIAL K-POINTS (reduced coord):
{lU}= 0.2500 0.6250 0.6250
{lW}= 0.2500 0.5000 0.7500
{sG}= 0.0000 0.0000 0.0000
{lX}= 0.0000 0.5000 0.5000
{lW}= 0.2500 0.5000 0.7500
{lL}= 0.0000 0.5000 0.0000

BAND STRUCTURE SCHEME:
{lU}-{lW}-{sG}-{lX}-{lW}-{lL}-{sG}

.
.
.
DATABASE KEY:
ecut: 2.5 
natom: 2.0 
nband: 10.0 
occopt: 1.0 
toldfe: 0.0 
toldff: 0.0 
tolvrs: 0.0 
tolwfr: 1e-12 
typat: 1 1 
reciprocalvectors: -0.097371 0.097371 0.097371 0.097371 -0.097371 0.097371 0.097371 0.097371 -0.097371 
reducedcoordinates: 0.0 0.0 0.0 0.25 0.25 0.25

STEP 3 : produce a .agr ﬁle


/Si_band> python /home/algerien/abinitio/abinit-7.10.5/scripts/post_processing/AbinitBandStructureMaker.py Si_bands.out.dbs

=========================================
 AbinitBandStructureMaker.py version 1.3
=========================================

"Si_bands.out.agr" file created successfully

STEP 4 : plot the band structure