How to calculate the Band structure and DOS of Aluminium

This tutorial is prepared using the siesta-4.1-b4 version.

To download and install siesta-4.1-b4 version click here 

 

We take the example of Aluminium. We need input file and pseudopotential

algerien1970@linux-ml0a:~/abinitio/siesta-tutorials/Al_BAND-DOS> ls
Al_bulk.fdf  Al.psf

Al_bulk.fdf

#General system specifications
SystemName          FCC Al
SystemLabel         Al
NumberOfAtoms       1
NumberOfSpecies     1

%block ChemicalSpeciesLabel
 1  13 Al      # Species index, atomic number, species label
%endblock ChemicalSpeciesLabel
#Experimental lattice parameter 4.05 Ang
LatticeConstant 4.05 Ang

%block LatticeVectors
0.000000    0.500000   0.5000000
0.500000    0.000000   0.5000000
0.500000    0.500000   0.0000000
%endblock LatticeVectors

# Basis set definition
PAO.EnergyShift 200 meV
PAO.SplitNorm   0.15
PAO.BasisSize   SZ 

#Atomic coordinates
AtomicCoordinatesFormat  scaledcartesian

%block AtomicCoordinatesAndAtomicSpecies
  0.000000      0.000000      0.000000   1
%endblock AtomicCoordinatesAndAtomicSpecies


#Real space grid 
MeshCutoff 125.0 Ry

# K-sampling (alternative specification using kgrid_cutoff)
%block kgrid_Monkhorst_Pack
     4  0  0  0.5
     0  4  0  0.5
     0  0  4  0.5
%endblock kgrid_Monkhorst_Pack

# Convergence of SCF 
MaxSCFIterations 50
DM.MixingWeight 0.5
DM.NumberPulay  3
ElectronicTemperature 300 K

# Type of solver
SolutionMethod diagon

# Output (Band structure calculation)
BandLinesScale pi/a

%block BandLines
1   1.0000 1.0000 1.0000  L       # Begin at L
20  0.0000 0.0000 0.0000  \Gamma  # 20 points from L to gamma
25  2.0000 0.0000 0.0000  X       # 25 points from gamma to X
30  2.0000 2.0000 2.0000  \Gamma  # 30 points from X to gamma
%endblock BandLines

 

Pseudopotential  Al.psf

 

Calculation

 For metals there are electronic bands that are not completely filled and therefore for an accurate description of the total energy, forces and all properties of the materials it is necessary to use a better sampling in reciprocal space (Bloch vectors) than for insulators. In the input file Al_bulk.fdf a 4x4x4 grid is used. This might be insufficient for a good description of aluminium.

You should explore the convergence of total energy, the lattice parameter, and density of states respect to the fineness of the k-sampling.

SCF calculation

algerien1970@linux-ml0a:~/abinitio/siesta-tutorials/Al_BAND-DOS> siesta < Al_bulk.fdf | tee Al_bulk.out

 

.

siesta: Final energy (eV):
siesta:  Band Struct. =     -26.737425
siesta:       Kinetic =      22.741982
siesta:       Hartree =       0.071668
siesta:       Eldau   =       0.000000
siesta:       Eso     =       0.000000
siesta:    Ext. field =       0.000000
siesta:       Enegf   =       0.000000
siesta:   Exch.-corr. =     -21.753754
siesta:  Ion-electron =     -21.281362
siesta:       Ion-ion =     -36.130810
siesta:       Ekinion =       0.000000
siesta:         Total =     -56.352275
siesta:         Fermi =      -3.972284

. 

 

DOS calculation

To plot the DOS we will use the utility program 'Eig2DOS'. This program reads the information contain in the file Al.EIG which contains all the eigenvalues for each k-point, and the Al.KP file which contains the k-point sampling information.  Useful options to the program (type 'Eig2DOS -h' for a full list) are the broadening for each state in eV (a value of the order of the default (0.2 eV) is usually reasonable), the number of energy points where the DOS will be calculated (200 by default) and the Emin and Emax of the energy window where the DOS will be calculated (the default is to compute the DOS in the whole range of energies available in the EIG file).

(Eig2DOS is an enhanced version of the old 'eig2dos' program)


For example:

algerien1970@linux-ml0a:~/abinitio/siesta-tutorials/Al_BAND-DOS> Eig2DOS -k Al.KP Al.EIG > dos

 

will compute the DOS in the whole range, using a grid of 200 points, a broadening ("smearing") of 0.2 eV, and using the k-point info from Al.KP. (The k-point file information is important when different k-points have different weights).

The content of the 'dos' file can be plotted using gnuplot:

gnuplot> plot "dos" using 1:2 with lines title "Up" ,"" using 1:3 with lines title "Dn" 

,"" using 1:4 with lines title "Tot" 

 

 

Or

Al_BAND-DOS> Eig2DOS -s 0.1 -n 400 -m -18.0 -M 4.0 -k Al.KP  Al.EIG > dos  

will compute the DOS in the (18 eV ,4 eV) range, using a grid of 400 points and a broadening of 0.1 eV. will compute the DOS in the (18 eV ,4 eV) range, using a grid of 400 points and a broadening of 0.1 eV.

 

BAND calculation

The file Al_bulk.fdf will also produce a file Al.bands containing the band structure along the several lines in the Brillouin zone (BZ) as specified using the block BandLines. To learn more about the BZ for this case,
you can visit:

http://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-kv-list?gnum=225&fig=fm3qmf

or

http://lamp.tu-graz.ac.at/~hadley/ss1/bzones/fcc.php

(Note that the final Gamma point in the BandLines sequence is actually
an image along (1,1,1) of the Gamma point at the origin.)

To plot the band structure you need to use the utility program 'gnubands'

 

algerien1970@linux-ml0a:~/abinitio/siesta-tutorials/Al_BAND-DOS> gnubands -G -o out.bands Al.bands

 

gnuplot> load "out.gplot"

 or 

algerien1970@linux-ml0a:~/abinitio/siesta-tutorials/Al_BAND-DOS> gnuplot -persist out.gplot

 

 For more information check the following link:

https://docs.siesta-project.org/projects/siesta/tutorials/basic/first-crystals/index.html