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bulk_optimization

Lattice parameter

In this section, we explain how to optimize the lattice parameter of Si bulk diamond structure. The diamond structure is characterized by two distinct atom per unit cell with relative coordinates (0 ,0 ,0) and (1/4, 1/4, 1/4). The lattice vector is defined in the relative coordinates alat*(1/4, 1/4, 1/4). Detail description of the diamond structure can be found elsewhere. There is an elegant way to rescale atomic coordinates, lattice vector and k-points by only one parameter rescal defined in the section &OPTIONS. Our input atomic coordinates written in Si.bas look like:

 2
14   0.00000   0.00000   0.00000
14   0.25000   0.25000   0.25000

the lattice vector is defined in Si.lvs file:

 0.50000   0.00000   0.50000
 0.00000   0.50000   0.50000
 0.50000   0.50000   0.00000

and we use Oh symmetry group to generate a k-points set (file Si.kpts)

        60
 -2.74889350   -2.74889350   -2.74889350           0.00390625
 -1.96349549   -1.96349549   -3.53429174           0.01171875
 -1.17809725   -1.17809725   -4.31968975           0.01171875
 -0.39269909   -0.39269909   -5.10508823           0.01171875
  0.39269909    0.39269909   -5.89048624           0.01171875
  1.17809725    1.17809725    5.89048608           0.01171875
  1.96349549    1.96349549    5.10508807           0.01171875
 -3.53429190   -3.53429190   -1.96349581           0.01171875
 -2.74889350   -1.17809725   -2.74889350           0.01171875
 -1.96349549   -0.39269909   -3.53429174           0.02343750
 -1.17809725    0.39269909   -4.31968975           0.02343750
 -0.39269909    1.17809725   -5.10508823           0.02343750
  0.39269909    1.96349549   -5.89048624           0.02343750
 -5.10508815   -3.53429190   -0.39269932           0.02343750
 -4.31968991   -2.74889366   -1.17809733           0.02343750
 -2.74889350    0.39269909   -2.74889350           0.01171875
 -1.96349549    1.17809725   -3.53429174           0.02343750
 -1.17809725    1.96349549   -4.31968975           0.02343750
 -0.39269909    2.74889350   -5.10508823           0.02343750
 -5.89048631   -2.74889366    0.39269916           0.02343750
 -5.10508815   -1.96349565   -0.39269932           0.02343750
 -2.74889350    1.96349549   -2.74889350           0.01171875
 -1.96349549    2.74889350   -3.53429174           0.02343750
 -1.17809725    3.53429174   -4.31968975           0.02343750
  5.89048631   -1.96349565    1.17809717           0.02343750
 -5.89048631   -1.17809717    0.39269916           0.02343750
 -2.74889350    3.53429174   -2.74889350           0.01171875
  4.31968991   -1.96349565    2.74889366           0.02343750
  5.10508815   -1.17809717    1.96349565           0.02343750
  3.53429190   -1.17809717    3.53429190           0.01171875
  4.31968991   -0.39269916    2.74889366           0.02343750
  3.53429190    0.39269932    3.53429190           0.01171875
 -1.96349549   -1.96349549   -1.96349549           0.00390625
 -1.17809725   -1.17809725   -2.74889350           0.01171875
 -0.39269909   -0.39269909   -3.53429174           0.01171875
  0.39269909    0.39269909   -4.31968975           0.01171875
  1.17809725    1.17809725   -5.10508823           0.01171875
 -4.31968991   -4.31968991    0.39269916           0.01171875
 -1.96349549   -0.39269909   -1.96349549           0.01171875
 -1.17809725    0.39269909   -2.74889350           0.02343750
 -0.39269909    1.17809725   -3.53429174           0.02343750
  0.39269909    1.96349549   -4.31968975           0.02343750
  1.17809725    2.74889350   -5.10508823           0.02343750
 -1.96349549    1.17809725   -1.96349549           0.01171875
 -1.17809725    1.96349549   -2.74889350           0.02343750
 -0.39269909    2.74889350   -3.53429174           0.02343750
  0.39269909    3.53429174   -4.31968975           0.02343750
 -1.96349549    2.74889350   -1.96349549           0.01171875
 -1.17809725    3.53429174   -2.74889350           0.02343750
 -1.96349549    4.31968975   -1.96349549           0.01171875
 -1.17809725   -1.17809725   -1.17809725           0.00390625
 -0.39269909   -0.39269909   -1.96349549           0.01171875
  0.39269909    0.39269909   -2.74889350           0.01171875
  1.17809725    1.17809725   -3.53429174           0.01171875
 -1.17809725    0.39269909   -1.17809725           0.01171875
 -0.39269909    1.17809725   -1.96349549           0.02343750
  0.39269909    1.96349549   -2.74889350           0.02343750
 -1.17809725    1.96349549   -1.17809725           0.01171875
 -0.39269909   -0.39269909   -0.39269909           0.00390625
  0.39269909    0.39269909   -1.17809725           0.01171875

to make the total energy calculation of several lattice parameters automatic, we use a script:

alat=" 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0"
for i in $alat;
do
 echo $i
 mkdir $i
 lattice="`echo $i`";
 sed "s/AAA/$lattice/g"  fireball.sample > fireball.in;
 ./runTG.com > a-$i.out
 grep "etot/atom" a-$i.out | cut -b50-65
 mv CHARGES $i/
 mv a-$i.out $i/
done

the script runs several tasks for defined lattice vectors, it creates a directory for each lattice parameter and it saves there CHARGES and an output file. It also dumps the energy per atom for a given lattice parameter. A file fireball.sample has following syntax:

&OPTION
basisfile = Si.bas
lvsfile = Si.lvs
kptpreference = Si.kpts
nstepf = 1
rescal = AAA
&END

Afterwards, we simply dump the total energy vs. lattice parameter into a file:

 grep ETOT */*.out | cut -b1-3,34- > etot.dat

and we plot using gnuplot

 gnuplot
 gnuplot> set title "Etot vs. alat"
 gnuplot> set xlabel "alat [Ang]"
 gnuplot> set ylabel "Etot [eV]"
 gnuplot> set format y "%8.2f"
 gnuplot> plot 'etot.dat' with linespoints

The bulk modulus

$ ls
Fdata  uno.bas  uno.kpts  uno.lvs  vol.sh

$ head uno.bas
2
14      0.000000      0.000000      0.000000
14      0.250000      0.250000      0.250000

$ head uno.kpts
32 
-2.35619449         -2.35619449         -2.35619449        0.03125000
-3.92699081         -0.78539816         -0.78539816        0.03125000
-5.49778713          0.78539816          0.78539816        0.03125000
-7.06858347          2.35619449          2.35619449        0.03125000
-0.78539816         -3.92699081         -0.78539816        0.03125000
-2.35619449         -2.35619449          0.78539816        0.03125000
-3.92699081         -0.78539816          2.35619449        0.03125000
-5.49778713          0.78539816          3.92699081        0.03125000
 0.78539816         -5.49778713          0.78539816        0.03125000 

$ head  uno.lvs
0.5000    0.5000    0.0000
0.5000    0.0000    0.5000
0.0000    0.5000    0.5000

The script to calculate the bulk modulus

$ cat vol.sh 
#!/bin/bash
 
##----- Parametros de control (el parametro de red tiene que encontrase entre ini fin  --------##
N=10
ini=5.0
fin=6.0 
 
##----------Funcion analisis para dos atomos/celda-----------------------------------------##
function analisis {
ETOT=$(grep 'ETOT' salida.out|cut -d'=' -f2)
sigma=$(grep sigma salida.out | cut -d'=' -f16 | tail -1)
charge=$(head -2 uno.bas | tail -1 | tr -s ' ' | cut -d' ' -f2)' -> '$(head -2 CHARGES | tail -1)
charge=$charge' ;'$(head -3 uno.bas | tail -1 | tr -s ' ' | cut -d' ' -f2)' -> '
charge=$charge$(tail -1 CHARGES)
echo $rescal$'\t'$ETOT$'\t'$sigma$'\t'$charge$'\t'>>salida
}
##------------------------------------------------------------------------------------------##
function start {
rm -fr salida
for((i=0;i<=N;i++))
do
rescal=$(python -c "print '%.6f' % ($i*1.0*($fin-$ini)/$N+$ini)")
echo "&option
basisfile = uno.bas
lvsfile = uno.lvs
kptpreference = uno.kpts
rescal = $rescal
sigmatol = 0.000001
nstepf = 1
&end
&output
iwrtxyz = 1
&end" > fireball.in 
../progs/fireball.x > salida.out    

analisis
done
}
##----------------------------------1º start  ----------------------------------------------##
start
##-----------------------------buscamos el minimo ------------------------------------------##
min=$(python -c "
x0 = []
y0 = []
for line in file(\"salida\"):
   line = line.split()
   x = line[0]
   y = line[1]
   x0.append(x)
   y0.append(y)  

j=0
for i in range(len(x0)):
  if y0[j]< y0[i]:
    j=i
print x0[j]")
cp salida borrar
rm -fr aux.py		        

##----------------------------------2º start -----------------------------------------------##
N=40
d=0.4
ini=$(python -c "print '%.6f' % (1.0*($min-$d))")
fin=$(python -c "print '%.6f' % (1.0*($min+$d))")
start
mv salida Vol.dat
##------------------------------------------------------------------------------------------##  

In the 1º start of the script “vol.sh” takes 10 points between 5-6:

In the 2º start of the script “vol.sh” takes 40 points between the minimum of the 1º start

The scripts uses the parameter rescal in fireball.in and unitary positions and lattice vectors with 2 atoms/cell to obtain the kpts points we used xeo:

The bulk mudulus can be calculed also with xeo (Utilities→Bulk modulus), in the in line command:

$ xeo -Bulk Vol.dat zincblende
E_min =     -214.35239    eV
a_min =        5.43719    angs 
Volumen =       40.18518 ang**3 
Bulk modulus =      100.79399  GPa
bulk_optimization.txt · Last modified: 2014/02/09 11:23 (external edit)