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 ===== 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 [[http://cst-www.nrl.navy.mil/lattice/struk/a4.html|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

{{:si-bulk:etot-alat.png|}}
===== 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:

{{:bulk-si-10.png|}}

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

{{:si-bulk-40.png|}}

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:

{{:xeo-menu-kpts.png|}}

{{:xeo-kpts.png|}}

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
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