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--- band_structure [2014/10/20 12:42]
+++ band_structure [2014/10/20 12:42]
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+===== The band structure =====
+To obtain the band structure of Si bulk of given lattice parameter we have to perform two steps.
+First, we need to achieve SCF solution. Therefore, we run a standard bulk calculation as described in the previous [[bulk optimization|chapter]]. Let's calculate the band structure
+for the lattice parameter ''alat = 5.5 Å'', than we have the **''fireball.in''** file containing:
+  &OPTION
+  basisfile = Si.bas
+  lvsfile = Si.lvs
+  kptpreference = Si.kpts
+  nstepf = 1
+  rescal = 5.5
+  &END
+where **''Si.bas''**, **''Si.lvs''** and **''Si.kpts''** files are identical as those used in previous [[bulk optimization|chapter]].
+Once we obtain the SCF solution, we can determine the Fermi level from an output file:
+  mac135> grep "Fermi Level" $output_file | tail -1
+   Fermi Level =   -4.33045968490834
+In next step, we run the ''FIREBALL'' code again, but now with fixed charges (**''ifixcharge = 1''**) and with a new set of k-points in desired high-symmetry directions in the first Brillouin zone. Remember we need having **''CHARGES''** file in a working directory for a restart. In this particular case,we have chosen a direction ''L-Γ-X-Γ'' stored in a **''{{:lgxg.kpts|lgxg.kpts}}''** file (see also fig. 1).
+{{:si-bulk:fcc_brillouin.png?400|Brillouin zone FCC}}
+In addition, we have to write out a list of eigenvalues at each k-point switching on **''iwrteigen''** variable. Our input file **''fireball.in''** has following form now:
+  &OPTION
+  basisfile = Si.bas
+  lvsfile = Si.lvs
+  kptpreference = lgxg.kpts
+  nstepf = 1
+  ifixcharge = 1
+  rescal = 5.5
+  &END
+  &OUTPUT
+  iwrteigen = 1
+  &END
+After the run, we obtain a file **''ek.dat''** appears in a working directory. This file contains at each line set of eigenvalues for given k-points ordered in ascending form. The Fermi level can
+Now we have all information to plot the band structure of the Si bulk.
+  mac135> gnuplot
+  gnuplot> set xrange [0:300]
+  gnuplot> set yrange [-17:0]
+  gnuplot> set xlabel "k-points"
+  gnuplot> set ylabel "Energy [eV]"
+  gnuplot> set nokey
+  gnuplot> set multiplot
+  multiplot> plot "ek.dat" using 1:2 with lines
+  multiplot> plot "ek.dat" using 1:3 with lines
+  multiplot> plot "ek.dat" using 1:4 with lines
+  multiplot> plot "ek.dat" using 1:5 with lines
+  multiplot> plot "ek.dat" using 1:6 with lines
+  multiplot> plot "ek.dat" using 1:7 with lines
+{{:si-bulk:si-bulk.png?400|Si-bulk Band Structure}}
+===== DOS =====
+To plot Density of state, first, we have to achieve SCF solution in the same way as above (see previous [[band_structure|section]]).
+Next we perform calculation with fixed SCF charges (switching on **''ifixcharge =1''**). The DOS calculation is initialized via variable **''iwrtdos''** in the section **''&OUTPUT''**. Hence, our **''fireball.in''** file looks like that:
+  &OPTION
+  basisfile = Si.bas
+  lvsfile = Si.lvs
+  kptpreference = Si.kpts
+  nstepf = 1
+  ifixcharge = 1
+  rescal = 5.5
+  &END
+  &OUTPUT
+  iwrtdos = 1
+  &END
+In addition, **''dos.optional''** has to be presented in a working directory having following distance:
+.0                   ! scale factor (leave 1.0)
+        2            ! list of atoms to analyze DOS
+                   ! number of energy steps
+  -18.0   0.05          ! initial energy, energy step
+                     ! leave untouched
+.0     0.0           ! leave untouched
+.05                  ! imaginary part of Green function (controls energy level smearing)
+After finishing a run, we obtain **''dens_001.dat''**,**''dens_002.dat''** including projected DOS on two Si atoms in the unit cell (including projected DOS onto individual shells of atoms). Additionally, there is a file **''dens_TOT.dat''** containing DOS. Here, a first column means energy and a second one DOS.
+  mac135> gnuplot
+  gnuplot> set xrange [0:1]
+  gnuplot> set yrange [-17:0]
+  gnuplot> set xlabel "DOS [arb. units]"
+  gnuplot> set ylabel "Energy [eV]"
+  gnuplot>  plot "dens_TOT.dat" using 2:1 title 'Total DOS' with lines, \
+            "dens_001.dat" using 11:1 title 'PDOS Si atom ' with lines
+{{:si-bulk:pdos-si_bulk.png?400|DOS Si Bulk}}

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