======= Analyzing defects in bulk silicon =======

In the following exercise we are going to investigate the effect of defects in bulk silicon (mainly on the energy).

Use the input file as given below:

<code - silicon8.inp>
&GLOBAL
  PROJECT silicon8
  RUN_TYPE ENERGY
  PRINT_LEVEL MEDIUM
&END GLOBAL
&FORCE_EVAL
  METHOD Quickstep
  STRESS_TENSOR ANALYTICAL
  &DFT
    BASIS_SET_FILE_NAME  BASIS_SET
    POTENTIAL_FILE_NAME  POTENTIAL
    &POISSON
      PERIODIC XYZ
    &END POISSON
    &SCF
      SCF_GUESS ATOMIC
      EPS_SCF 1.0E-8
      MAX_SCF 500
    &END SCF
    &XC
      &XC_FUNCTIONAL PBE
      &END XC_FUNCTIONAL
    &END XC
  &END DFT
  &SUBSYS
    &KIND Si
      ELEMENT   Si
      BASIS_SET DZVP-GTH-PBE
      POTENTIAL GTH-PBE
    &END KIND
    &CELL
      ABC 5.430697500 5.430697500 5.430697500
      PERIODIC XYZ
    &END CELL
    &COORD
      SCALED
      Si    0    0    0
      Si    0    2/4  2/4
      Si    2/4  2/4  0
      Si    2/4  0    2/4
      Si    3/4  1/4  3/4
      Si    1/4  1/4  1/4
      Si    1/4  3/4  3/4
      Si    3/4  3/4  1/4
    &END COORD
  &END SUBSYS
&END FORCE_EVAL
</code>

Create a second input file ''silicon64.inp'' based on the above with 64 atoms in the cell (do not use ''MULTIPLE_UNIT_CELL'' but actually replicate the ''Si ...'' entries by hand and make sure you don't forget to update the ''CELL'').

Run the calculation for both geometries and compare the single atom energy for both of them to make sure you got it right.

<note tip>To speed up the calculation, use
<code>
mpirun -np 4 cp2k.popt -i silicon64.inp -o silicon64.out
</code>
</note>

For both geometries create a vacancy by removing one Silicon atom, re-calculate the total energy and compare it to the total energy of the intact bulk Silicon minus the single atom energy (= vacancy formation energy). What do you observe? Why?

<note tip>You may have to employ some of the techniques mentioned in [[PDOS|Projected density of states and Band structure for WO$_3$]] to make the calculations converge.</note>

====== Observing changes in the density of states ======

Finally we are going to look at the change of the density of states due to the vacancy:

Alter the input files for the small geometry (the ''silicon8'') with and without the vacancy to print out the projected density of states as shown in [[PDOS|a previous exercise]] and plot the total density of states for both cases, comment. Can you explain why the 
''vacancy'' calculation is harder to converge ?

Now do a geometry optimization on the ''silicon8'' structure with the vacancy and plot the total density of states on that relaxed structure again. Compare again to the total density of states for the unaltered structure, what do you see?

Your last task is to compare the total energy of the geometry optimized (with the vacancy) ''silicon8'' structure to that of the standard one minus the energy of a single atom. That is, compute the vacancy formation energy with the relaxed structure and compare it to the one obtained previously. Which of those is the best representation of reality and why ?