Analyzing defects in bulk silicon

In the following exercise we use what we already did to investigate defects in bulk Silicon.

Use the input file as given in the Calculating the bulk modulus of Silicon exercise (only renamed to distinguish it from the second input file):

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

Create a second input file silicon64.inp based on the above with 64 atoms in 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.

To speed up the calculation, use

mpirun -np 8 cp2k.popt -i silicon64.inp -o silicon64.out

For both geometries create a vacancy by removing one Silicon, re-calculate the total energy and compare the it to the total energy of the intact bulk Silicon minus the single atom energy.

You may have to employ some of the techniques mentioned in Projected density of states for graphene and h-BN to make the calculations convergence.

Finally, calculate the band structure for the silicon8 geometries (with and without vacancy) as shown in the exercise Getting the band structure of graphene between $\Gamma$, $X$, $K$, $\Gamma$ and compare them.