In the following exercise we are going to look at the density of states of two similar 2D structures:

• Graphene
• hexagonal Boron Nitride

Both feature the same 2D crystal structure with the only difference being the lattice constant and that one consists of only carbons and the other of boron and nitride.

Similar to the previous exercise we write the coordinates in term of the unit cell:

graphene_pdos.inp

&GLOBAL
  PROJECT graphene_pdos
  RUN_TYPE ENERGY 
  PRINT_LEVEL MEDIUM
&END GLOBAL

&FORCE_EVAL
  METHOD Quickstep
  &DFT
    BASIS_SET_FILE_NAME  BASIS_MOLOPT
    POTENTIAL_FILE_NAME  POTENTIAL

    &POISSON
      PERIODIC XYZ
    &END POISSON
    &SCF
      SCF_GUESS ATOMIC
      EPS_SCF 1.0E-6
      MAX_SCF 300

      # The following settings help with convergence:
      ADDED_MOS 100
      CHOLESKY INVERSE
      &SMEAR ON
        METHOD FERMI_DIRAC
        ELECTRONIC_TEMPERATURE [K] 300
      &END SMEAR
      &DIAGONALIZATION
        ALGORITHM STANDARD
        EPS_ADAPT 0.01
      &END DIAGONALIZATION
      &MIXING
        METHOD BROYDEN_MIXING
        ALPHA 0.2
        BETA 1.5
        NBROYDEN 8
      &END MIXING
    &END SCF
    &XC
      &XC_FUNCTIONAL PBE
      &END XC_FUNCTIONAL
    &END XC
    &PRINT
      &PDOS
        # print all projected DOS available:
        NLUMO -1
        COMPONENTS
      &END
    &END
  &END DFT

  &SUBSYS
    &CELL
      # create a hexagonal unit cell:
      ABC 2.4612 2.4612 15.0
      ALPHA_BETA_GAMMA 90. 90. 60.
      SYMMETRY HEXAGONAL
      PERIODIC XYZ
      # and replicate this cell (see text):
      MULTIPLE_UNIT_CELL 2 2 1
    &END CELL
    &TOPOLOGY
      # also replicate the topology (see text):
      MULTIPLE_UNIT_CELL 2 2 1
    &END TOPOLOGY
    &COORD
      SCALED
      C  1./3.  1./3.  0.
      C  2./3.  2./3.  0.
    &END
    &KIND C
      ELEMENT C
      BASIS_SET DZVP-MOLOPT-GTH
      POTENTIAL GTH-PBE
    &END KIND
  &END SUBSYS

&END FORCE_EVAL

The replication of the unit cell before doing the calculation is necessary since we are currently sampling only at he $\Gamma$ point and we will otherwise do not have enough sampling points for the density of states. Another option (which we will look into in the next exercise) is to sample over k-points instead.