======= Analyzing defects in graphene =======

Now we are going to draw our attention towards surfaces and the effect of defects on them. 

Use the following input file as a starting point for this exercise, noting that you will have to make some modifications to it:

<code cp2k grapehene.inp>
&GLOBAL
  PROJECT graphene
  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
        # split the density by quantum number:
        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
    &END CELL
    &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
</code>

<note tip>When comparing scaled coordinates between papers and code input scripts, always make sure that they use the same coordinate systems and definitions for a unit cell (both real and reciprocal space). For example while many sources (like the [[http://www.sciencedirect.com/science/article/pii/S0927025610002697|paper of Curtarolo, Setyawan]]) assume a 120° degree angle between $a$ and $b$ for a hexagonal cell, you can also define it to be a 60° angle (like the default in CP2K).</note>


<note important>Once you have verified that your calculation setup works, use ''nohup mpirun -np 4 cp2k.popt ... &'' again to run the calculations in parallel and in the background since they may take longer to complete than before.</note>

====== Vacancy in graphene ======

===== Comparing energies =====

Use the provided template and its initial geometry to setup a single point energy calculation for a 6x6x1 supercell of graphene.

Create a vacancy by removing one carbon atom from this supercell and perform the energy calculation again.

Quick question: Does it matter which carbon atom you remove? (hint: what kind of boundary conditions do we impose?)

Calculate the energy of the vacancy formation, that is $E_v = E_2 - \frac{N-1}{N} \cdot E_1$ where $E_1$ is the energy of the complete system, $E_2$ that of the system with a vacancy and $N$ the number of atoms.

===== Analyze the PDOS =====

Would you expect the vacancy to haven any influence on the projected density of states? Check whether your assumption was right by visualizing the PDOS.

===== Replacement with oxygen =====

Now, instead of removing one carbon atom from the 6x6x1 supercell, simply replace it with an oxygen atom (remember: you have to a ''KIND'' section for oxygen). Perform first a single point calculation and second a geometry optimization (as shown in a [[[[geometry_optimization|previous exercise]]) and compare the energy of adsorption for both cases.