### Table of Contents

# 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:

- 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

`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.
# 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 previous exercise) and compare the energy of adsorption for both cases.