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Analyzing defects in graphene

In this exercise we follow-up on what was started previously with defects in silicon, but this time you will have to figure out the setup as well.

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 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).

Vacancy in graphene

Comparing energies

Use the template and initial geometry provided when calculating the projected density of states for graphene 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 $E_v = E_2 (N-1)/N \cdot E_1$ where $E_1$ is energy of the complete system, $E_2$ that of the system with a vacancy and $N$ the number of atoms.

Oxygen atom adsorbed on graphene