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

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

<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 8 cp2k.popt ... &'' 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 template and initial geometry provided when [[calculating_pdos|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 $E_v = E_2 - \frac{N-1}{N} \cdot E_1$ 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. Perform first a single point calculation and second a geometry optimization and compare the energy of adsorption for both cases.

====== Oxygen atom adsorbed on graphene ======

Now we are going to investigate the effect an adsorbent has on graphene.

===== Change in energy =====


In order to adsorb an oxygen atom on top of a graphene layer, modify the coordinate section by adding one oxygen atom which has them same coordinates as a carbon (except the z-component of course). Check whether the addition of an oxygen atom has an effect on the structure of graphene by optimizing its geometry and calculate the adsorption energy.

Use $E_\text{ad} = E_3 – (E_1 + \frac{1}{2}E_2)$, with:

  ; $E_\text{ad}$ : energy of adsorption
  ; $E_1$ : energy of graphene
  ; $E_2$ : energy of molecular oxygen (-31.929714235694995 a.u.)
  ; $E_3$ : energy of oxygen adsorbed on graphene


<note tip>The formation of oxygen is more difficult to obtain, here we use $\frac{1}{2}$ of the total energy of molecular oxygen. This approximation introduces a large uncertainty to our calculations because the calculation of dioxygen is difficult using KS-DFT.

Try to explain based on the lecture what might be the problem.</note>
===== Displacements =====

We are furthermore interested in the change of structure this adsorbent causes. Try to visualize which atoms have to assume a new position in order to minimize the total energy. That is: plot $\sqrt{(x^i-x^i_0)^2 + (y^i-y^i_0)^2 + (z^i-z^i_0)^2}$ in a sensible manner (one which also retains the geometry of graphene).


======= Analyzing defects in hexagonal Boron-Nitride =======

Repeat the calculations of the vacancy formation, defect formation and adsorption for the h-BN-layer structure, taking into account that now both the N and the B can be replaced.

Compare the energies for the two cases, where is a vacancy more likely to be and on top of which atom does an oxygen atom preferably adsorb.

<note tip>Use the total energy of a B or N atom when calculating the vacancy formation energy.</note>

Since N and B are radicals, you have to include the following keywords/options in the right places (use the CP2K manual):

  * ''UKS = .TRUE.''
  * ''MULITPLCITY = ...''