exercises:2017_uzh_cmest:adsorption

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In this exercise, you will be asked to calculate the adsorption energy of CO molecule on the graphene surface, in an attempt to reproduce a part of the experiments presented in this paper.

As you have seen in earlier exercises, the actual energy – and therefore also the stress tensor – depends on many parameters, like the selected functional. This means that geometrical parameters like the lattice constant may also vary and therefore needs to be optimized first when building a new geometry. While this could be done using CP2K's `CELL_OPT`

run type, optimizing both the lattice/cell constants and the geometry simultaneously, we are going to do it manually here.

What we are using to determine the center volume (the volume for which the energy is minimal) is the Birch–Murnaghan equation of state (to be precise: the BM equation integrated over pressure), which links the energy and the volume using the minimal energy $E_0$, the center volume $V_0$, the bulk modulus $B_0$ and its derivative $B_1$:

\begin{align*} E(V) = E_0 + \frac{9 V_0 B_0}{16} \Bigg\{ \left[ \left(\frac{V_0}{V}\right)^{2/3} - 1 \right]^3 B_1 \; + \left[ \left(\frac{V_0}{V}\right)^{2/3} - 1 \right]^2 \left[ 6 - 4 \left(\frac{V_0}{V}\right)^{2/3} \right] \Bigg\} \end{align*}

Use the following input file as a starting point, and an adapted version of the script you documented in a previous exercise to generate a number of input files for different lattice constants and run the respective calculation. Extract the energies and fit $E_0$, $V_0$, $B_0$, $B_1$ using the Birch–Murnaghan EOS and using the new $V0$ determine the lattice constant.

- graphene.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

The following commands may be useful.

Doing calculations on the command line using the `bc`

tool:

bc -l <<< "5.6 * 12.3" # you can also use variables and capture the output again in a variable: x=1.025 a=$(bc -l <<< "$x * 2.4612")

Replacing numbers (or any text) inside a file and write the changed file to a new file:

a=3.54 sed -e "s/2.4612/$a/g" graphene.inp > "graphene_V-${x}.inp"

Adsorb one CO molecule on the graphene 6X6X1 supercell at the top(T), bridge(B) and center(C) sites and optimize the geometry. You need change the RUN_TYPE to GEO_OPT and also specify the coordinate by yourself. One can get 6x6x1 unit cell by using MULTIPLE_UNIT_CELL which was mentioned in previous exercises.

&GLOBAL PROJECT graphene RUN_TYPE GEO_OPT PRINT_LEVEL MEDIUM &END GLOBAL

The adsorption energy is given by:$ E_{ad} = E_{CO-graphene} - E_{CO} - E_{graphene}$

Find the most stable adsorption site and study the coverage effect such like 1/2 and 1. What do you observe when increasing the coverage?

exercises/2017_uzh_cmest/adsorption.1509981718.txt.gz · Last modified: 2017/11/06 15:21 by tmueller

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