### Table of Contents

# Electronic structure calculation using DFT

In this exercise, you will perform geometry optimization using DFT.

## 1. Step: Single point energy calculation with separate coordinate file

In the previous exercises we initially specified all parameters – pseudopotential and basis set coefficients as well as atom coordinates – in the input file. Later we used the pseudpotentials and basis sets from a file provided by CP2K.

Now we go further and also factor out the atomic structure to make it easier to automate different calculations for the same structure or the same calculation for different structures. The format used for this is the same you will get for trajectories from MD for example.

First create two files with (different) coordinates for Ethane C_{2}H_{8} (do not confuse with Ethene C_{2}H_{6} from before):

- ethane1.xyz
8 C 0.750 0.000 0.000 C -0.750 0.000 0.000 H -1.050 0.000 -0.850 H -1.050 0.736 0.425 H -1.050 -0.736 0.425 H 1.050 0.000 -0.850 H 1.050 0.736 0.425 H 1.050 -0.736 0.425

- ethane2.xyz
8 C 0.750 0.000 0.000 C -0.750 0.000 0.000 H -1.050 0.000 0.850 H -1.050 0.736 -0.425 H -1.050 -0.736 -0.425 H 1.050 0.000 -0.850 H 1.050 0.736 0.425 H 1.050 -0.736 0.425

The input file for CP2K looks almost the same as the one for the previous calculations:

- ethane.inp
&GLOBAL PROJECT ethane RUN_TYPE ENERGY PRINT_LEVEL MEDIUM &END GLOBAL &FORCE_EVAL METHOD Quickstep ! Electronic structure method (DFT,...) &DFT BASIS_SET_FILE_NAME BASIS_MOLOPT POTENTIAL_FILE_NAME POTENTIAL &POISSON ! Solver requested for non periodic calculations PERIODIC NONE PSOLVER WAVELET ! Type of solver &END POISSON &SCF ! Parameters controlling the convergence of the scf. This section should not be changed. SCF_GUESS ATOMIC EPS_SCF 1.0E-6 MAX_SCF 300 &END SCF &XC ! Parameters needed to compute the electronic exchange potential &XC_FUNCTIONAL PBE &END XC_FUNCTIONAL &END XC &END DFT &SUBSYS &CELL ABC 10 10 10 PERIODIC NONE ! Non periodic calculations. That's why the POISSON section is needed &END CELL &TOPOLOGY ! Section used to center the atomic coordinates in the given box. Useful for big molecules &CENTER_COORDINATES &END COORD_FILE_FORMAT xyz COORD_FILE_NAME ./ethane1.xyz &END &KIND H ELEMENT H BASIS_SET DZVP-MOLOPT-GTH POTENTIAL GTH-PBE-q1 &END KIND &KIND C ELEMENT C BASIS_SET DZVP-MOLOPT-GTH POTENTIAL GTH-PBE-q4 &END KIND &END SUBSYS &END FORCE_EVAL

and should give the following energy once you run it:

ENERGY| Total FORCE_EVAL ( QS ) energy (a.u.): -14.746153797151329

You can also directly open a XYZ file in VMD to visualize it:

$ vmd ethane1.xyz

## 2. Step: Optimizing the geometry

The only thing you have to change to get a geometry optimization instead of a single point energy calculation is the following:

- ethane1_opt.inp
&GLOBAL PROJECT ethane1_opt RUN_TYPE GEO_OPT PRINT_LEVEL MEDIUM &END GLOBAL [...]

Note the different `RUN_TYPE`

and the changed `PROJECT`

name. The latter is not strictly necessary but recommended, since CP2K automatically creates additional files using this project name as a prefix.

After running this, you will have the following files:

$ ls ethane1_opt* ethane1_opt-1.restart ethane1_opt-1.restart.bak-3 ethane1_opt.out ethane1_opt-RESTART.wfn.bak-1 ethane1_opt-1.restart.bak-1 ethane1_opt-BFGS.Hessian ethane1_opt-pos-1.xyz ethane1_opt-RESTART.wfn.bak-2 ethane1_opt-1.restart.bak-2 ethane1_opt.inp ethane1_opt-RESTART.wfn ethane1_opt-RESTART.wfn.bak-3

Take a look at the output file, especially the following section (repeated the number of cycles it took to reach convergence):

-------- Informations at step = 1 ------------ Optimization Method = BFGS Total Energy = -14.9417142787 Real energy change = -0.1955604816 Predicted change in energy = -0.1885432833 Scaling factor = 0.0000000000 Step size = 0.2677976891 Trust radius = 0.4724315332 Decrease in energy = YES Used time = 19.018 Convergence check : Max. step size = 0.2677976891 Conv. limit for step size = 0.0030000000 Convergence in step size = NO RMS step size = 0.1458070233 Conv. limit for RMS step = 0.0015000000 Convergence in RMS step = NO Max. gradient = 0.0287243359 Conv. limit for gradients = 0.0004500000 Conv. for gradients = NO RMS gradient = 0.0180771987 Conv. limit for RMS grad. = 0.0003000000 Conv. for gradients = NO ---------------------------------------------------

For each convergence criterion you see the value which is used to check whether convergence is reached and convergence is only reached if all of them are satisfied simultaneously.

From the output file, extract the following data and generate 3 plots with the values vs the iteration number:

`Total FORCE_EVAL ( QS ) energy`

`Max. gradient`

.. the maximal force (seen over all atoms)`Max. step size`

.. the maximal displacement (seen over all atoms)

## 3. Step: Optimizing the geometry with an alternative geometry

Now change the used coordinate file to `ethane2.xyz`

and update the `PROJECT`

name to not overwrite the results from the previous simulation and run it again.

- Compare the final energy reached for both structures and the total number of optimization steps required
- Open the two output XYZ files (
`<PROJECT>-pos-1.xyz`

) in VMD and compare them. Is there a difference? What is it? - Which one is likely to be more stable and why?

## 4. Step: Visualize the geometry optimization

Append the following section to your input file (does not matter for which structure) and run the simulation (it does not matter which one) again.

&MOTION &PRINT &TRAJECTORY LOG_PRINT_KEY .TRUE. FORMAT XYZ ADD_LAST NUMERIC &END TRAJECTORY &END PRINT &END MOTION

If you check the output XYZ file now (`<PROJECT>-pos-1.xyz`

) and compare it to the input structure, you will notice that the same molecule is now specified multiple times as so-called *frames*. Checking the CP2K output file you will also notice the following entry:

[...] Writing TRAJECTORY 1_1 to ethane2_opt_traj-pos-1.xyz [...]

Open this new XYZ file again with VMD, choose an appropriate drawing method (*Licorice* or *CPK*), hit the play button and enjoy: