# Catalysis¶

This exercise studies the splitting of the N2 molecule on a Ruthenium surface. N2 splitting is the critical step in ammonia synthesis, which is the main source of biologically accessible nitrogen for fertilizers.

Note that the N2 splitting occurs most readily at the bottom of a step on the close-packed (0001) surface. However, to keep system sizes and computer time down at a manageable level, we shall look at a flat surface.

Tools used in this exercise:

• Structural energy minimization.
• Nudged Elastic Band (NEB) for finding transition states.
• If you have time: Extra exercise on vibrational energy

## Part 1: N2 adsorption on a flat Ru surface¶

The notebook n2_on_metal.ipynb shows how to set up a molecule on a flat metal surface.

• Set up a clean metal surface.
• Relax the topmost layer (ca. 10 min running time).
• While running: study the gpaw text output, to learn about e.g. number of irreducible k-points (important for parallel simulations).
• Set up and relax a single N2 molecule (ca. 1 min running time).
• Add the molecule standing on the metal on an on-top site.
• Relax the combined system.

## Part 2: Splitting N2: initial and final geometry¶

(Begin this while the last step above runs)

The N2 molecule will not split while standing up on an on-top site. The molecule can also bind to the surface in a flat geometry - we here ignore the barrier between the two states and just use the lying-down molecule as the initial configuration.

Create scripts setting up and energy-minimizing the initial and final structures, as described in the final part of the notebook from Part 1. Submit these scripts as parallel batch jobs. When submitting make sure that the number of CPU cores matches the number of irreducible k-point in the calculation, as k-point parallelization is much more efficient than other forms of parallelization.

## Part 3: Learning about Nudged Elastic Band¶

neb.ipynb

While the calculations from the previous step runs, you can learn about the Nudged Elastic Band method for finding transition states and barriers from the notebook neb.ipynb.

## Part 4: Run a parallel NEB calculation¶

Prepare a script running NEB using the GPAW calculator and the initial and final states from part 2 to find the barrier for N2 dissociation.

When doing this you should parallelize over the images in the NEB calculation. A more detailed description of how to do this can be found in the Exercise part of the neb.ipynb along with some suitable input parameters for the NEB.

## Extra exercise: Vibrational energy¶

The notebook vibrations.ipynb will guide you through how to calculate the vibrations of the adsorbate in the inital and final state and use the Thermochamistry module to calculate the reaction free energy. The final part of the exercise shows what happens when you calculate the vibrations of a well-converged NEB transition state.

## Extra material: Convergence test¶

We look at the adsorption energy and height of a nitrogen atom on a Ru(0001) surface in the hcp site. We check for convergence with respect to:

• number of layers
• number of k-points in the BZ
• plane-wave cutoff energy