Comparative study of cluster- and supercell-approaches for investigating heterogeneous catalysis by electronic structure methods: tunneling in the reaction N + H --> NH on Ru(0001).

Different ruthenium clusters of various sizes are constructed with the aim to model the Ru(0001) surface with a sufficient accuracy for predicting catalysis by hybrid density functional methods (B3LYP). As an example reaction the hydrogenation step N(ads) + H(ads) --> NH(ads) from the catalytic production cycle of ammonia is chosen. A cluster of 12 ruthenium atoms is found to reproduce experimental geometries and frequencies of the various reactants on the surface satisfyingly. To get the geometries of adsorbed hydrogen qualitatively correct it is shown that second layer atoms have to be included in the model cluster. Boundary effects are believed to have minor effects on optimized geometries, whereas the effects on reaction barriers are significant. A comparison of model cluster calculations to a periodic supercell approach employing plane waves and density functional methods (RPBE) reveals similar barriers for reaction. The influence of tunneling in this reaction is determined by the small curvature tunneling approach on the electronic surfaces.