π adsorption of ethene on to the {111} surface of copper: A periodic ab initio study of the effect of k-point sampling on the energy, atomic and electronic structure

Abstract

The adsorption of ethene on the {111} surface of copper has been studied by using density functional theory calculations with gradient corrections. The surface is described by a periodic (3×3) slab, three layers thick, with ethene adsorbed on one side. The energy of the adsorption shows great sensitivity to the k-point sampling employed, with single k-point calculations overestimating the binding by over 800% when compared with a calculation converged with respect to the k-point sampling. In addition, the structure of the adsorbed molecule is considerably distorted, which is in contradiction with conclusions drawn from the experimental vibrational frequencies. Calculations that are converged with respect to the k-point sampling indicate a much weaker interaction between the molecule and the surface, with adsorption energies of 11.1 and 10.9 kJ mol −1 for atop-h and atop-b, respectively. This weaker interaction leads to a geometry for the adsorbed molecule that is close to the gas-phase ethene structure, in agreement with the vibrational frequencies. We have proposed a model of molecular adsorption that is a balance between attraction, resulting from localised bond formation, and repulsion, due to interaction between the extended electronic states and the molecule's electron density. If the extended electronic states are underestimated, as in cluster or low k-point calculations, the repulsion is underestimated. This results in stronger bonding to the surface and overestimation of the adsorption energy.