In the present work, we apply an ab initio approach to study the dissociative adsorption of a hydrogen molecule on the palladium (111) surface. Our approach is based on the density functional theory (DFT) with a generalized gradient approximation (GGA). The wave-functions are expanded in a plane-wave basis and the electron-ion interaction is described by ultrasoft pseudopotentials. Several pathways for the dissociative adsorption are studied in details. The potential energy surface for each path is determined. Spontaneous dissociation paths are found which have a very small barrier of about 70 meV. This agrees fairly well with the estimation based on the molecular beam experiments, 50 meV. We find that the geometric factor plays an important role: larger stretching of the hydrogen molecule bond leads to a higher barrier. Our results give also some indication for the existence of a precursor state.
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