The dissociation of fast hydrogen and nitrogen molecular ions with kinetic energies ranging from 200 to 2000 eV/atom is studied for grazing collisions with various fcc metal surfaces. Within this energy range, the dissociation is either caused by electron capture into antibonding molecular states or by vibrational and rotational excitation. In contrast to hydrogen, nitrogen is chemically inert and interacts mainly elastically with the surfaces; thus there is no dissociation via electron capture. The processes of vibrational and rotational excitation are simulated using a molecular dynamics simulation with interaction potentials based on density functional theory. The comparison with the data obtained from Time-Of-Flight experiments reveals that an additional electronic effect has to be taken into account: The intramolecular bond of the molecules is softened due to electronic screening during the interaction with the surface. Hence, the softened molecules are more likely to dissociate through elastic collisions with surface atoms. The dissociation of hydrogen at low energies on metallic surfaces is dominated by electronic processes. An analysis of the kinetic energy distributions of the scattered dissociation products reveals information about the energy which is released during the dissociation process. The model of electronically induced dissociation is clearly confirmed by this method. However, an increasing contribution of additional mechanical processes becomes apparent at higher energies.