Non-Adiabatic Effects in Chemisorption.

The effects of non-adiabaticity are studied for an atom adsorbed on a metallic surface. The adiabatic potential energy of the adatom may be calculated, assuming that the electrons can adjust instantaneously to any displacement of the adatom, as a function of the distance between the adatom and the surface. It is shown to be a well in which harmonic oscillations can take place. However, non-adiabaticity may occur because of the possible energy transfer between the adsorbate and the substrate. Although phonons can also play a role in this transfer, only electron-hole pairs are considered here. An electron-phonon Hamiltonian describing this system is derived, and the non-adiabatic terms corresponding to the coupling between the vibrations of the adatom and the electronic states of the substrate are kept to first order. It is shown that this coupling creates an effective potential which must be added to the adiabatic harmonic term. This results in a deformation of the well: the potential energy becomes a double well if the coupling is strong enough. Two simple models are considered: a one-dimensional case describing the vibrations of a whole slab parallel to the surface, and a localized case describing the situation in which the adatom forms a surface molecule with one of the atoms of the substrate. Both cases can be reduced to a two-level system and give similar results for the adatom energy. The double-well description is compared with previous studies of infrared absorption properties for adatoms vibrating on metallic surfaces.