The binding energy of an adsorbed atom

Summary We discuss the effect of substrate vibrations on the binding of an adsorbed atom. At zero temperature, we compute the binding energyD ₀-E, whereD ₀ is the surface well depth (classical binding energy) andE is the quantum correction. For several simple models, we find thatE is surprisingly model independent. We compareD ₀-E with the binding energies to a rigid substrate,D ₀-E _rs, and to a vibrationally averaged substrate,D ₀-E _va. We prove thatE _va≥E≥E _rs and that similar relations hold at finite temperature for the free energy of binding. We find that in most casesE _rs is better thanE _va as an approximation toE. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.