Effect of surface charge fluctuations on the spectral density of chemisorbed atoms

Abstract

Basing our analysis on the Anderson-Newns model for H chemisorption, we develop a systematic method of calculating the adatom self-energy arising from the effect of substrate charge fluctuations. Using the method of functional derivatives, we generate a Dyson equation for the adatom Green's function and evaluate the self-energies due to the hopping and Coulomb interactions between metal and atom to second order. The latter involves the substrate density response function, and this allows us to include the effect of surface plasmons, bulk plasmons, and the particle-hole continum of the metal surface on an equal footing. The latter become increasingly important close to the surface, where simple image-potential arguments are no longer adequate. We formulate our theory treating the adatom Coulomb repulsion $U$ perturbatively (Newns, Hertz and Handler) as well as in the atomic limit (Brenig and Sch\"onhammer, Bell and Madhukar). Keeping only surface plasmons, we discuss the relaxation shifts and surface-plasmon satellites of the H-atom spectral density within the context of the Brenig-Sch\"onhammer approximation. In particular, we show how the effective Coulomb repulsion $U$ is reduced to $U\ensuremath{-}2{V}_{I}$. We also prove that the substrate-induced self-energy term which gives rise to the above changes on the spectral density has no effect on the net chemisorption energy. The small image-potential energy shift of the main resonance is canceled by the large shift associated with the weak surface-plasmon satellite. Much of our theoretical analysis is applicable to the core-level spectrum, and not just the valence electrons involved in chemisorption.