Interaction of adsorbates with electric-field fluctuations near surfaces: Nonradiative lifetimes and energy-level shifts

Abstract

In the vacuum above surfaces, there are zero-point fluctuations in the electromagnetic field generated by zero-point charge fluctuations in the substrate. A molecule near the surface will couple to such fluctuations, with the consequence that excited states may decay via nonradiative transitions in which energy is transferred to the electronic excitations of the substrate (surface plasmons, particle hole pairs). In addition, coupling to the fluctuations will produce energy-level shifts not included in the standard version of density-functional theory. We develop a formalism that allows one to calculate the nonradiative lifetimes from this interaction, and also the energy-level shifts. We treat the electric-field fluctuations within the framework of a phenomenological theory that relates their amplitude and frequency spectrum to the optical dielectric constants of the materials from which the substrate complex is fabricated. We demonstrate that when the formalism is applied to a structureless, highly localized electron, the energy-level shift is just that given by the image potential of classical dielectric theory. In real systems one must include the effect of virtual transitions to excited states in the analysis of the level shifts. We present a quantitative study of the nonradiative lifetime of the lowest unoccupied molecular orbital $(\mathrm{LUMO})+1$ state of the magnesium porphine molecule, adsorbed on the oxide covered NiAl(110) surface, along with calculations of the energy-level shifts induced by the field fluctuations for this system. Our calculated nonradiative lifetime is in good accord with experimental data.