Direct and indirect electron transfer at a semiconductor surface with an adsorbate: Theory and application to Ag3Si(111):H

We consider two pathways of electron transfer induced by a light pulse between a metal cluster and a semiconductor surface. In direct excitation the pulse excites the system directly to the final (electron transferred) state. In indirect excitation the pulse first photoexcites the system to an intermediate state, which then undergoes nonadiabatic transitions to the final state. Quantum state populations are affected by energy dissipation, which occurs on two different time scales-a fast dissipation is due to electronic energy relaxation and a slow (delayed) dissipation arises from vibrational energy relaxation. A theoretical and computational treatment of these phenomena has been done in terms of a reduced density matrix satisfying a generalized Liouville-von Neumann equation. Instantaneous dissipation is described by a Lindblad term containing electronic transition rates, while the delayed dissipation is given by a time integral with a memory supermatrix term derived from the time correlation of atomic displacements in the medium. Populations and quantum coherences during photoinduced excitations are derived from Franck-Condon overlap factors and nonadiabatic electronic couplings. Photoinduced time dependent electric dipoles and related absorption intensities are given. We also examine the viability of using a memory time in the integration of the equations of motion for the reduced density matrix, where the delayed dissipation involves a limit on the duration of the memory effects, and find that this provides significant savings of computational time. We present the results for Ag3Si(111):H photoexcited by light in the visible region using electronic parameters from ab initio density functional calculations. We find that indirect electron transfer is a lot more likely for the studied transitions of this nanostructured system, and that it leads to a longer lasting electronic charge separation.