Two-step model for ultrafast interfacial electron transfer: limitations of Fermi’s golden rule revealed by quantum dynamics simulations

Abstract

Interfacial electron transfer (IET) is one of the crucial steps in the light-harvesting process that occurs in various assemblies for solar energy conversion, such as dye-sensitized solar cells or dye-sensitized photoelectrosynthesis cells. Computational studies of IET in dye–semiconductor assemblies employ a variety of approaches, ranging from phenomenological models such as Fermi’s golden rule to more complex methods relying on explicit solutions of the time-dependent Schrödinger equation. This work investigates IET in a model pyridine–TiO₂ assembly, with the goals of assessing the validity of Fermi’s golden rule for calculation of the IET rates, understanding the importance of conformational sampling in modeling the IET process, and establishing an approach to rapid computational screening of dye-sensitizers that undergo fast IET into the semiconductor. Our results suggest that IET is a two-step process, in which the electron is first transferred into the semiconductor surface states, followed by diffusion of the electron into the nanoparticle bulk states. Furthermore, while Fermi’s golden rule and related approaches are appropriate for predicting the initial IET rate (i.e., the initial transfer of an electron from the dye into the semiconductor surface states), they are not reliable for prediction of the overall IET rate. The inclusion of conformational sampling at room temperature into the model offers a more complete picture of the IET process, leading to a distribution of IET rates with a median rate faster than the IET rate obtained for the fully-optimized structure at 0 K. Finally, the two most important criteria for determination of the initial IET rate are the percentage of electron density on the linker in the excited state as well as the number of semiconductor acceptor states available at the energy of the excited state. Both of these can be obtained from relatively simple electronic structure calculations at either ab initio or semiempirical levels of theory and can thus be used for rapid screening of dyes with the desired properties.