Functional Mode Hot Electron Transfer Theory

Abstract

Charge carriers that have been driven out of thermal equilibrium by their excessive vibrational energies are termed hot carriers. A theory has been developed to model the injection of these vibrationally excited electrons by explicitly accounting for the time-dependent thermal relaxation of the electron-transfer driving vibrational mode, as ascertained using functional mode analysis. Specifically, the thermal relaxation rate of the driving mode is first determined through the so-called frozen-phonon approach after which the energy-dependent line shape function is revisited to include memory effects for the vibrational quanta within the framework of Fermi’s golden rule. As shown by the numerical simulations of a 6-methyl-azulene-2-carboxylic acid dye molecule bound to an anatase TiO2[101] surface, our new theory not only yields persistently faster electron injection rates with higher incident photon energy but also exhibits a sharp increase when the vibrational quanta of the photoexcited dye molecule chang...