Charge carriers that have been driven out of thermal equilibrium by their excessive vibrational energies are term 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 before 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 TiO<sub>2</sub> [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 photo-excited dye molecule changes from 2 to 3, in excellent agreement with a recent femtosecond pump-probe spectroscopy study. These methods comprise a practical first-principles simulation protocol to model vibrationally resolved electron injection by accommodating the subtle coupling between molecular vibration, thermal relaxation and electron transfer under arbitrary thermalization conditions. Moreover, only trivial extensions are needed to enable the application of our new theory to vibrationally controlled electron transfer reactions in a wide range of chemical and biological systems, particularly those engineered using time-delayed laser pulses.

Functional mode hot electron transfer theory

253rd National Meeting (2017)

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