Dynamics of photoinduced proton-coupled electron transfer at molecule-semiconductor interfaces: A reduced density matrix approach

A theoretical model for describing the dynamics of photoinduced proton-coupled electron transfer (PCET) at molecule-semiconductor interfaces is presented. In this model, the electron is photoexcited to a molecular electronic state near the semiconductor surface, and the subsequent electron transfer to the conduction band of the semiconductor is coupled to a proton transfer reaction. The electron could be photoexcited from the ground to an excited electronic state within a dye molecule at the interface or from the defect band in the semiconductor to a molecular adsorbate layer. A model Hamiltonian is developed to describe this PCET process, and the equations of motion for the reduced density matrix elements in the basis of electron-proton vibronic states are derived. This formulation is used to calculate the time-dependent electronic and vibronic state populations for a series of model systems. These calculations provide insight into the hydrogen/deuterium isotope effect on the dynamics of the donor state population decay for ultrafast interfacial PCET. This isotope effect depends on the initial proton wavepacket and the relative time scales of the donor electronic state population decay and proton vibrational relaxation. The effects of the electronic coupling, temperature, and energy of the donor state on the population dynamics are also investigated for photoinduced interfacial electron transfer and PCET. The resulting theoretical predictions about the qualitative impact of altering system properties on the population decay time scales could be useful for designing catalysts that activate bonds containing hydrogen atoms.