Time-dependent theory of the rate of photo-induced electron transfer

A novel approach based on constrained real-time time-dependent density functional theory (C-RT-TDDFT) is introduced to accurately evaluate the electronic Hamiltonian coupling associated with photoinduced electron transfer (PIET) using diabatic states that are defined using constrained DFT (C-DFT). In combination with the semiclassical Marcus theory, the photoexcited ET rate for coherently coupled photoexcitation and electron transfer is determined for a given incident wavelength by combining this Hamiltonian coupling with free energy changes and ground state reorganization energies that are obtained using an implicit solvation model. As an application of this method, we consider PIET for the (Ag₂₀-Ag)⁺ complex as a model of a plasmon-enhanced electron transfer process. Using solar radiation intensity, the fastest PIET rate is found to be induced by an incident wavelength that is distinct (blue-shifted) from the wavelength of strongest plasmon-like excitation associated with the Ag20₊ cluster, particularly for large donor-acceptor separations, which suggests a much more efficient coupling Hamiltonian for higher-energy molecular orbitals. Through a comparison between the PIET and absorption cross sections, the quantum efficiency for PIET is found to be a few percent at most at short donor-acceptor distances, and it decays exponentially as they separate.