Photoinduced homogeneous proton-coupled electron transfer: model study of isotope effects on reaction dynamics

A model Hamiltonian for photoinduced homogeneous proton-coupled electron transfer reactions is presented, and the equations of motion for the reduced density matrix elements in an electron-proton vibronic basis are derived. This formalism enables a detailed analysis of the proton vibrational dynamics, as well as the dynamics of the electronic state populations, following photoexcitation. The application of this theory to model systems provides insight into the fundamental physical principles underlying these types of processes. The initial nonequilibrium state is prepared by vertical photoexcitation from the ground electronic state to a coherent vibrational mixture in the donor electronic state. This nonstationary state relaxes to the equilibrium distributions in the donor and acceptor electronic states via dynamical processes arising from nonadiabatic transitions between the donor and acceptor vibronic states concurrent with energy dissipation to the bath. During the initial stage, when the proton vibrational population in the donor state is distributed among higher vibrational states and the donor proton wavepacket is oscillating with large amplitude, the electronic state population dynamics exhibits virtually no hydrogen/deuterium isotope effect. After vibrational relaxation, when the proton vibrational population in the donor state becomes concentrated in the lower vibrational states and the donor proton wavepacket becomes more localized near the minimum of the donor potential, a significant hydrogen/deuterium isotope effect on the electronic state population dynamics is exhibited. These model system calculations lead to experimentally testable predictions about the qualitative behavior of these isotope effects.