Adiabatic and non-adiabatic electrochemical electron transfer in terms of Green's function theory

We present a model Hamiltonian for electrochemical electron transfer, and use Green's functions as the starting point for three different approaches to the calculation of rate constants: first order perturbation theory, which is equivalent to the Levich and Dogonadze theory, the calculation of adiabatic free energy surfaces, and propagation in time. We discuss the similarities and differences between these methods.