Exact eigenenergies of a model of vibronically coupled electron transfer reactions.

We present the first exact solution to the time-independent Schrödinger equation of a model Hamiltonian consisting of a vibrational mode coupled to three electronic states. This Hamiltonian serves as a generic model for photo-induced electronic transfer reactions. The solution is non-perturbative and can be applied to ET reactions with weak and strong electronic and vibrational coupling strengths. This work suggests a new direction towards understanding the vibronic effects in ET dynamics beyond the non-adiabatic limit and Condon approximation.