Removal of the double adiabatic approximation for proton-coupled electron transfer reactions in solution

A dynamical theory that removes the double adiabatic approximation for proton-coupled electron transfer reactions in solution is presented. In this formulation mixed electronic/proton vibrational adiabatic states are expressed as linear combinations of double adiabatic states that each correspond to the product of an electronic and a proton vibrational state. This methodology includes all nonadiabatic coupling terms in a computationally practical way. The electron–proton nonadiabatic coupling is incorporated into the adiabatic states, while the electron–solvent and proton–solvent nonadiabatic couplings are incorporated through nonadiabatic transitions among these states. Two model proton-coupled electron transfer reactions are investigated.