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.