Electron transfer through time dependent bridges: Differences between Franck-Condon and Born-Oppenheimer breakdown

We consider tunneling-mediated electron transfer through time dependent bridges. An approach is developed for computing corrections to the time dependent tunneling matrix element that arise from the breakdown of the Born-Oppenheimer Adiabatic approximation. Differences between Franck-Condon and Born-Oppenheimer breakdown are discussed in the context of bridge-mediated tunneling.