The critical role of the transition-state cusp diameter in understanding adiabatic and non-adiabatic electron transfer

The equation of Levich and Dogonadze describing the rate of electron-transfer processes in the weak-coupling non-adiabatic limit is understood in terms of the properties of general adiabatic electron-transfer theory. The cusp diameter describing the continuous changeover of Born-Oppenheimer adiabatic surfaces from donor-like to acceptor-like character is shown to be the critical property controlling reaction rates and intervalence spectra. Their work is presented in the context of general Born-Oppenheimer breakdown phenomena and linked to the overarching cusp catastrophe.