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.