Tunneling Time and the Breakdown of Born-Oppenheimer Approximation

In electron-transfer reactions in proteins and other molecular systems involving long-distance electron tunneling, the tunneling time, i.e., the time that an electron spends in the barrier region between redox centers, can be comparable to vibrational periods of the nuclei. One consequence of this is the breakdown of the Born-Oppenheimer (BO) approximation at the far tails of the tunneling electronic wave functions. These tails define the coupling of redox centers exchanging electrons and hence the rates of electron transfer. We discuss the transition in the distance dependence of the rate of electron transfer that separates the BO and non-BO behavior of the tunneling reaction and show how the crossover is related to tunneling time.