ET Rate for Nonadiabatic Reaction

Equation 10.51 is a typical expression for a rate constant if it is assumed that the nuclei are moving by classical mechanics with the ground state PES as potential. 

FIGURE 10.11 The natural logarithm of the reaction rate k as a function of driving force (-AG ) according to the Marcus model. 

The derivation here, taken from N. Sutin and B. S. Brunschwig, leads to the simplest approximation for the rate. However, in ET reactions it is unavoidable that we have to consider not only the barrier, but also the avoided crossing between two different PES. In other words, there is a probability that the system may jump to the upper surface. In that case, the system is in a new electronic state, but the character of the wave function does not change, meaning that ET does not take place. 

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