Quantum tunneling and activated flow of particles

In contrast, the probability of activated flow is given by the Boltzmann distribution function in Eqn. 7-29  

In tunneling electron transfer, the transfer rate Vt at the energy level e can be given by the product of the state density occupied by electrons in the initial state, the state density vacant for electrons hi the final state of the step, the tunneling probability Wt, and the transmission coefficient K( as expressed in Eqn. 7-30  

As is described in Chap. 8, the current of electron transfer (the rate of electron transfer) can be given, to a first approximation, as an exponential function of the overvoltage ii as shown in Eqn. 7-32  

For the activated transfer of ions, the transfer current can be derived from the theory of absolute reaction rates as shown in Eqn. 7- 3 [Horiuti-Nakamura, 1967]  

These reaction currents given by Eqns. 7-32 and 7-33 are formally in agreement with the Tafel equation of Eqn. 7-19 obtained by experimental observations. Note that the rate equations in Eqns. 7-32 and 7-33 apply to the forward reaction only and disregard the backward reaction rate. 

---