It has been shown in a previous paper that classical mechanics are not adequate to treat the transition of a hydrogen atom or proton across an energy barrier of the dimensions commonly met with in chemical reaction. The treatment given was based on an exact solution of the Schrödinger equation and a type of potential curve having no discontinuities in slope, but owing to the laborious nature of the computations involved, no attempt was made to investigate quantitatively the effect of variations in the heat of activation, the width of the barrier, or the mass of the particle. The present paper describes an approximate treatment leading to simple equations which can be applied directly to investigate these points. In a recent paper, Wigner has given a method of treatment applicable to any form of potential curve. His final equations are, however, only valid for the case in which the difference between the quantum mechanical and classical results can be expressed as a small correction term, and cannot be applied when there are large deviations from classical behaviour.
Electron transfer in the nonadiabatic regime: Crossover from quantum-mechanical to classical behaviour