Description of Nonadiabatic Reactions

The Born-Oppenheimer approximation (adiabatic approximation) becomes unsatisfactory when the potential energy surfaces draw closer or intersect so that the energy difference between them turns comparable with the vibrational quantum hv. In the region of the mixing of electron states, a strong interaction between the electron and the nuclear motion arises, which was termed the vibronic interaction. The narrow energy gap between the ground and the excited 

The intersection or drawing together of the PES s ordinarily occurs in a quite small and localized region of internal coordinates so that one may retain the notion of adiabatic surfaces using a special approach only for the intersection region. 

The probability of the Pj transition depends essentially on the form of the potential surfaces , and E. Its correct calculation for real multidimensional PES s constitutes a complex mathematical problem, which is why it is a common practice to perform in this case one-dimensional approximation (the reaction coordinate is approximated by one parameter) and make use of the classical expression for the probability of a transition between the PES s ( and known as the Landau-Zener formula. 

In the nonadiabaticity region, a PES can satisfactorily be described by hyperbolas with asymptotes  

The probability of a transition between the PES s E, and in the case of uniform motion along the coordinate E at a constant velocity v is  

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