Integral encounter theory transfer

We have seen in Section IV that the study of the reversible reaction of energy transfer was made possible only by means of integral encounter theory. The same is true for reversible electron transfer (3.354) that was first considered with IET in Ref. 188 and then in a much wider context in subsequent publications [107,189],... 

This behavior, inherent to the IET description of either reversible or irreversible transfer, can be eliminated using modified integral encounter theory (MET) [41,44], or an improved superposition approximation [51,126],... 

This is a clear demonstration that a differential encounter theory is not a reasonable alternative to an integral one, when the energy transfer is reversible and occurs between the unstable reactants. Since the lifetimes are not equal, the rate constant of the energy transfer from the short-lived to the long-lived particle does not exist (diverges) at long times. In contrast, in integral formalism we do not encounter any difficulties. This is illustrated by the simplest example of contact transfer considered below. 

We are starting with the simplest though matrix integral theory. It is outlined by the example of the quasi-resonant energy transfer, which is first considered in an immobile pair and only then in the course of encounter diffusion. 

A number of different approaches may be subsumed under this heading—approaches which are not restricted to nonadiabatic reactions. In remote encounters, the initial and final states refer to separated reactants and products, respectively, and the transition probability may be computed from the corresponding energy defect this model is familiar for charge-transfer processes, but has been applied to chemical reactions. The effect of spin and symmetry conservation on such crossings has also been assessed qualitatively. The importance of the Franck-Condon overlap integral in determining the transition probability has also been treated semiempirically. In the theoretical discussion of nonadiabatic reactions, it is standard practice to compute the transition probability between the surfaces, for example, by Landau-Zener theory. ... 

---