Exponential model normal regions

The current evidence concerning the details of the temperature dependence of e.t. processes, cannot be considered as decisive one way or the other it may be surmised that this will become an area of very active research in the future. The reported observations of a bell-shaped temperature dependence of some e.t. processes at least is, however, not in favour of the radiationless transition model, because this does not predict the existence of any normal region in the rate constant vs energy function. On the other hand, the observation of temperature independent e.t. processes of widely different exergonicities (Ref. 101) would certainly speak against the Marcus model, which according to Eq. 3 predicts that the exponential factor which contains the AG /RT term becomes constant only in the special condition AG° X. 

Figure 3.41. The diffusional dependence of the recombination efficiency Z in the contact approximation (dotted line) at starting distance ro — 1.124 a and the same for the remote recombination in a normal (solid line) and inverted (dashed line) Marcus region, in highly polar solvents. The horizontal dashed-dotted line represents the exponential model result, Z — z — const. (From Ref. 152.)...

The simplest theory of diffusion-assisted ET assumes that the reaction occurs only when donor and acceptor make contact (Collins-Kimball or the gray sphere model) [334-336]. Some experiments were analyzed on the basis of such theory [16, 337]. However, according to the Marcus expression, the ET rate can exhibit a peculiar dependence on the interparticle distance [17, 329, 338] as a result of the interplay between different dependencies of V, E, and AG, as shown in Figure 9.31. While in the normal region conventional exchange-type exponential dependence is at least qualitatively valid, kjyj(r) is generally nonmonotonic and acquires a bell-shaped form with increasing exothermicity. 

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