Marcus theory normal region

Figure 2 Energy surfaces corresponding to the normal, barrierless, and inverted electron-transfer reactivity regions of Marcus theory.

There are however essential differences between the Marcus model and the theory of radiationless transitions. In the former, the decrease of the rate constant in the inverted region results from an activation barrier which must be overcome by thermal energy, whereas the rates of radiationless transitions are in principle temperature independent. As implied in [14], there is no normal region in the case of nonradiative transitions, a no bell-shaped curve is expected from the plot of the rate constant against the energy gap. 

The Marcus theory also predicts the Bronsted slope magnitude in the normal Marcus region ... 

In contrast to the experimentally based work discussed above, in the most recent comprehensive theoretical discussion [21d], Bixon and Jortner state that the question of whether non-adiabatic or adiabatic algorithms describe electron-transfer reactions was settled in the 1960s, and that the majority of outer-sphere electron-transfer reactions are non-adiabatic. This is certainly true for the reactions that occur in the Marcus inverted region in which these authors are interested, but we think the question of whether reactions in the normal region are best treated by adiabatic theory that includes an electronic transmission coefficient or by non-adiabatic equations remains to be established. 

The temperature dependence of electron-transfer rate constants is interesting. In the normal region, it shows an activation energy as predicted from simple Marcus theory. In the inverted region, the activation energy is very small or zero. This agrees with the quantum mechanical version of the theory (Kestner et al., 1974 Fischer and Van Duyne, 1977), which makes it clear that the transition from the upper to the lower surface behaves just like ordinary internal conversion. 

An indirect consequence of the considerable interest in Marcus s theory is that, as brilliantly suggested by Marcus himself in 1965, the inverted region is responsible for most chemiluminescent effects. Indeed, as shown in Fig. 36.30, when the Vr and Vp curves intersect with a high activation barrier AG because of the inverted region effect, there may be an electron transfer to a more easily accessible Vp curve. In this case, one of the products is electronically excited and intersects the Vr curve in the normal region with a low activation barrier. 

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. 

The reduction potential of the 3/4 couple, normally undetermined because of the fast following reaction, can be estimated. If the rate constant k, for a series of mediator couples PQ is measured by the HRC (case 1) method, an application of linearized Marcus theory (simple LFER) leads to a plot of the measured rate constant versus the driving force as shown in Figure 3-17. The plot has three regions ... 

Decarboxylation of the acyloxy radical then competes with electron transfer (k f) for formation of ion pairs. The rates of electron transfer for both substituted 1-naphthylmethyl 2 and benzyl substrates 6 follow Marcus theory in both the normal and inverted region when correlated with the oxidation potential of the arylmethyl radical. The meta-methoxy compounds give high yields of ion-derived products because the oxidation potentials of their arylmethyl radicals place them near the maximum on the Marcus plot therefore, kg is competitive with fcco2- This work has been reviewed in the previous volume of this Handbook and in other places." ... 

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