Inverted region reaction rates

One striking prediction of the energy gap law and eq. 11 and 14 is that in the inverted region, the electron transfer rate constant (kjjj. = ket) should decrease as the reaction becomes more favorable (lnknr -AE). Some evidence has been obtained for a fall-off in rate constants with increasing -AE (or -AG) for intermolecular reactions (21). Perhaps most notable is the pulse radiolysis data of Beitz and Miller (22). Nonetheless, the applicability of the energy gap law to intermolecular electron transfer in a detailed way has yet to be proven. 

The best way to search for the existence of an inverted region (if any) would be to use a single electrochemical electron transfer reaction in one solvent medium at a particular electrode and determine the effect of high overpotential on the reaction rate or the current density. Many experiments were carried out at organic spacer-covered ( 2.0 nm thick) electrodes to search for the inverted region for the outer-sphere ET reactions however, no inverted region was observed." ... 

Table 1 summarizes the behavior, in the form of activation enthalpies (AH ), for each of 18 reactions. The values listed are somewhat larger than published values [36], reflecting corrections for unrecognized thermal control errors in the original investigation. As expected from classical Marcus theory, decreases in rate are accompanied by increases in AH. Curiously, however, as the reaction is pushed progressively further into the inverted region, AH increases by... 

Tests of the inverted region for bimolecular electron transfer have proven to be more elusive. As mentioned above, a major difficulty is that, for many bimolecular reactions, vetKA > kD and a large portion of the free energy region of experimental interest is lost because the rate constants... 

This quadratic dependence of the activation energy on the reaction free energy leads to the prediction of an inverted region in which the reaction rate constant (which depends on AG ) falls when the overall reaction free energy becomes more favourable. This is readily seen from the simple picture shown in Figure 4.14. When the intersection point of the wells leads to A G = 0 the reaction becomes free of an activation barrier, but as the products well sinks deeper the point of intersection rises again. 

A consequence of Eq. (18) is that the maximum electron transfer rate occurs when AG° = —X. A plot of ln(ket) versus AG° is shown in Fig. 4. Electron transfer reactions with AG° more positive than —X define the normal region, where the rate of electron transfer increases with increasing exergonicity, whereas free energies negative relative to —X define the inverted region in which the rate decreases as AG° becomes more negative. For most ECL reactions, the... 

The Marcus Inverted Region (MIR) is that part of the function of rate constant versus free energy where a chemical reaction becomes slower as it becomes more exothermic. It has been observed in many thermal electron transfer processes such as neutralization of ion pairs, but not for photoinduced charge separation between neutral molecules. The reasons for this discrepancy have been the object of much controversy in recent years, and the present article gives a critical summary of the theoretical basis of the MIR as well as of the explanations proposed for its absence in photoinduced electron transfer. The role of the solvent receives special attention, notably in view of the possible effects of dielectric saturation in the field of ions. The relationship between the MIR and the theories of radiationless transitions is a topic of current development, although in the Marcus-Hush Model electron transfer is treated as a thermally activated process. 

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