Marcus theory inverted region

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

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... 

The theoretical results obtained for outer-sphere electron transfer based on self-exchange reactions provide the essential background for discussing the interplay between theory and experiment in a variety of electron transfer processes. The next topic considered is outer-sphere electron transfer for net reactions where AG O and application of the Marcus cross reaction equation for correlating experimental data. A consideration of reactions for which AG is highly favorable leads to some peculiar features and the concept of electron transfer in the inverted region and, also, excited state decay. 

Comparison of the Marcus Model with the Theory of Radiationless Transitions Is the Marcus Inverted Region Related to the Energy Gap Law .126... 

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. 

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 second article deals with probably the most fascinating predictions of modem electron transfer theories i.e. the Marcus Inverted Region (M.I.R.) . It was shown only one decade ago, nearly 20 years after the first formulation of the Marcus theory, that the M.I.R. does indeed exist First for thermal charge shifts and later for charge recombination. Even a charge separation reaction was recently found to behave according to the Marcus theory. Nevertheless, many reactions do not follow the Marcus model and therefore the second contribution of this issue is mainly concerned with this question. 

The theory for this intermolecular electron transfer reaction can be approached on a microscopic quantum mechanical level, as suggested above, based on a molecular orbital (filled and virtual) approach for both donor (solute) and acceptor (solvent) molecules. If the two sets of molecular orbitals can be in resonance and can physically overlap for a given cluster geometry, then the electron transfer is relatively efficient. In the cases discussed above, a barrier to electron transfer clearly exists, but the overall reaction in certainly exothermic. The barrier must be coupled to a nuclear motion and, thus, Franck-Condon factors for the electron transfer process must be small. This interaction should be modeled by Marcus inverted region electron transfer theory and is well described in the literature (Closs and Miller 1988 Kang et al. 1990 Kim and Hynes 1990a,b Marcus and Sutin 1985 McLendon 1988 Minaga et al. 1991 Sutin 1986). 

Using the Marcus theory, the a value (see -> charge-transfer coefficient) can be predicted, and its dependence on the potential applied. For low - over potentials, and when neither Ox nor Red are specifically adsorbed on the electrode surface, a should be approximately equal to 0.5. Further, the theory describes the relation between homogeneous and heterogeneous rate constants characteristic of the same redox system. An interesting prediction from Marcus theory is the existence of a so-called inverted region for the homogeneous electron transfer reactions, of importance to the phenomenon of... 

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