Marcus cross-reaction equation electron transfer

Manganese(IV) complexes magnetic behavior, 272 Manganese(V) complexes magnetic behavior, 272 Mannich reaction metal complexes, 422 Marcus cross-reaction equation electron transfer, 355 Marcus Hush theory electron transfer, 340 Masking... 

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. 

Rate constants for outer-sphere electron transfer reactions that involve net changes in Gibbs free energy can be calculated using the Marcus cross-relation (Equations 1.24—1.26). It is referred to as a cross-relation because it is derived from expressions for two different self-exchange reactions. 

Equation (29) is also verified with several electron transfer reactions between coordinated metal ions [60,69]. The consideration of the role of the mixing entropy parameter can even explain anomalous "cross-reaction" estimates given by the theory of Marcus [60,70] and shines light on the controversy of the "inverted region" at low AG. 

Table 9.2 Test of the Marcus cross-relation Comparison of observed rate constants for electron-transfer reactions between metal complex ions with values calculated from rate constants observed for the related electron-exchange reactions (Equation (9.41)). Data from R.A. Marcus and N. Sutin, Ref. [13]...

The Marcus theory model is derived for unimolecular electron transfer. It is applied to bimolecular reactions by assuming that the reactants weakly associate in a precursor complex within which ET occurs to give the successor complex. The cross relation analyses above have implicitly adopted this same model, but HAT precursor complexes are quite different then ET ones. This is because proton transfer occurs only over very short distances, so HAT precursor complexes have distinct conformations, rather than the weakly interacting encounter complexes of ET. In this way, HAT resembles proton transfer and inner-sphere electron transfer. Including the equilibria for precursor and successor complex formation expands equation (1.1) into equation (1.20). 

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