Electron exchange Marcus theory

This section contains a brief review of the molecular version of Marcus theory, as developed by Warshel [81]. The free energy surface for an electron transfer reaction is shown schematically in Eigure 1, where R represents the reactants and A, P represents the products D and A , and the reaction coordinate X is the degree of polarization of the solvent. The subscript o for R and P denotes the equilibrium values of R and P, while P is the Eranck-Condon state on the P-surface. The activation free energy, AG, can be calculated from Marcus theory by Eq. (4). This relation is based on the assumption that the free energy is a parabolic function of the polarization coordinate. Eor self-exchange transfer reactions, we need only X to calculate AG, because AG° = 0. Moreover, we can write... 

Azo-bridged ferrocene oligomers also show a marked dependence on the redox potentials and IT-band characteristics of the solvent, as is usual for class II mixed valence complexes 21,22). As for the conjugated ferrocene dimers, 2 and 241 the effects of solvents on the electron-exchange rates were analyzed on the basis of the Marcus-Hush theory, in which the t/max of the IT band depends on (l/Dop — 1 /Ds), where Dop and Ds are the solvent s optical and static dielectric constants, respectively (155-157). However, a detailed analysis of the solvent effect on z/max of the IT band of the azo-bridged ferrocene oligomers, 252,64+, and 642+, indicates that the i/max shift is dependent not only on the parameters in the Marcus-Hush theory but also on the nature of the solvent as donor or acceptor (92). 

Figure 1.13 Potential energy diagrams describing electron transfer processes according to Marcus theory. (A) Self-exchange (B) Cross Reaction.

The theory of homogeneous electron transfer processes, as well as of the closely-related electron exchanges with metallic electrodes, has been the subject of considerable study. The proposal by Hush and by Marcus that these processes are, for simple systems, either usually electronically adiabatic or... 

Eberson introduced the concept of a dissociative ET to peroxides some time ago. There have been attempts to apply Marcus Theory to the ET reduction of diaroyl peroxides in connection with the mechanism of the chemically initiated electron exchange luminescence (CIEEL)." " The... 

The qualitative elements of Marcus theory are readily demonstrated. For example, the process of transferring an electron between two metal ions, Fe2+ and Fe3 +, may be described schematically by Fig. 33 (Eberson, 1982 Albery and Kreevoy, 1978). The reaction may be separated into three discrete stages. In the first stage the solvation shell of both ions distorts so that the energy of the reacting species before electron transfer will be identical to that after electron transfer. For the self-exchange process this of course means that the solvation shell about Fe2+ and Fe3+ in the transition state must be the same if electron transfer is not to affect the energy of the system. In the second phase, at the transition state, the electron is transferred without... 

The qualitative operation of Marcus theory can be illustrated most easily by considering how it might estimate the rate constant for electron transfer between two metal complexes M and N. If we assume M and N to be structureless spheres, the first step leading to electron exchange involves diffusion of the two reagents toward each other, either aided or impeded by electro-... 

Electron transfer may also dominate the excited state chemistry of open shell radical ions. The fluorescence of the radical anions of anthraquinone and 9,10-dicyanoanthracene and the radical cation of thianthrene are quenched by electron acceptors and donors, respectively, although detailed kinetic analysis of the electron exchange do not correspond exactly either with Weller or Marcus theory (258). The use of excited radical cations as effective electron acceptors represents a... 

The self-exchange electron-transfer (SEET) process, in which a radical is trapped by the parent molecule, has been studied using the intersecting-state model (ISM).91 Absolute rate constants of SEET for a number organic molecules from ISM show a significant improvement over classical Marcus theory92-94 in the ability to predict experimental SEET values. A combination of Marcus theory and the Rips and Jortner approach was applied to the estimation of the amount of charge transferred in the intramolecular ET reactions of isodisubstituted aromatic compounds.95... 

The Marcus theory provides an appropriate formalism for calculating the rate constant of an outer-sphere redox reaction from a set of non-kinetic parameters[347 350]. The simplest possible process is a self-exchange reaction, where AG = 0. In an outer-sphere electron self-exchange reaction the electron is transferred within the precursor complex (Eq. 11.5). 

Thus the Marcus theory gives rise to a free energy relationship of a type similar to those commonly used in physical organic chemistry. It can be transformed into other relationships (see below) which can easily be subjected to experimental tests. Foremost among these are the remarkably simple relationships that were developed (Marcus, 1963) for what have been denoted cross reactions. All non-bonded electron-transfer processes between two different species can actually be formulated as cross reactions of two self-exchange reactions. Thus the cross reaction of (59) and (60) is (61), and, neglecting a small electrostatic effect, the relationship between kn, k22 and kl2... 

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