Theory of Outer-Sphere Electron Transfer

Chemical and electrochemical reactions in condensed phases are generally quite complex processes only outer-sphere electron-transfer reactions are sufficiently simple that we have reached a fair understanding of them in terms of microscopic concepts. In this chapter we give a simple derivation of a semiclassical theory of outer-sphere electron-transfer reactions, which was first systematically developed by Marcus [1] and Hush [2] in a series of papers. A more advanced treatment will be presented in Chapter 19. 

In the case of stepwise electron-transfer bond-breaking processes, the kinetics of the electron transfer can be analysed according to the Marcus-Hush theory of outer sphere electron transfer. This is a first reason why we will start by recalling the bases and main outcomes of this theory. It will also serve as a starting point for attempting to analyse inner sphere processes. Alkyl and aryl halides will serve as the main experimental examples because they are common reactants in substitution reactions and because, at the same time, a large body of rate data, both electrochemical and chemical, are available. A few additional experimental examples will also be discussed. 

Fig. 1 Comparison of Marcus theory of outer sphere electron transfer (a) with the Saveant theory (b) of concerted dissociative electron transfer. The reaction coordinate is a solvent parameter. The reaction coordinate, r, is the A—B bond length.

According the Marcus theory of outer-sphere electron-transfer (Eq. 4), the slope of a linear correlation between logki and °ox can be derived as given by Eq. 5. 

The Marcus Theory of Outer-Sphere Electron Transfer 703... 

THE MARCUS THEORY OF OUTER-SPHERE ELECTRON TRANSFER AN INTRODUCTION... 

C. Mechanism and theory of outer sphere electron transfer reactions... 

Hush N. S. (1961), Adiabatic theory of outer sphere electron transfer at electrodes , J. Chem. Soc. Faraday Trans. 57, 557-580. 

Outer-sphere electron transfers can be treated in a more general way than inner-sphere processes, where specific chemistry and interactions are important. For this reason, the theory of outer-sphere electron transfer is much more highly developed, and the discussion that follows pertains to these kinds of reactions. However, in practical applications, such as in fuel cells and batteries, the more complicated inner-sphere reactions are important. A theory of these requires consideration of specific adsorption effects, as described in Chapter 13, as well as many of the factors important in heterogeneous catalytic reactions (56). 

For electrodes based on conducting organic charge-transfer salts such as TTF + TCNQ (a complex of the radical cation of tetrathiafulvalene and the radical anion tetracyano-p-quinodimethane) or NMP +TCNQ " (N-methylphenaziniumtetracyano-p-quinodimethane), direct [155, 169] and mediated [154] electron transfer mechanisms have been described. In analogy with the theory of outer-sphere electron transfer [170], Kulys and co-workers [118,171] have developed a mathematical model which permits to evaluate the depth of the active site of some oxidoreductases from the steric requirements of inorganic redox couples (Table 14-4). 

In contrast to cerium, outer-sphere electron transfer appears to be the dominant reaction route for europium redox reactions with both organic species and transition metal complexes. Interpretation of europium redox reactions in terms of the Marcus theory of outer-sphere electron transfer reactions is limited by the enduring controversy over the self-exchange rate for the Eu(II)/Eu(III) couple. Since the selfexchange rate for the Eu(II)/Eu(IlI) couple has so far proven inaccessible to direct... 

In our group, we have developed a theoretical framework that can be applied to both kinds of reactions. It is based on a model Hamiltonian incorporating concepts from theories of outer sphere electron transfer [49-51], Anderson-Newns theory [52, 53], and our own ideas. The model as was developed in the 1990s [54, 55] and at that time, it was applied to various processes such as metal deposition/dissolution, anion adsorption, and outer-sphere electron transfer. However, this was at a time when DFT was not widely available, and several important system parameters had to be estimated, so that the applications had a qualitative character nevertheless, they provided a basic understanding of these processes at the molecular level. 

Electron-transfer reactions have been attracting interest of theoretical chemists for many years. An important contribution to the theory of outer-sphere electron transfer is that of R. A. Marcus. ... 

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