Marcus theory of outer-sphere electron transfer

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... 

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... 

Marcus 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. 

A quasi-linear correlation of log/c or AG with the ionization potentials of the electron donors as observed in the FeL3 - + reactions is predicted by Marcus theory for outer-sphere electron transfers. Accordingly, the free-energy dependence of AG can be satisfactorily simulated with the Marcus equation (Eq. 90), taking a (constant) value of A = 41 kcal mol as reorganization energy for all tetraalkyltin compounds (see Figure 19A) [32]. 

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. ... 

Marcus theory is based on certain assumptions that will be discussed later. The main goal of computer simulations of electron transfer is to check some of these assumptions and to provide additional microscopic insight into the mechanism of electron transfer and the microscopic factors that influence the rate of transfer. We discuss these issues in the following section for the simple case of outer-sphere electron transfer reactions. 

In contrast to the experimentally based work discussed above, in the most recent comprehensive theoretical discussion [21d], Bixon and Jortner state that the question of whether non-adiabatic or adiabatic algorithms describe electron-transfer reactions was settled in the 1960s, and that the majority of outer-sphere electron-transfer reactions are non-adiabatic. This is certainly true for the reactions that occur in the Marcus inverted region in which these authors are interested, but we think the question of whether reactions in the normal region are best treated by adiabatic theory that includes an electronic transmission coefficient or by non-adiabatic equations remains to be established. 

According to Marcus theory [7, 8], the activation free energy (AG ) of outer-sphere electron transfers depends on the free energy (AGet) and the reorganization energy (A) as follows (Eq. 90). 

Because outer-sphere reactions are mechanistically simple (no bond making and breaking occurs), they are amenable to theoretical treatment. Marcus theory, which allows the prediction of outer-sphere electron transfer rates between two species, was developed in the 1960s by Rudolph Marcus, who won the Nobel prize for his work in 1992. His simple equation is given below ... 

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