Marcus—Hush electron transfer theory

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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. 

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. 

The forbidden retro-[ls -I- 2s]-cycloaddition can now be treated using a simple curve-crossing model analagous to the Marcus-Hush theory of electron-transfer [11]. The ground state at the quadricyclane-like geometry is the... 

The energy curves in Figure 22 are closely related to the Marcus-Hush theory for electron transfer. The formalism we employ emphasizes a dipole model for the solute solvent interaction, i.e., an Onsager cavity model. However, a Born charge model based on ion solvation as something in between [135] would be essentially equivalent because we do not attempt to calculate Bop and Bor but rather determine them empirically. 

In the classical Marcus-Hush theory, the initial nuclear geometry of the reactant state undergoes reorganization to the transition state prior to electron transfer [30, 31, 39]. The energy of the transition state, AGe, is gained by intermolecular collisions, in order to satisfy conservation of energy and momentum. The nuclear factor is related to the activation energy, i.e.,... 

An alternative theory to the Butler-Volmer theory for electron transfer is provided by the Marcus-Hush theory (Marcus, 1968 Hush, 1968) which assumes a potential-dependent a. Since in most cases a is essentially independent of potential, use of the simpler Butler-Volmer equation is usually adequate. 

Overall, the outer-sphere electron-transfer reactions of transition metal complexes reactions are consistent with the expectations of the semiclassical Marcus-Hush theory. h22,25,32,43,57,7i,75 78 agreement... 

In the absence of ion pairing and rate limitation by solvent dynamics, the volume of activation for adiabatic outer-sphere electron transfer in couples of the type j (z+i)+/z ju principle, be calculated as in equation 2 from an adaptation of Marcus-Hush theory. In equation 2, the subscripts refer respectively to volume contributions from internal (primarily M-L bond length) and solvent reorganization that are prerequisites for electron transfer, medium (Debye-Huckel) effects, the Coulombic work of bringing the reactants together, and the formation of the precursor complex. 

The most accepted modern activation theory for the outer electron transfer is that of Rudolph A. Marcus (Nobel Prize in Chemistry in 1992) [14], which is different from the transition state theory. His studies on unimolecular reactions and the transition and collision theories committed him to elaborate on the Rice-Ramsperger-Kassel-Marcus (RRKM) theory in 1952. This theory is an extension of the previous RRK theory proposed by Rice, Ramsperger, and Kassel between 1927 and 1928. Moreover, Hush and Marcus further extended the electron transfer theory of Marcus for inner electron transfers [15-17]. 

The resulting theory, named as the Marcus-Hush theory [17], has been the widest and most accepted theory for kinetics overviews since then. However, the theory is based basically on classical kinetics for electron transfer, and the quantum nature of the process is almost shielded by using other related concepts. This is rather strange since, between 1960 and 1970, electron quantum mechanics by Jortner and Kuznetsov [18-20] was well accepted in the specialized literature for non-radiant transitions. 

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