Marcus model of electron transfer

Smith BB, Halley JW, Nozik AJ (1996) On the Marcus model of electron transfer at immiscible liquid interface and its application to the semiconductor liquid interface. Chem Phys 205 245-267... 

Summary of the principles of a classical treatment of the Marcus model of electron-transfer reactions of metal complex ions... 

The 1977 review of Martynov et al. [12] discusses existing mechanisms of ESPT, excited-state intramolecular proton transfer (ESIPT) and excited-state double-proton transfer (ESDPT). Various models that have been proposed to account for the kinetics of proton-transfer reactions in general. They include that of association-proton-transfer-dissociation model of Eigen [13], Marcus adaptation of electron-transfer theory [14], and the intersecting state model by Varandas and Formosinho [15,16], Gutman and Nachliel s [17] review in 1990 offers a framework of general conclusions about the mechanism and dynamics of proton-transfer processes. 

The introduction of VB structures (the empirical nature of EVB does not matter here) makes easier the description of the process in terms of diabatic potential surfaces. The latter have been used to describe reactions in vacuo since long time, more than 30 years before the formal definition given by Smith (1969), and continue to represent an important tool for an accurate study of many chemical processes in vacuo (see e.g. the reviews given by Sidis (1992) and by Pacher et al. (1993)), and for qualitative and semiquantitative characterizations of organic reactions (see e.g. Shaik and Hiberty, 1991). Their use in solution has been spurred by Marcus model on electron transfer (ET) reactions (Marcus, 1956), and extended by the Russian school in the sixties to other chemical processes (Levich and Dogonadze, 1959 Levich, 1966 Dogonadze, 1971 German et al., 1971, Albery, 1980). 

Electron transfer reactions at metal electrodes had been studied long before investigations of processes at semiconductor electrodes were started. They were even studied long before Marcus published his model of electron transfer processes. Early in this century, kinetic models on electron transfer processes had already been developed, which are still used for analyzing experimental data obtained with metal electrodes. Since the corresponding descriptions of the electrochemical kinetics and the application of various techniques are also of importance in semiconductor electrochemistry, the essential results obtained with metal electrodes will be briefly presented in the first section. 

Many electron transfer reactions of inorganic radicals conform to the outer-sphere model and hence can be modeled with the Marcus theory of electron transfer.71 This model relies, in part, on the concept of self-exchange reactions, and the inference that self-exchange reactions can be defined for radicals. For many years, it was simply... 

In order to connect the oxidation stability of the model electrolyte complexes to LSV experimental data, one needs to consider the reaction rates for the oxidation reaction of each complex. Indeed, the H-transfer reaction in the solvent-solvent or solvent-anion complexes leads to a significant molecular rearrangement and distortion thus, one expects a significant barrier for these oxidation reactions compared to the oxidation of an isolated EC. Rates for each electron transfer reaction can be estimated in a first approximation using Marcus theory of electron transfer, where the rate (k) of the activation-controlled reaction is proportional to... 

A prominent and widely appUed model of electron transfer in organic molecules is Marcus theory. It is thoroughly introduced in Section 4.3.1.1 and hence we concentrate here on its applicabiUty to triplet energy transfer supported by recently reported experimental studies of the temperature dependence of the triplet diffu-sivity and of the effect of disorder on triplet transfer in organic molecules. We would also like to refer the interested reader to a recent overview on experimental and theoretical work concerning a unified description of triplet energy transfer by Kohler and Bassler [30]. 

The diagram shown in Fig. 3.10 is now widely used to describe electron transfer processes at electrodes, and it has the merit that it can be extended readily to the discussion of electron transfer at semiconductor and insulator electrodes [16]. The theoretical basis for the diagram is to be found in the fluctuating energy level model of electron transfer which has been discussed by Marcus [12,13], Gerischer [17-19], Levich [20], and Dogonadze [21]. 

Computer modeling of electrochemical interfaces has become a well-established branch of interfacial electrochemistry. In recent years the interest shifted from studies of pure water near smooth model walls to increasingly realistic models of the metal phase (e. g., [1-11]), the properties of electrolyte solutions near the interface (e. g., [12-24]), and to free energy studies within the framework of the Marcus theory of electron transfer (e. g., [20, 25-27]), partial charge transfer [28] and ion transfer reactions [29]. 

Fig. 19 Recombination in a DSC according to the Marcus model of charge transfer in an exponential distribution of surface states. Horizontal axis is the voltage or equivalently the electron Fermi level. The position of the conduction band, Eq, is indicated. Plots at different values of reorganization energy as indicated, (a) Electron transfer probability, (b) Electron recombination resistance. Simulation parameters are T = 300 K, Tq = 1,200 K, a = 0.25, / = 0.75, e = 1 eV vs E edox, = 1 x 10 cm s Rqx = 10 cm ...

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