The Marcus Theory of Charge Transfer

Po is a prefactor mobility (zero held, inhnite temperature), C is an empirical constant of 2.9 X 10 (cm/V), a and S express the energetic (diagonal) and positional disorder (off-diagonal), respectively. Other approaches also exist, one of them being based on the Marcus theory of charge transfer [247, 248]. 

In this chapter, we have exposed the Marcus theory of charge transfer reaction in solution and rephrased it in a now standard, modern statistical mechanics language in terms of the microscopic energy gap variable. The key assumption in Marcus developments is to assume that this collective variable obeys an exact Gaussian statistics. This was shown to be equivalent to a linear response approximation. 

Transfer of the electron takes place without movement of the nuclei. The total energy of the system is increased (because the species formed in Eq. (5.38) is not in its most stable state). The energy released when the product of charge transfer decays to its equilibrium state is referred to as the solvent reorganization energy, X, which is of central importance in the Marcus theory of charge transfer. 

The extent to which steric effects adversely affect the attainment of such intimate ion-pair structures would be reflected in an increase in the work term and concomitant diminution of the inner-sphere rate. This qualitative conclusion accords with the reactivity trend in Figure 16. However, Marcus theory does not provide a quantitative basis for evaluating the variation in the work term of such ion pairs. To obtain the latter we now turn to the Mulliken theory of charge transfer in which the energetics of ion-pair formation evolve directly, and provide quantitative informa-... 

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]. 

Turning to the Marcus theory of electron transfer (Marcus and Sutin (1985)) for guidance in efforts to improve the 4% overall yield of charge separated species, we note that in other studies of dyad systems in solvents such as methylene chloride the total reoiganization energy, X, is around... 

One of the most important new areas of theory of charge transfer reactions is direct molecular simulations, which allows for an unprecedented, molecular level view of solvent motion during reactions in this class. One of the important themes for research of this type is to ascertain the validity at a molecular level of the linear response theory estimates of solvent interactions that are inherent in Marcus theory and related approaches. In addition, the importance of dynamic solvent effects on charge transfer kinetics is being examined. Recent papers on this subject have been published by Warshel [71], Hynes [141] and Bader and Chandler [137, 138],... 

Based on careful work on Fe(III)(C204)3 reduction, Sluyters considers that the potential dependence of a, observed with certain electrode processes, really arises from kinetic complications and that the transfer coefficient for the elementary step of charge transfer is constant at —0.5. However, the work of Hupp and Weaver on the Cr(OH2)6 system demonstrated a relation between the temperature and potential dependence of the rates, and showed that at overpotentials of ca. 0.7 — 0.9 V the potential dependence of rate arises extensively from the entropic factor (p. 133). It was also shown that the Marcus theory was able to predict a potential dependence of A5" " comparable to or > that of A// when the system has a large entropic asymmetry, i.e., a large net reaction entropy change. 

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