Sumi-Marcus treatment

It is clear in the present system that ET occurs much faster than the diffusive solvation process. To explain exponential and non-exponential kinetics of ET, the idea of Sumi-Marcus two-dimensional reaction coordinate is used. In this treatment, instead of the usual one dimensional reaction coordinate (solvent coordinate), two coordinates are used, i.e., the solvent coordinate and the vibrational nuclear coordinate. A free energy surface is drawn in a two-dimensional plane spanned by the solvent coordinate, X, and the nuclear coordinate, q. 

In the remaining part of Section II.A we review the formal relationship of C(t) to fundamental quantities in the statistical mechanical description of solvation. The derivation we review is adopted from the work of Van der Zwan and Hynes. A useful result of the derivation is that a physical basis for the solvent coordinate in Figure 1 is established [54], The reader is referred to papers by Bagchi et al. [53], and Sumi and Marcus [54] for related treatments. 

Most polaron models consider only electron transfer steps parallel and antiparallel to the applied field. Van der Auweraer et al. (1994) derived an expression for the mobility that takes into account isotropic hopping in three dimensions. The treatment is based on the Marcus theoiy (Marcus, 1964, 1968, 1984 Kester et al., 1974 Jortner, 1976 Sumi and Marcus, 1986 Jortner and Bixon, 1988) and assumes that energetic and positional disorder can be neglected. 

Forty years after Kramers seminal paper on the effect of solvent dynamics on chemical reaction rates (Kramers, 1940), Zusman (1980) was the first to consider the effect of solvent dynamics on ET reactions, and later treatments have been provided by Friedman and Newton (1982), Calef and Wolynes (1983a, 1983b), Sumi and Marcus (1986), Marcus and Sumi (1986), Onuchic et al. (1986), Rips and Jortner (1987), Jortner and Bixon (1987) and Bixon and Jortner (1993). The response of a solvent to a change in local electric field can be characterised by a relaxation time, r. For a polar solvent, % is the longitudinal or constant charge solvent dielectric relaxation time given by, where is the usual constant field dielectric relaxation time... 

The recent theoretical approaches include a theory of barrierless electronic relaxation which draws on the model of nonradiative excited state decay, and a general treatment of the effect of solvent dielectric relaxation based on the theory of optical line shapes, as well as treatments based on classical and quantum rate theories. Equation(5) does not hold for all solvents and, more generally, may be frequency-dependent. Papers by Hynes, Rips and Jortner, Sumi and Marcus, and Warshel and Hwang " contain good overviews of the theoretical developments. 

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