Rate control by reorganisation dynamics

We have so far assumed that thermal equilibrium is maintained at every point along the reaction coordinate, that is, that the nnclear flnctuations that take the reactant complex R to the transition-state configuration R in Fig. 4.7 are fast compared with the effective rate k i at which the system moves through the transition-state region. If this is so, will be independent of nuclear dynamics, as is usually the case, both for thermal ET and for PET reactions. However, when the transition-state crossing is very fast, the reorganisation dynamics of the solvent or an internal vibrational mode of the reactant complex can become rate-limiting. 

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 

Solvent dynamics have no influence on the ET rate when g 1, but they start to limit the rate as g approaches 1. Substituting eqs. 4.70and4.71 into the high-temperature limit semiclassical equation for eq. 4.47, and setting g 1 to find the solvent- 

Thus it appears that even very fast ET rates are not significantly restrained by solvent dynamics. This is an important finding as far as photoconversion is concerned since it indicates that ET (and PET) can be very fast even in viscous or rigid media. 

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