Effects of Fast Solvent Relaxation Processes

In fluid solutions, the resolvation times can be in the subnanosecond time regime. For example, the rapid ( 100 ps) relaxation of the excited-state absorption spectra of ruthenium polypyridyl complexes following metal-to-ligand charge-transfer (MLCT) excitation in aqueous solutions have been ascribed to diffusional resolvation of the MLCT excited state. Finally, Robinson and co-workers have provided evidence that the rate of ionization of the singlet excited state of 6-p-toluidine-2-naphthalenesulfonate is determined by the rate at which neighboring solvent fluctuations can form a 3-4 water molecule cluster capable of solvating the electron. 

There are features of these reactions which have attracted a great deal of attention to the problem of the coupling between outer-sphere electron transfer processes and solvent relaxation processes (a) the electron-transfer potential-energy surface is presumably somewhat cusp-like in the surface-crossing region, and this makes the reactions unusually sensitive to solvent fluctuations (b) the electron transfer step is often very fast and the bulk solvent translational diffusion properties are often not pertinent to the observed frictional effects. 

Much of the work in this area has been stimulated by Kosower s observation of a 1 1 correspondence between the dielectric relaxation rate of the solvent and the rate of formation of a charge transfer (or zwitterionic) state from relaxation of the singlet excited state of an amino-sulfone substituted naphthalene, and this has recently been reviewed/ In this correlation, the dielectric relaxation rate of the solvent around the ion pair is related to the bulk solvent relaxation time ( ) by equation (10), where Ds and D p are the static and optical dielectric 

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. 

The Marcus-Hush formula (11) is an integral of equation (9) assuming spherical ions of radii and 2 separated by distance R, but neglecting image 

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