Does Marcus-Hush theory really work? The solvent dependence of intervalence charge-transfer energetics in (NH₃)₅Ru^II-4,4′-bipyridine-Ru ^III(NH₃)₅⁵⁺ in the limit of infinite dilution

Because of concern about ion-pairing artifacts, the solvent dependence of the intervalence charge-transfer absorption energy for a prototypical mixed-valence system, (NH₃)₅Ru^III-4,4′-bipyridine-Ru ^II(NH₃)₅⁵⁺, has been reexamined in the limit of infinite dilution. New data are reported for 14 solvents. While one of these (hexamethylphosphoramide) yields anomalous energetics, the absorption energies for the remaining 13 solvents agree qualitatively with the predictions of the Marcus-Hush theory (i.e., two-sphere dielectric continuum theory). On a quantitative basis, however, there is substantial disagreement with theory, at least when the charge-transfer distance is equated with the metal-to-metal separation distance (as conventionally done). Replacement of this distance with a much shorter distance inferred from by electronic Stark-effect spectroscopy (Oh et al. J. Am. Chem. Soc. 1990, 112, 8161) leads to a 3-fold decrease in the magnitude of calculated solvent reorganizational contributions to the overall intervalence energy (and therefore, very good agreement with experiment). Unfortunately, the use of such a short charge-transfer distance (d = 5.1 ± 0.7 Å) also leads to a violation of one of the boundary conditions for use of the two-sphere model. Reformulation of the problem in terms of a generalized dipole-inversion, dielectric cavity problem (Brunschwig et al. J. Phys. Chem. 1986, 90, 3657), however, leads to nearly perfect agreement between theory and experiment. Additional analysis shows that experiment now also agrees reasonably well with theory regarding the magnitude of solvent-independent energy contributions. Finally, it is noted that downward revision in the estimated charge-transfer distance (from 11.3 to 5.1 Å) leads to a substantial upward revision in the experimental (i.e., oscillator-strength based) estimate of the electronic coupling element, H_if, for intervalence transfer. Further analysis, based on published data for longer bridges, suggests that charge-transfer distance revisions can also account (at least partially) for the seemingly weak dependence of H_if on distance in decaammineruthenium systems.