Does Marcus-Hush theory really work? The solvent dependence of intervalence charge-transfer energetics in pentaamineruthenium(II)-4,4'-bipyridine)-pentaamineruthenium(III)]5+ in the limit of infinite dilution

Abstract

Because of concern about ion-pairing artifacts, the solvent dependence of the intervalence charge-transfer absorption energy for a prototypical mixed-valence system, (NH~)sR~"~-4,4'-bipyridine-Ru~~(NH~)s~+, 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 (Le., 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 f 0.7 A) 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 alsoagrees reasonably well with theory regarding the magnitudeof solvent-independent energy contributions. Finally, it is noted that downward revision in the estimated charge-transfer distance (from 11.3 to 5.1 A) leads to a substantial upward revision in the experimental (Le., oscillator-strength based) estimate of the electronic coupling element, Hir, 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 Hir on distance in decaammineruthenium systems.

Activation entropy of electron transfer reactions

“…The dominance of longitudinal polarization fluctuations in solvation thermodynamics is also responsible for experimentally observed linear trends of the reorganization energy with the Pekar factor [50,124,125] [Eq. (48)].…”

Probing the Transition between the Localised (Class II) and Localised‐to‐Delocalised (Class II–III) Regimes by Using Intervalence Charge‐Transfer Solvatochromism in a Series of Mixed‐Valence Dinuclear Ruthenium Complexes

“…This effect should be manifested by a decrease in the slope of the n max and M 1 solvatochromism plots due to the inverse dependence of 5 + . [65] Secondly, the influence of appreciable electronic delocalisation may be considered through the introduction of "effective amount of charge transfer", (1À2b 2 )e, rather than e. The slope of the solvatochromism plot is given by e 2 A C H T U N G T R E N N U N G (1/aÀ1/d) according to Equation (3); however, this equation is frequently expressed in terms of the effective amount of charge transferred, and the slope is given instead as (De) 2 …”

Synthesis and Photophysics of a Neutral Organic Mixed‐Valence Compound

“…[10] Unfortunately, this method is complicated for charged species because of ion migration in the electric field, which can be circumvented by using glass matrices. [11][12][13] Further disadvantages of charged MV compounds are the low solubility especially in nonpolar solvents [14][15][16] and ion-pair effects. [17,18] These disadvantages can be avoided by using neutral MV compounds, a class of compounds that has not been described and studied so far to the best of our knowledge, [19] which is therefore the subject of this communication.…”