Energetics of charge transfer reactions in solvents of dipolar and higher order multipolar character. II. Results

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Abstract
We apply the theories developed in the preceding paper (paper I) to calculate various energy quantities of charge transfer (CT) reactions in nine solvents that cover a wide range of polarity, and for which interaction site models (ISM’s) may be found in the literature. Besides the two surrogate Hamiltonian theories developed in paper I, the renormalized site-density theory (RST) and the renormalized dielectric theory (RDT), we also investigate a simple harmonic approximation (HXA) for the diabatic free energy profiles, whose characteristic parameters are calculated taking specific advantage of the expression given by the extended reference interaction site method (XRISM) for the free energy of solvation. For each CT process we analyze (a) the solvent reorganization energy λ, (b) the shift of the absorption transition energy due to the solvatochromic effect, and (c) the solvent contribution to the free energy change ΔA. In addition, for a few selected examples, we also report the detailed diabatic free energy profiles. The calculations reported rely on solute–solvent and solvent–solvent pair correlation functions obtained with the XRISM integral equation method applied to nonpolarizable (with fixed mean partial charges) ISM representations of the solute and solvent molecules. To rectify the omission of the solvent electronic degrees of freedom, we correct the dielectric part of the solvent reorganization energy with an additive term designed to compensate for the use of fixed charge ISM models. Contact with theories in which the solvent is represented as a dielectric continuum medium (with or without spatial dispersion) and the solute as a set of charges inside spherical cavities carved out of the dielectric is made straightforwardly within the RDT theory by considering a particularly simple form of the solute–solvent RISM site–site direct correlation functions. Using simple ISM models for several solute species, including Reichardt’s betaine-30 dye and a porphyrin-quinone (PQ) ‘‘dyad’’ recently studied by Mataga and co-workers, we examine the ability of the molecular theories to explain the dependence of charge-transfer energetics on dipolar and nondipolar solvents. We find that the solvatochromic effect on the absorption energy of betaine-30, which forms the basis of the ET(30) empirical solvent polarity scale, is reproduced reasonably well by the RST, RDT, and HXA theories for solvents ranging from carbon tetrachloride to water. In the case of the PQ dyad, we find that the calculated values of λ in dipolar and nondipolar solvents are in good agreement with experimental estimates. Our results indicate that the molecular theories of solvation discussed in this paper can explain the observation that a solvent with vanishing molecular dipole moment, like benzene, can show unmistakable ‘‘polarity,’’ as reflected by its influence on the energetics of CT reactions. We also present calculations that corroborate the suggestion (Sec. VII of paper I) that, compared with the behavior in dipolar solvents, in nondipolar solvents the dependence of λ with the donor–acceptor separation distance is practically negligible.