A frequency-resolved cavity model (FRCM) for treating equilibrium and non-equilibrium solvation energies: 2: Evaluation of solvent reorganization energies

The frequency-resolved cavity model (FRCM), a generalized continuum reaction field model, which allows for distinct effective solute cavities pertaining to optical (op) and inertial (in) solvent response, has been implemented and applied to the evaluation of solvent reorganization energy (E_s) for a number of intramolecular electron transfer (ET) processes in polar media. Specifically, effective radii are defined for the solute atoms: r_∞=κ·r_vdW (where κ is taken as a universal scale factor) and r_in=r_∞+δ (where δ is specific to a particular solvent). Optimal values of κ and δ are determined through the use of solvation free energy data for small atomic and molecular ions, together with the experimental estimates of solvation reorganization energy (E_s) for intramolecular ET in the steroid-based radical ions studied by Closs, Miller and co-workers [G.L. Closs, L.T. Calcaterra, N.J. Green, K.W. Penfield, J.R. Miller, J. Phys. Chem. 90 (1986) 3673; M.D. Johnson, J.R. Miller, N.S. Green, G.L. Closs, J. Phys. Chem. 93 (1989) 1173; J.R. Miller, B.P. Paulson, R. Bal, G.L. Closs, J. Phys. Chem. 99 (1995) 6923]. With these optimal parameters, E_s is then evaluated for a number of other intramolecular ET processes, yielding results which are in generally good agreement with experimentally based estimates, and which give support for some of the assumptions employed in the analysis of the experimental data. Calculations with conventional solute atom radii (r_∞= r_in, with κ=1.2 and δ=0) fitted to equilibrium solvation data yield E_s values exceeding the FRCM results by factors of ≥2.