Quantum-chemical evaluation of energy quantities governing electron transfer kinetics: Applications to intramolecular processes

Important energy quantities governing electron transfer (ET) kinetics in polar solutions (reorganization energy, E(r), and net free energy change, Delta U) are evaluated on the basis of quantum-chemical self-consistent reaction-field (SCRF) models. Either self-consistent field (SCF) or configuration interaction (CI) wavefunctions are used for the solute, which occupies a molecular cavity of realistic shape in a dielectric continuum. A classical SCRF model together with unrestricted Hartree-Fock SCF wavefunctions based on the semiempirical PM3 Hamiltonian is applied to the calculation of the solvent portion of E(r) (denoted E(s)) for two different series of radical ion ET systems: radical cations and anions of biphenylyl/naphthyl donor/acceptor (D/A) pairs Linked by cyclohexane-based spacer groups and trans-staggered radical anions of the type (CH2)(2m), m = 2-5. Results for E(s) based on two-configurational CI wavefunctions and an alternative reaction field (the so-called Born-Oppenheimer model, which recognizes the fast timescales of solvent electrons relative to those involved in ET) are also noted. Results for inner-sphere (i.e. intra-solute) reorganization, E(i), and for Delta U are also reported. The semiempirical E(s) results are quite similar to corresponding ab initio results and display the form of the two-sphere Marcus model for E(s) as a function of D/A separation. Nevertheless, in the one case where direct comparison is possible, the calculated E(s) result is more than twice the magnitude of the estimate based on experimental ET kinetic data. To reconcile this situation, a generalized SCRF model is proposed, which assigns different effective solute cavity sizes to the optical and inertial components of the solvent response, using ideas based on non-local solvation models.