In this paper we present the results of a theoretical study of outer-sphere electron transfer (ET) in a polar solvent, with the modification of the nuclear states by the change in the charge distribution originating solely from the response of the exterior medium. The model Hamiltonian for the system corresponds to two parabolic diabatic potential surfaces with adiabatic coupling between them. The real-time path integral formalism is utilized to derive the general expressions for the influence functional of the medium in the Gaussian approximation and for the ET rate. The ET rate is explicitly evaluated for the particular case of a medium characterized by the Debye dielectric relaxation function. We explore the relation between the dynamics of the reaction coordinate and the character of the ET process, deriving an expression for the ET rate, which bridges between the nonadiabatic and the solvent-controlled adiabatic limits. We establish simple criteria for the validity range of various descriptions of ET dynamics, i.e., the transition state theory, the solvent-controlled ET as well as the adiabatic and nonadiabatic limits. The results are applied to intramolecular ET in alkanols, establishing the adiabatic nature of these processes, whose dynamics is dominated by the (slow) longitudinal dielectric relaxation rate of the solvent.with € "" and €s being the optical and the static dielectric 2090

The quantum-mechanical version of the Kramers turnover problem is considered. The multidimensional character of the problem is taken into account via transformation to normal modes. This eliminates the coupling to the bath near the barrier top allowing the use of a simple harmonic transmission coefficient for the barrier dynamics. The well dynamics is described by a continuum form of a master equation for the energy in the unstable normal mode. Within first-order perturbation theory, the equations of motion for the stable normal modes have the form of a forced oscillator. The transition probability kernel is found using the known solution for the quantum forced oscillator problem. An expression for the quantum escape rate is derived. It encompasses all previously known limiting results in the thermally activated tunneling regime. The depopulation factor, which accounts for the nonequilibrium energy distribution is evaluated. The quantum transition probability kernel is broader than the classical and is skewed towards lower energies. Interplay between these two effects, together with a positive tunneling contribution, determines the relative magnitude of the quantum rate compared to the classical one. The theory is valid for arbitrary dissipation. Its use is illustrated for the case of a cubic potential with Ohmic (Markovian) dissipation.

In this paper we apply the stochastic Liouville equation for the study of outer sphere electron transfer (ET) in a polar solvent, which is characterized by a Debye dielectric relaxation. Explicit expressions, which bridge between the nonadiabatic and solvent-controlled adiabatic limits, are derived for the ET rates spanning a broad range of the energetic parameters, which include normal ET, activationless ET, and ET in the inverted region. The many-body result for the ET rate, which is accurate for symmetric ET, constitutes a useful approximate interpolation formula, which accounts well for the ET dynamics over a broad range of the energetic parameters.

Dynamics of solvation in simple polar liquids is studied within the framework of the mean spherical approximation. Exact results are derived for the Born solvation energy and for the correlation function for the solvation time of an instantaneously formed ion (or dipole) in a polar solvent. The results are in qualitative agreement with the recent approximate treatment by P. Wolynes [J. Chem. Phys. 86, 5133 (1987)]. Implications of the results for the solvation dynamics of dipoles and of excess electrons in polar solvents are considered.

Ion and dipole solvation kinetics is studied within the framework of the mean-spherical approximation (MSA). The solvation dynamics in nonassociated polar solvents involves a hierarchy of relaxation times in accordance with Onsager's "inverted snowball" picture. The average solvation time is determined by the relative solvent and solute sizes and by the dynamic screening. The dipole solvation is slower than ion solvation due to the shorter spatial range of interaction. The theoretical results are confronted with experimental data on timeresolved fluorescence shifts of dipolar probe molecules in nonassociated polar solvents. The experimental kinetic data exhibit a crossover from a short-time dipole solvation behavior to ion solvation at intermediate and long times. For associated polar solvents the Onsager picture has to be modified to account for structure breaking in the first solvation shell(s).