Solvent dynamical effects in electron transfer: Predicted consequences of non-Debye relaxation processes and some comparisons with experimental kinetics

The consequences of non-Debye solvent relaxation upon the barrier-crossing dynamics of adiabatic electron-transfer processes have been explored numerically using a rate formulation due to Hynes for several common forms of the dielectric response function Ê(s), with the objective of assessing the likely experimental importance of such effects. For the ‘‘multiple Debye’’ form of Ê(s), analytic expressions for the required time-correlation function can be obtained, whereas for the Davidson–Cole and Cole–Cole forms numerical solutions to the inverse Laplace transform were required. Illustrative numerical results are presented of the increases in the adiabatic barrier-crossing frequency, νn, predicted to be engendered by the presence of higher-frequency relaxation components for dielectric conditions of likely experimental relevance. Substantial (five- to ten fold) rate enhancements are often obtained, resulting from the disproportionately large influence upon νn predicted to arise from the higher-frequency components of Ê(s). Neither νn, nor the non-Debye influence upon νn, are found to be affected greatly by alterations in the shape of the barrier top caused by variations in the electronic coupling matrix element. Comparisons between these numerical predictions and corresponding experimental solvent-dependent νn values extracted from metallocene self-exchange kinetics indicate that the former can account for a substantial fraction of the νn accelerations observed in alcohols and other non-Debye solvents. Roughly concordant non-Debye effects are also predicted from some other, but not all, recent rate formulations. The desirability of utilizing subpicosecond dynamical solvation information from fluorescence Stokes shifts to predict non-Debye effects upon electron-transfer barrier-crossing frequencies is pointed out.