SOLVENT FREE ENERGY CURVES FOR ELECTRON TRANSFER REACTIONS - A NONLINEAR SOLVENT RESPONSE MODEL

摘要

Marcus theory for electron transfer assumes a linear response of the solvent so that both the reactant and product free energy curves are parabolic functions of the solvent polarization, each with the same solvent force constant k characterizing the curvature. Simulation data by other workers indicate that the assumption of parabolic free energy curves is good for the Fe2+-Fe3+ self-exchange reaction but that the k of the reactant and product free energy curves are different for the reaction D-0 + A(0) --> D1- + A(1+). However, the fluctuations sampled in these simulations were not large enough to reach the activation barrier region, which was thus treated either by umbrella sampling or by parabolic extrapolation. Here, we present free energy curves calculated from a simple model of ionic solvation developed in an earlier paper by Hyun, Babu, and Ichiye, which we refer to here as the HBI model. The HBI model describes the nonlinearity of the solvent response due to the orientation of polar solvent molecules. Since it is a continuum model, it may be considered the first-order nonlinear correction to the linear response Born model. Moreover, in the limit of zero charge or infinite radius, the Born model and the Marcus relations are recovered. Here, the full free energy curves are calculated using analytic expressions from the HBI model. The HBI reactant and product curves have different k for D-0 + A(0) --> D1- + A(1+) as in the simulations, but examining the full curves shows they are nonparabolic due to the nonlinear response of the solvent. On the other hand, the HBI curves are close to parabolic for the Fe2+-Fe3+ reaction, also in agreement with simulations, while those for another self-exchange reaction D-0-A(1+) show greater deviations from parabolic behavior than the Fe2+-Fe3+ reaction. This indicates that transitions from neutral to charged species will have the largest deviations. Thus, the second moment of the polarization is shown to be a measure of the deviation from Marcus theory. Finally, since the HBI expressions for the free energy curves are not simple, the ABI curves are compared with various approximate parabolic descriptions of the curves, including Marcus parabolas. (C) 1996 American Institute of Physics. [References: 24]