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

Marcus theory for electron transfer assumes a linear response of the s olvent so that both the reactant and product free energy curves are pa rabolic functions of the solvent polarization, each with the same solv ent force constant k characterizing the curvature. Simulation data by other workers indicate that the assumption of parabolic free energy cu rves is good for the Fe2+-Fe3+ self-exchange reaction but that the k o f the reactant and product free energy curves are different for the re action D-0 + A(0) --> D1- + A(1+). However, the fluctuations sampled i n these simulations were not large enough to reach the activation barr ier region, which was thus treated either by umbrella sampling or by p arabolic 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. Th e HBI model describes the nonlinearity of the solvent response due to the orientation of polar solvent molecules. Since it is a continuum mo del, it may be considered the first-order nonlinear correction to the linear response Born model. Moreover, in the limit of zero charge or i nfinite radius, the Born model and the Marcus relations are recovered. Here, the full free energy curves are calculated using analytic expre ssions from the HBI model. The HBI reactant and product curves have di fferent k for D-0 + A(0) --> D1- + A(1+) as in the simulations, but ex amining the full curves shows they are nonparabolic due to the nonline ar response of the solvent. On the other hand, the HBI curves are clos e to parabolic for the Fe2+-Fe3+ reaction, also in agreement with simu lations, while those for another self-exchange reaction D-0-A(1+) show greater deviations from parabolic behavior than the Fe2+-Fe3+ reactio n. This indicates that transitions from neutral to charged species wil l have the largest deviations. Thus, the second moment of the polariza tion is shown to be a measure of the deviation from Marcus theory. Fin ally, since the HBI expressions for the free energy curves are not sim ple, the ABI curves are compared with various approximate parabolic de scriptions of the curves, including Marcus parabolas. (C) 1996 America n Institute of Physics.