Time-dependent electron transfer rate between geminate ions with strong Coulomb interaction and distance-dependent reactivity

Previous analytic expressions for the time-dependent rate of diffusion-influenced electron-transfer between geminate ions were obtained for the case when the reaction occurs at a contact separation. By applying a recently developed solution method for the Fredholm integral equation of the second kind, we obtain an accurate analytic expression for the time-dependent electron-transfer rate with the account of the distance-dependent reactivity. We also consider the dependence of the rate on the initial separation between the geminate ions. We check the accuracy of the solution against numerical results obtained by solving the equation for the survival probability. The solution is found to be accurate enough for most reasonable parameter values.