Hydration model for the energy barrier in self-exchange electron transfer reactions in solution

This paper presents two new theoretical models for accurately determining activation energy and reorganization energy for an electron exchange reaction in solution. The hydration process of an ion is considered and two accurate potential functions (Morse function and anharmonic oscillator potential function) are defined in terms of experimental spectroscopic and hydration thermodynamic data. These functions are then used to depict the energy dependence of the reacting system on the separation between the central ion and the inner-sphere water molecules and the solvent reorganization. The activation energy and reorganization energy are obtained in terms of the proposed activation and reorganization models and the hydration potential functions. The experimental activation energy is corrected by taking into account the actual electronic transmission coefficient. The slopes of the potential energy surfaces are obtained from the proposed accurate hydration potential functions, and the coupling matrix element is determined by the two-state model and numerical integral method over the perturbed d-electron double-zeta Slater-type wave functions. The theoretical values of the activation energy are compared with the experimental values, and the relationship between the activation energy and the reorganization energy is tested. The applicability of these models are also discussed.