Reorganization energies of electron hetero-exchange reactions of hydrated redox pairs in solution from a hydration function model

Abstract

A new hetero-exchange reorganization model and a hydration function model and its application in determining the reorganization energy are first presented in this paper. According to the feature of the hydration process of an ion, two accurate potential functions (Morse function and anharmonic oscillator potential function) are determined in terms of the experimental spectroscopic and hydration thermodynamic data and then used to depict the energy dependence of the reacting system on the separation between the central ion and the surrounding water molecules and on the solvent reorganization. The reorganization energies are obtained in terms of the newly proposed hetero-exchange reorganization model and the hydration potential functions for the hydrated transition metal redox ion pairs in solution. The experimental activation energies in the Marcus approximate scheme are corrected by taking into account the actual electronic transmission coefficient, which is generally taken as unity in the traditional evaluation of the experimental activation energy, the slopes of the potential energy surfaces are obtained from the proposed accurate hydration potential functions, and the coupling matrix element is determined from the energy difference between the activation energy and the energy of the reacting system at the crossing point. The theoretical values of the activation energy are compared with those from the Marcus approximate scheme and the other classical methods. The availability of these models is discussed.