Theoretical study of electronic transmission coefficient of outer-sphere electron self-exchange reactions in solution: a hydration function scheme

Abstract

On the basis of the thermodynamic characteristics of the hydration process of metal ions, a new theoretical scheme is presented. It is applied to determining the theoretical values of the electronic transmission coefficient of electron self-exchange reactions in solution in terms of the original Landau-Zener formalism. This scheme gets around the shortcomings of the summation method of the inner-sphere and outer-sphere contributions and directly adopts accurate hydration potential functions to determine relevant quantities. The hydration potential functions are analytically determined from the experimental spectroscopic data and the hydration energy data. Two important quantities are the slopes of the potential energy surfaces and the coupling matrix elements. The slopes are obtained from the hydration potential functions and the activation parameters are obtained in terms of a new proposed self-exchange activation model. The coupling matrix elements are determined from adiabatic and diabatic activation energies which are obtained from the new activation model and experiment, and are compared with the ab initio values in recent literature. Theoretical results of the electronic transmission coefficients of electron transfer reactions obtained using the values of slopes from the hydration potential functions are found to be in close agreement with the corresponding experimental values obtained from the experimental rate data. These theoretical values of the electronic transmission coefficient and the experimental values are found to be less than unity. This indicates that outer-sphere electron transfer reactions in solution involving hydrated transition metal ions studied in this work are nonadiabatic in nature. The applicability of this scheme is also discussed.