Theoretical Study of Landau−Zener Electronic Transmission Factor for Outer-Sphere Electron Transfer Reactions in Solution

Abstract

On the basis of the original Landau−Zener formalism, this paper presents an accurate scheme for determining the theoretical values of the electronic transmission factor in terms of the experimental vibrational spectroscopic and thermodynamic data of the complex ions in solution. The quantity of central importance in this regard is the slope of the potential energy surface, and it is obtained from the accurate Morse function and the modified harmonic oscillator potential function determined from the experimental vibrational spectroscopic data and thermodynamic data. Also, the slopes are obtained using the classical improved average dipole orientation method. The various activation parameters are obtained in terms of a new improved self-exchange activation model. The coupling matrix elements are determined from adiabatic and nonadiabatic activation energies which are obtained from the new activation model and experiments, and are compared with the ab initio values in recent literatures. Theoretical results of electronic transmission factors of electron transfer reactions obtained using the values of slopes from the accurate potential functions (the Morse function and the modified harmonic oscillator potential) as well as the harmonic oscillator potential and the classical ion−dipole capture force field potential are found to be in close agreement with the experimental values of electronic transmission factor obtained from experimental data of the rate constants. These theoretical values of electronic transmission factors, as well as those from experimental data of rate constants, are found to be less than unity. These results indicate that outer-sphere electron transfer reactions in solution involving aquo complexes of the transition metal ions studied in this work are nonadiabatic in nature. The further extension of this theoretical scheme is also discussed.