Electronic transmission coefficient for outer-sphere electron transfer reactions in solution: A Landau–Zener formalism

Abstract

The Landau–Zener formulation and literature values of electronic transition matrix were utilized to compute the theoretical values of electronic transmission coefficient of several outer-sphere electron transfer reactions in solution. The slopes of the energy surfaces that are needed for the Landau–Zener equation were obtained using both intermediate neglect of differential overlaps (INDO/2) molecular orbital and classical improved average dipole orientation (IADO) methods. Theoretical results of electronic transmission coefficient of electron transfer reaction obtained using values of slopes from INDO/2-MO (molecular orbital) as well as IADO methods are found in close agreement with the quasiexperimental values of electronic transmission coefficient obtained from experimental data of rate constant. These theoretical values of electronic transmission coefficient, as well as those from experimental values of rate constant are found to be less than unity. These results indicate that outer-sphere electron transfer reactions in solution involving aquo and amine complexes of the transition metal ions studied in this work are nonadiabatic in nature. Theoretical results of electronic transmission coefficient obtained using values of slopes from the classical improved average dipole orientation (IADO) method is found in close agreement with those obtained from the quantum chemical INDO/2-MO method and also with those from experimental values of rate constant and hence justifies the validity of the use of the former.