On the Theory of Oxidation-Reduction Reactions Involving Electron Transfer. I

TLDR

The authors describe an electron‑transfer mechanism in which the reacting molecules’ orbitals overlap minimally in the activated complex. They aim to develop a quantitative theory for the rates of oxidation‑reduction reactions in solution based on this slight‑overlap mechanism. By treating the solvent polarization of an intermediate state X* as non‑equilibrium, the authors compute its free energy using a previously derived electrostatic equation, identify the most probable X* via variational minimization, and show that X* can either revert to reactants or jump to a product‑like state X. The resulting expression for the electrostatic free‑energy contribution ΔF* leads to an overall rate of k = κ exp(−ΔF*/kT) when the jump dominates, and quantitative comparisons with experimental data agree well without adjustable parameters.

Abstract

A mechanism for electron transfer reactions is described, in which there is very little spatial overlap of the electronic orbitals of the two reacting molecules in the activated complex. Assuming such a mechanism, a quantitative theory of the rates of oxidation-reduction reactions involving electron transfer in solution is presented. The assumption of ``slight-overlap'' is shown to lead to a reaction path which involves an intermediate state X* in which the electrical polarization of the solvent does not have the usual value appropriate for the given ionic charges (i.e., it does not have an equilibrium value). Using an equation developed elsewhere for the electrostatic free energy of nonequilibrium states, the free energy of all possible intermediate states is calculated. The characteristics of the most probable state are then determined with the aid of the calculus of variations by minimizing its free energy subject to certain restraints. A simple expression for the electrostatic contribution to the free energy of formation of the intermediate state from the reactants, ΔF*, is thereby obtained in terms of known quantities, such as ionic radii, charges, and the standard free energy of reaction. This intermediate state X* can either disappear to reform the reactants, or by an electronic jump mechanism to form a state X in which the ions are characteristic of the products. When the latter process is more probable than the former, the over-all reaction rate is shown to be simply the rate of formation of the intermediate state, namely the collision number in solution multiplied by exp(—ΔF*/kT). Evidence in favor of this is cited. In a detailed quantitative comparison, given elsewhere, with the kinetic data, no arbitrary parameters are needed to obtain reasonable agreement of calculated and experimental results.