Exchange reactions and electron transfer reactions including isotopic exchange. Theory of oxidation-reduction reactions involving electron transfer. Part 4.—A statistical-mechanical basis for treating contributions from solvent, ligands, and inert salt

Abstract

The mechanism for electron transfer is discussed in terms of an atomic motion on a potential-energy surface in many-dimensional atomic configuration space. In the absence of electronic coupling between the reactants, a surface for the reactants intersects one for the products. Electronic coupling causes the usual removal of this degeneracy and permits the products to be formed adiabatically or nonadiabatically by an atomic motion across the "intersection" surface. \n \nThe properties of a system on this latter surface are formulated in terms of statistical mechanics, in order to treat in a consistent manner the ligands microscopically and the exterior solvent macroscopically. A concept of "equivalent equilibrium distribution" is introduced to evaluate the surface integral. A macroscopic quantity is invoked only in the last step of the derivation, replacing its statistical-mechanical equivalent. \n \nA relatively simple expression is obtained thereby for the reaction rate, which reduces to that obtained in part 1 when ligand and salt contributions are omitted. Applications can be made to a number of problems, such as prediction of non-isotopic electron-transfer rates from isotopic ones, relation between chemical and electrochemical electron transfers inert salt effects and possibility of an inverted chemical effect.