The reduced force constant for the C0(NH3)36 +/2+ couple was used in calculating the inner-sphere reorganization energy for the Co(bpy)33 +/2+ couple.

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 oxidationreduction 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 INTRODUCTION

A theoretical treatment is given for the effect of intramolecular vibrational and diffusive solvent orientational motions on the rate of electron transfer reactions. Four limiting cases are considered for the two-electronic state problem: slow reaction, wide and narrow reaction window, and nondiffusing limits. With the aid of a decoupling approximation, an expression is derived for the reaction rate which reduces to the appropriate expression for each limiting case when the latter is approached. Under certain conditions the time dependence of the survival probability is multiexponential rather than single exponential. Because of this behavior two average survival times are defined and expressions for each are obtained. Experimental data are considered with the present treatment in mind. One feature of the present work is a more general analysis for the case that both vibrational and solvent diffusive motion contribute to the activation process. The relation to previous works in the literature is described.

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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 absencc of electronic coupling between the reactants, a surface for the reactants intersects one for the products. Electronic coupling causes the usual removal of this degcncracy and permits the products to be formed adiabatically or nonadiabatically by an atomic motion across the " intersection " surface.The 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.A relatively simple expression is obtained thereby for the reaction rate, which rcduces 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.