Theory of rates of S(N)2 reactions and relation to those of outer sphere bond rupture electron transfers

A model is considered for S(N)2 reactions, based on two interacting states. Relevant bond energies, standard electrode potentials, solvent contributions (nonequilibrium polarization), and steric effects are included. A unified approach is introduced in which there can be a flux density for crossing the transition state, which is either bimodal, one part leading to S(N)2 and the other to ET products, of unimodal with a less marked energy-dependent separation of the rates of formation of these products. in a unified description an expression is given for the reorganization energy, which reduces in the appropriate limits to the pure S(N)2 and ET/bond rupture cases. Expressions are obtained for the S(N)2 rate constant and for its relation to that of the concerted electron transfer/bond rupture reaction. Applications of the theory are made to the cross-relation between rate constants of cross and identity reactions, experimental entropies and energies of activation, the relative rates of S(N)2 and ET reactions, and the possible expediting of an outer sphere ET reaction by an incipient S(N)2-type interaction. Results on the photoelectron emission threshold energies of ions in solution provide some information on a solvation term, and another quantity can be estimated using data from gas phase S(N)2 reactions or from quantum chemistry calculations. Also introduced for comparison is an adiabatic model that is an extension of a bond energy-bond order formulation for gas phase reactions.