Marcus Theory - The Problem

The Problem

So, in outer sphere redox reactions no bonds are formed nor broken, only an electron transfer (ET) takes place. A quite simple example is the Fe2+/Fe3+ redox reaction, the self exchange reaction which is known to be always occurring in an aqueous solution containing both FeSO₄ and Fe₂(SO₄)₃ (of course, with equal and measurable rates in both directions and with Gibbs free reaction energy G0 = 0).

From the reaction rate's temperature dependence (e.g. the S_N2-substitution reaction of the saponification of an alkyl halide) an activation energy is determined, and this activation energy is interpreted as the energy of the transition state in a reaction diagram. The latter is drawn, according to Arrhenius and Eyring, as an energy diagram with the reaction coordinate as the abscissa. The reaction coordinate describes the minimum energy path from the reactants to the products, and the points of this coordinate are combinations of distances and angles between and in the reactants in the course of the formation and/or cleavage of bonds. The maximum of the energy diagram, the transition state, is characterized by a specific configuration of the atoms. Moreover, in Eyring’s TST a quite specific change of the nuclear coordinates is responsible for crossing the maximum point, a vibration in this direction is consequently treated as a translation.

For outer sphere redox reactions there cannot be such a reaction path, but nevertheless one does observe an activation energy. The rate equation for activation-controlled reactions has the same exponential form as the Eyring equation,

is the Gibbs free energy of the formation of the transition state, the exponential term represents the probability of its formation, A contains the probability of crossing from precursor to successor complex.