《涉及電子轉移的氧化還原反應理論》

A large class of reactions in solution does nothing but pass an electron between two species — the exchange Fe²⁺ + Fe³⁺ → Fe³⁺ + Fe²⁺ is the type case — with no bonds made or broken. Transition-state theory, built for reactions that rearrange atoms along a single coordinate, gave no handle on them: why is one such electron exchange fast and another slow, when chemically nothing seems to happen?

Because the electronic coupling is weak, the electron cannot simply hop whenever the partners collide: the solvent, polarized around the old charge distribution, would be left out of equilibrium with the new one, and energy would not be conserved (the Franck–Condon principle, applied to the nuclei). Marcus required instead that thermal fluctuations of the solvent polarization — and of the reactants' own bond lengths — first carry the system to a nuclear configuration in which the reactant and product electronic states have equal energy. Only there can the electron move at constant energy; the solvent then relaxes about the new charges.

Treating the solvent as a dielectric continuum, Marcus showed that the free energy of the reactant state and of the product state are each, to a good approximation, a parabola in a collective reaction coordinate measuring the nonequilibrium polarization. The reaction proceeds through their intersection. The height of that intersection — the activation free energy — is fixed by just two quantities: the driving force ΔG° and the reorganization energy λ, the energy it would take to distort the reactants' nuclei and surrounding solvent into the products' equilibrium arrangement without moving the electron.

The result is compact — ΔG‡ = (λ + ΔG°)² / 4λ — and for the solvent contribution Marcus gave λ as a continuum expression in the reactant radii, their separation, and the optical and static dielectric constants of the medium.

The formula carries a startling consequence. As the reaction is made more favourable (−ΔG° rising from zero) the barrier falls — until, at −ΔG° = λ, it vanishes and the rate is greatest. Push further and the barrier returns: the rate now decreases as the driving force grows. This 'inverted region' was thought so implausible that it was doubted for some twenty-five years, until rigid donor–acceptor molecules confirmed it in 1984.

This was the first of a celebrated series running through the 1950s and 1960s, in which Marcus added the cross-relation linking a reaction's rate to its self-exchange rates. N. S. Hush reached closely related results; Levich and Dogonadze recast the theory quantum-mechanically; the experimental foundation came from Taube, Sutin, and others. The work brought Marcus the 1992 Nobel Prize in Chemistry.