Marcus treatment of endergonic reactions: a commentary

Two forms of the equation for expression of the rate constant for electron transfer through a Marcus-type treatment are discussed. In the first (exergonic) form, the Arrhenius exponential term was replaced by its classical Marcus term; in the second (endergonic) form, the forward rate constant was replaced by the reverse rate constant (the forward rate constant in the exergonic direction), which was expanded to an equivalent Marcus term and multiplied by the equilibrium constant. When the classical Marcus treatment was used, these two forms of the rate equation give identical curves relating the logarithm of the rate constant to the driving force. The Marcus term for the relation between activation free-energy, DeltaG#, reorganization energy, lambda, and driving force, DeltaG(o), derived from parabolas for the reactant and product states, was identical when starting from exergonic or endergonic parabolas. Moser and colleagues introduced a quantum mechanical correction factor to the Marcus term in order to fit experimental data. When the same correction factor was applied in the treatment for the endergonic direction by Page and colleagues, a different curve was obtained from that found with the exergonic form. We show that the difference resulted from an algebraic error in development of the endergonic equation.