A general statistical mechanical approach for modeling redox thermodynamics: the reaction and reorganization free energies

By using rigorous statistical mechanical derivations we obtain a general theoretical model providing the thermodynamics of redox processes, with a focus on the reaction and reorganization free energies and on the relationship between these key thermodynamic quantities. In particular, we define two distinct reorganization free energies, lambda(P) and lambda(R), for the reactants (R) -> products (P) reaction and for the inverse process, respectively. We first derive in principle exact relationships, then gradually introduce different levels of approximation to obtain more and more simplified, though less general, working equations. The results of the calculation of thermodynamic properties for two model systems are then used to compare general and more approximated expressions and critically assess their applicability to the description of redox processes. Finally, we obtain specific relationships that can be used as a diagnostic tool to test the actual reliability of the assumption of Gaussian fluctuations, a priori accepted within Marcus theory, for any redox system under investigation. For both benchmark molecules studied in the present paper, the Gaussian approximation turns out to be inappropriate to describe the redox thermodynamics.