A Thermodynamic Derivation of the Cross-Relations for Rates of Electron-Transfer Reactions

A derivation of the cross-relations first given by Marcus, which predict the rate of electron-transfer reactions from the rates of electron-exchange reactions and the standard free energy change, is given. The derivation is based solely on thermodynamic cycles and the principle of detailed balance; the usual microscopic or mechanistic assumptions are not necessary, but we do assume independent activation of the reaction partners. Thus cross-relations should hold even in many cases for which other predictions of any given electron-transfer theory may fail. Comments are made on the possible causes for breakdown of the cross-relations; in particular, a correction factor akin to the one introduced by Marcus becomes apposite when the overall exoergicity is large, and under these conditions independent activation is no longer a valid assumption.