The semi-classical Marcus equation derives from quantum-mechanical treatments of the Marcus model, which consider in wave-mechanical terms the overlap of electronic wave-functions in the donor-acceptor system, and the effects of this overlap on electronic and nuclear motions (see Section 9.1.2.8 above). Such treatments are essential for a satisfactory theory of D-A systems in which the interaction between the reactant and product free-energy profiles is relatively weak, such as non-adiabatic reactions. A full quantum-mechanical treatment, unfortunately, is cumbrous and (since the wave-functions are not accurately known) difficult to relate to experimental measurements but one can usefully test equations based on simplified versions. In a well-known treatment of this type, leading to the semi-classical Marcus equation introduced in Section 9.1.2.8, the vibrational motions of the atomic nuclei in the reactant molecule (as well as the motions of the transferring electron) are treated wave-mechanically, while the solvent vibrations (usually of low frequency) are treated classically. The resulting equation, already quoted (Equation (9.25)), is identical in form with the classical equation (9.16) (Section 9.1.2.5), except that the factor [Pg.299]

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