Marcus-Hush formula

The Marcus-Hush formula (11) is an integral of equation (9) assuming spherical ions of radii and 2 separated by distance R, but neglecting image... 

In eqn (12.19), the effects of nonadiabatic transition including the nuclear tunneling are properly taken into account by rj and naturally the main task is to evaluate the thermally averaged transition probability P fl, < ), which has to be evaluated using the Monte Carlo technique for multi-dimensional systems. It is easily shown that the Marcus-Hush formula in adiabatic and nonadiabatic limits can be recovered from eqn (12.19) and eqn (12.20) within the high-temperature approximation. 

The breakdown of the Condon approximation can actually lead to gating phenomena if particular angles are very much favored. It can also lead to situations in which the Marcus-Hush-Jortner formula must be generahzed to deal with the Condon breakdown, and the results can be quantitatively important. DNA seems to be a situation in which Condon breakdown is striking, and this should be kept in mind when comparing adiabatic and nonadiabatic transport mechanisms. 

Zeng Y, Smith RB, Bai P, Bazant MZ (2014) Simple formula for Marcus-Hush-Chidsey kinetics. J Electroanal Chem 735 77-83... 

Expressions (1) and (2) are the basis for the Hush-Marcus model. They allow the construction of potential energy curves of parabolic shapes, when the energy is plotted as a function of a composite reaction coordinate. These curves in turn are the basis for an elementary description of the thermal and optical processes in mixed valences complexes. In principle, it is possible to compute a rate constant from this model, using the total reorganization energy as an activation energy and introducing an electronic transmission factor calculated by the Landau-Zener formula. However this procedure is now supplanted by the quantum models. 

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