Electronic coupling decay constants

Fortunately, the partial decoupling of the ET and conformational processes afforded by the absence of synchronous events in principle and in practice allows for the identification of an observed decay rate constant. For example, if one constructs a series of systems in which the ET energetics (or electronic coupling) is modified without change in the conformational equilibrium, thus leaving the conformational rates unchanged, then the observed rate constants will be unchanged if the reaction is controlled by a conformational rate, but will vary if this is not so. 

The electronic coupling of the reactant state with the product state, F, is a function of the overlap of the donor and acceptor orbitals. This in turn depends on energetic, spatial, geometric, and symmetry factors. At relatively large donor acceptor separations, it can be assumed that the relevant orbitals decay exponentially with distance. In these cases, the electron transfer rate constant will depend on this separation as per Eq. 2, where Rda is the donor-acceptor separation and y is a constant that expresses the sensitivity of the... 

The distance decay constant / (see below) in Miller et al. s original study was 0.9 per CH2, using ferricyanide and iron(IH) hexahydrate [44]. In a later study which accounted more thoroughly for double layer effects, 2 was determined to be 1 eV for kinetically facile redox probes such as ferricyanide, 1.3 eV for Ru-hexamine and 2.1 eV for iron(III) hexahydrate. With a better understanding of the redox probe behavior, f was found to be 1.08 + 0.20 per CH2 and independent of the redox couple and electrode potential [96]. Pre-exponential factors were also extracted from the Tafel plots. The edge-to-edge rate constants (extrapolated) are approximately 10 -10 s for all redox probes, which is reasonable for outer-sphere electron transfer. The pre-exponential factors are 5 x lO s [96]. 

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