Approaches to determining reaction adiabaticity

A key element in the aforementioned theoretical treatments is the recognition that electron transfer may take place with significant probability over a range of reactant-electrode separations, r, (Sects. 3.1 and 3.3.2). At least for 

As noted in Sect. 3.1, the pre-exponential factor for outer-sphere reactions is sensitive to the effective electron-tunneling distance , SrK%. If the reaction is non-adiabatic at the plane of closest approach (i.e. if 1), given the functional dependence of fcel upon r one deduces that 5r 0.5 A if P 1.5 A 1 (vide supra), and hence drfCe, 0.5 A. If, however, adiabaticity is maintained for sites beyond the plane of closest approach (i.e. for r j), markedly larger 5nc values can result. 

Experimental estimates of 5r/c , are relatively difficult to obtain. While they can, in principle, be extracted from temperature-dependence studies, this approach is complicated by uncertainties in the entropic term (Sect. 4.3). An alternative method has recently been described for some Cr(III) reductions which involves comparing the work-corrected rate constants, kco , with unimolecular rate constants, ket, for structurally related reactants that reduce via ligand-bridged pathways [30]. Provided that the corresponding outer- and inner-sphere pathways involve the same activation barrier (Sect. 4.6) and the latter also follow adiabatic pathways, we can write [30] 

The resulting estimates of 5r/c i for Cr(III)/Cr(II) aquo couples, ca. 0.1-0.3 A, are close to that extracted from temperature-dependence measurements and indicate that these strongly hydrated species follow marginally non-adiab-atic pathways even at the plane of closest approach [30]. Markedly larger values of 5rK°eU ca. 5 A, were obtained for similar ammine complexes, as from a related comparison involving unimolecular outer-sphere reactivities [21], This is consistent with the smaller hydrated radii of the ammines allowing a closer approach to the metal surface, whereupon a 1 [15a, 30]. 

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