Hush equations

In many cases, the values of A n and k2i may be directly or indirectly determined. We shall say no more about this relationship here, other than to indicate that it proves to be generally applicable, and is sufficiently accepted that the Marcus-Hush equation is now used to establish when an outer-sphere pathway is operative. In the context of this chapter, the involvement of the Kn term is interesting for it relates to the relative stabilization of various oxidation states by particular ligand sets. The factors which stabilize or destabilize particular oxidation states continue to play their roles in determining the value of Kn, and hence the rate of the electron transfer reaction. 

Fig. 3 Plot of/ rin Aq vjACjg in CH3CN (/ = 0.1 M)at22 2°C. The theoretical line is that obtained by using the Marcus and Hush equation,...

Fig. 4 Plot of RT In vj aGj3 in CH3CN (n = 0.1 M) at 22 2°C for the quenching of [Ru (bipy)J+] by viologens. The theoretical line is that obtained by using the Marcus-Hush equation having k o) = 8.4 x 10 M" s and X = 17 kcal mol . (From Bock et ai, 1979b)...

From the values of and Ao, 2 Table 2 and by using the Hush equations the reorganization free energy, k, and the free energy change, AG°, corresponding to the electron transfer processes were obtained. The values of these parameters are also included in Table 2. 

The Marcus-Hush equation (which we shall not derive) is given by expression 25.58 and applies to outer-sphere mechanisms. 

Equation 25.59 gives a logarithmic form of equation 25.58 often, / 1 and so log / 0, allowing this term to be neglected in some cases. Thus, equation 25.60 is an approximate form of the Marcus-Hush equation. 

Wul-6 (In contrast to Marcus-Hush which refers to the theory of electron transfer activation, the Mulliken-Hush equation describes the preexponential factor of the rate constant. We spell out Mulliken-Hush each place it occurs in this chapter and use the acronym MH to refer to only Marcus-Hush.) In practice, however, FCWD(O) cannot be extracted from experimental spectra, and one needs a theoretical model to calculate FCWD(O) from experimental band shapes measured at the frequencies of the corresponding electronic transitions. This purpose is achieved by a band shape analysis of optical lines. 

Using the Marcus-Hush equation for ET, and defining the overall rate as the integral over all possible Rn Rm pathways (as defined above), a rate constant for ese of Rd is calculated at infinite ionic strength yielding kff = 1.7 x 10 s , in fortuitous agreement with experimental... 

The nature of the relationship between intervalence electronic bands and electron-transfer processes remains an open question. There appears to be a relationship between Eq and AGJoiv> but the quantitative interpretation in terms of the Hush equation is less than satisfactory, as noted by Hupp and Meyer. " A correlation between the AG for electron transfer and the metal-metal separation has been noted by Haim for the systems (HjNJjCo—U-Fe(CN)j and (HjNJjCo— -Ru(NH3)4(OH2>. For the (HjNJjRu —L—M "(NHj)5 systems, Geselowitz found that qp for = Ru correlates with AG for electron transfer for M = Co. He concluded that such systems have adiabatic electron transfer and the correlation works because is related to AG y when L gives reasonable coupling between metal centers. The suggestion of a complex relationship by Meyer and coworkers" was noted above. 

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