Barrier intrinsic electron transfer

One limitation of the redox catalysis method derives from the fact that when the follow-up is so fast as to thwart back electron transfer, the forward electron transfer becomes the rate-determining step, therefore preventing the derivation of kinetic information on the follow-up reaction. Even under these unfavorable conditions, the redox catalysis approach may still allow determination of the standard potential yB, provided that the intrinsic barrier for electron transfer is not too high. 

Figure 2.29. If the intrinsic barrier for electron transfer is small, the potential range within which the activation control prevails is accordingly narrow and the corresponding asymptote is approximately linear, as represented in the figure, where ks is the standard rate constant (i.e., the rate constant at zero driving force). Under these conditions, redox catalysts that offer a small driving force resulting in counter-diffusion control can be found. This behavior is identified by the value of the slope (F/TIT In 10). The intersection of the counter-diffusion and the diffusion asymptotes provides the value of the standard potential sought, , B.

The pH dependence of cytochrome c oxidation-reduction reactions and the studies of modified cytochrome c thus demonstrate that the coordination environment of the iron and the conformation of the protein are relatively labile and strongly influence the reactivity of the metallo-protein toward oxidation and reduction. The effects seen may originate chiefly from alterations in the thermodynamic barriers to electron transfer, but the conformation changes are expected to affect the intrinsic barriers also. One such conformation change is the opening of the heme crevice referred to above. The anation and Cr(II) reduction studies provide an estimate of 60 sec 1 for this process in Hh(III) at 25°C (59). To date, no evidence has been found for a rapid heme-crevice opening step in ferrocytochrome c. 

Using rate constants derived from reaction of H2A and HA" with [Co(ox)3] and [Fe(phen)3], comparisons of the Marcus-derived one-electron potentials for H2A /H2A and HA /HA" with molecular orbital calculations for the homo energy confirm the greater reactivity of HA" over H2A. It is pointed out that the Marcus-derived potential for HA /HA", 0.85-1.0 V, is greater than the best available measurement for this parameter, 0.68 V. The self-exchange rate for ascorbate radical is lO -lO" M s" and indicates a considerable barrier to electron transfer. The ascorbate radical A also has a high intrinsic barrier to electron transfer, and detection of second-order kinetics in the decomposition of A" suggests a dimerization step with subsequent acid catalysis. 

Further improvements can be achieved by replacing the oxygen with a non-physiological (synthetic) electron acceptor, which is able to shuttle electrons from the flavin redox center of the enzyme to the surface of the working electrode. Glucose oxidase (and other oxidoreductase enzymes) do not directly transfer electrons to conventional electrodes because their redox center is surroimded by a thick protein layer. This insulating shell introduces a spatial separation of the electron donor-acceptor pair, and hence an intrinsic barrier to direct electron transfer, in accordance with the distance dependence of the electron transfer rate (11) ... 

The first attempt to describe the dynamics of dissociative electron transfer started with the derivation from existing thermochemical data of the standard potential for the dissociative electron transfer reaction, rx r.+x-,12 14 with application of the Butler-Volmer law for electrochemical reactions12 and of the Marcus quadratic equation for a series of homogeneous reactions.1314 Application of the Marcus-Hush model to dissociative electron transfers had little basis in electron transfer theory (the same is true for applications to proton transfer or SN2 reactions). Thus, there was no real justification for the application of the Marcus equation and the contribution of bond breaking to the intrinsic barrier was not established. 

As with the Marcus-Hush model of outer-sphere electron transfers, the activation free energy, AG, is a quadratic function of the free energy of the reaction, AG°, as depicted by equation (7), where the intrinsic barrier free energy (equation 8) is the sum of two contributions. One involves the solvent reorganization free energy, 2q, as in the Marcus-Hush model of outer-sphere electron transfer. The other, which represents the contribution of bond breaking, is one-fourth of the bond dissociation energy (BDE). This approach is... 

Each of these free energy relationships employs the intrinsic barrier AGo+ as the disposable parameter. [The intrinsic barrier represents the activation energy for electron transfer when the driving force is zero, i.e., AG = AGo at AG = 0 or the equili-... 

This system illustrates the importance of both the thermodynamic and intrinsic barriers in determining the direction of electron transfer within a given reactant pair. In addition, systems such as the one considered here in which the oxidative and reductive pathways possess comparable rate constants afford an opportunity of controlling or switching the direction of electron transfer by modifying one of the barriers. 

This favorable situation may not be encountered in every case. With radical reductions endowed with high intrinsic barriers, the half-wave potential reflects a combination between radical dimerization and forward electron transfer kinetics, from which the half-wave potential cannot be extracted. One may, however, have recourse to the same strategy as with the direct electrochemical approach (Section 2.6.1), deriving the standard potential from the half-wave potential location and the value of the transfer coefficient (itself obtained from the shape of the polarogram) under the assumption that Marcus-Hush quadratic law is applicable. 

Comparison with the case of a purely repulsive product profile [equation (3.17)] vs. equations (3.3) and (3.4) reveals that the effect of an attractive interaction between the fragments in the product cluster is not merely described by the introduction of a work term in the classical theory of dissociative electron transfer. Such a work term appears under the form of —AG p, but there is also a modification of the intrinsic barrier. With the same Ap, the change in the intrinsic barrier would simply be obtained by replacement of Dr by /Dr — /D )2. It is noteworthy that small values of DP produce rather strong effects of the intrinsic barrier. For example, if DP is 4% of Dr, a decrease of 20% of the intrinsic barrier follows. The fact that a relatively small interaction leads to a substantial decrease of the activation barrier is depicted in Figure 3.4. 

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