Single outer-sphere electron transfer

For simple outer-sphere electron transfer reactions, the effective frequency co is determined by the properties of the slow polarization of the medium. For a liquid like water, where the temporal relaxation of the slow polarization as a response to the external field is single exponential, tfie effective frequency is equal to... 

The most important single development in the understanding of the mechanisms of redox reactions has probably been the recognition and establishment of outer-sphere and inner-sphere processes. Outer-sphere electron transfer involves intact (although not completely undisturbed) coordination shells of the reactants. In inner-sphere redox reactions, there are marked changes in the coordination spheres of the reactants in the formation of the activated complex. 

The solution of the riddle posed by Kornblum s dark Sj l reaction is as follows. The nucleophile does work as a single electron-transfer initiator of the chain process. However, the mechanism of initiation does not consist of a mere outer-sphere electron transfer from the nucleophile to form the anion-radical of the substrate. Rather, it involves a dissociative process in which electron transfer and bond breaking are concerted (Costentin and Saveant 2000). Scheme b at the beginning of Section 7.8 illustrates the concerted mechanism. 

Because the potential of the one-electron reduction of CO2 is — 1.9V (vs. NHE), neither the MLCT excited state nor the OER species of rhenium complexes can reduce CO2 with a single electron through outer-sphere electron transfer. As shown in Eq. (19), however, the potential for obtaining CO by two-electron reduction of CO2 shifts positively to —0.53 V (vs. NHE these potentials of CO2 reduction are close to the values in CH3CN vs. SCE (80)). Such two-electron reduction of CO2 has been reported to proceed efficiently using rhenium(I) complexes as electrochemical catalyst (Eqs. 20-22) (79,85). 

The simplest electrochemical reaction is an outer sphere electron transfer where the interactions with the electrode are weak. Hence, the details of the band structure are not important we can ignore the k dependence of the coupling constants and replace them by a single effective value. The sum over k in Eq. (16) then reduces to the surface density of states corresponding to the electrode and the chemisorption function h.(e) can be taken as constant. It corresponds to the interaction with a wide, stractureless band on the electrode. In this approximation" " the chemisorption K(s) functions vanishes (see Fig. 8a) ... 

The many thousands of articles on outer-sphere electron transfer reactions involving metal ions and their complexes cannot be properly reviewed in a single chapter. From this substantial literature, however, instructive examples will be selected. Importantly, they will be explaining in more detail than is typically found in review articles or treatises on outer-sphere electron transfer. In fact, the analyses provided here are quite different from those typically found in the primary articles themselves. There, in nearly all cases, the objective is to present and discuss calculated results. Here, the goal is to enable readers to carry out the calculations that lead to publishable results, so that they can confidently apply the Marcus model to their own data and research. 

Another useful linear relationship is based on electrochemical data and is obtained by recourse to the fact that AG° = —nFE°. For a series of outer-sphere electron transfer reactions that meet the criteria discussed in context with Equation 1.14, a plot of In k versus E° will have a slope of 0.5(nF/RT), and a plot of log k versus E° will have a slope of 0.5(nF)/2.303RTor 8.5 V-1 for n = 1 at 25°C.5 All the above methods can be used to obtain a common (approximate) value of X for a series of similar reactions. For single reactions of interest, however, X values can often be measured directly by electron self-exchange. 

Outer-sphere reactions are also considered. For the hypothetical reaction [Cr i Clsl +ECr Cls] ", it is suggested that the inclusion of a Na+ ion in the transition state is sufficient to transform the reaction from non-adiabatic to adiabatic, and that the overall effects of counterions on such reactions are too great to be regarded as mere electrostatic stabilization of the encounter complex. Less credible is the conclusion that water molecules themselves can act as effective catalysts for outer-sphere electron transfer, a single water molecule between the reacting complexes leading to a resonance energy increase of 6 kcal mol . 

Before we set up the model Hamiltonian for electrochemical electron transfer, we have to specify the models for the various parts of the system. For the electrons in the metal, we use the quasi-free electron model in which the electronic states are labeled by their quasi-momentum k. For outer-sphere electron transfer on metals, it is usually permissible to ignore the spin index - keeping it would introduce an additional factor of two, which can be incorporated into the interaction constants. On the reactant, we consider a single orbital, labeled a, with which the electrons are exchanged. 

For simple electrode processes, which involve the exchange of a single electron between electroactive redox species in solution and metal surface, aeff and b have a simple interpretation. For so-called outer-sphere electron transfer reactions, which... 

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