Electron-transfer reactions outer-sphere

A significant technical development is the pulsed-accelerated-flow (PAF) method, which is similar to the stopped-flow method but allows much more rapid reactions to be observed (1). Margerum s group has been the principal exponent of the method, and they have recently refined the technique to enable temperature-dependent studies. They have reported on the use of the method to obtain activation parameters for the outer-sphere electron transfer reaction between [Ti Clf ] and [W(CN)8]4. This reaction has a rate constant of 1x108M 1s 1 at 25°C, which is too fast for conventional stopped-flow methods. Since the reaction has a large driving force it is also unsuitable for observation by rapid relaxation methods. 

Outer-Sphere Electron Transfer Involving Mixed-Valent [Cu2]3+ Centers 

Although there is a huge body of research on the kinetics of outer-sphere electron-transfer reactions of mononuclear transition-metal complexes, there are only a small number of papers on dinuclear systems. When the valences of the two metal centers are localized, current evidence indicates that the metal centers typically react essentially independently. On the other hand, for delocalized systems this can hardly be the case. Experimental study of electron transfer with such 

X-ray crystallography shows that in the [Cu2L]3+ state the Cu-Cu distance is short ( 2.4A), and ESR and electronic spectroscopy indicate that the systems are delocalized with both Cu centers in the 1.5 oxidation state. One-electron reduction of both [C L1]3 and [Cu2L2]3+ leads to the corresponding [Cu2L]2+ complexes without any drastic perturbation to the coordination environments at the metal centers. In the case of [C L1]3, reduction causes the Cu-Cu distance to increase by 0.09 A, but for [Cu2L2]3+ the increase is much larger (0.51 A). 

The above results have great relevance to biochemistry, where it is found that dinuclear Cu2 ( CuA ) centers function as electron-transfer 

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Kinetics and mechanism of the outer sphere electron transfer reactions between complex ions. E. D. German, Rev. Inorg. Chem., 1983, 5,123-184 (132). 

Electrochemical reactions only involving a change of charge of simple or complex ions but not any change in inner geometry are commonly called outer-sphere electron transfer reactions. For some time, the reduction and oxidation of simple and... 

The elementary electrochemical reactions differ by the degree of their complexity. The simplest class of reactions is represented by the outer-sphere electron transfer reactions. An example of this type is the electron transfer reactions of complex ions. The electron transfer here does not result in a change of the composition of the reactants. Even a change in the intramolecular structure (inner-sphere reorganization) may be neglected in many cases. The only result of the electron transfer is then the change in the outer-sphere solvation of the reactants. The microscopic mechanism of this type of reaction is very close to that for the outer-sphere electron transfer in the bulk solution. Therefore, the latter is worth considering first. 

OUTER-SPHERE ELECTRON TRANSFER REACTIONS IN THE BULK SOLUTION... 

The height of the potential barrier is lower than that for nonadiabatic reactions and depends on the interaction between the acceptor and the metal. However, at not too large values of the effective eiectrochemical Landau-Zener parameter the difference in the activation barriers is insignihcant. Taking into account the fact that the effective eiectron transmission coefficient is 1 here, one concludes that the rate of the adiabatic outer-sphere electron transfer reaction is practically independent of the electronic properties of the metal electrode. 

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... 

Although somewhat more stable than its hexaammine relative, the air-sensitive [Co(en)3]2+ is still substitutionally labile and racemizes rapidly in solution. Chiral discrimination in its (racemic) solutions has been observed in outer sphere electron transfer reactions with optically active oxidants including [Coin(EDTA)], 209,210 [Cr(ox)3]3-,211,212 Co111 oxalate, malonate, and acetylacetonate (acac) complexes.213... 

Outer-sphere electron transfer reactions involving the [Co(NH3)6]3+/2+ couple have been thoroughly studied. A corrected [Co(NH3)6]3+/2+ self-exchange electron transfer rate (8 x 10-6M-1s-1 for the triflate salt) has also been reported,588 which is considerably faster than an earlier report. A variety of [Co(NH3)g]3+/2+ electron transfer cross reactions with simple coordination compounds,589 organic radicals,590,591 metalloproteins,592 and positronium particles (electron/ positron pairs)593 as redox partners have been reported. 

An expression of the type in Eq. (29) has been rederived recently in Ref. 13 for outer-sphere electron transfer reactions with unchanged intramolecular structure of the complexes where essentially the following expression for the effective outer-sphere reorganization energy Ers was used ... 

Unlike the simplest outer-sphere electron transfer reactions where the electrons are the only quantum subsystem and only two types of transitions are possible (adiabatic and nonadiabatic ones), the situation for proton transfer reactions is more complicated. Three types of transitions may be considered here5 ... 

The reduced species of an outer-sphere electron-transfer reaction is generated by a chemical reaction of the form ... 

Chemical and electrochemical reactions in condensed phases are generally quite complex processes only outer-sphere electron-transfer reactions are sufficiently simple that we have reached a fair understanding of them in terms of microscopic concepts. In this chapter we give a simple derivation of a semiclassical theory of outer-sphere electron-transfer reactions, which was first systematically developed by Marcus [1] and Hush [2] in a series of papers. A more advanced treatment will be presented in Chapter 19. 

Innumerable experiments have been performed on both inner- and outer-sphere electron-transfer reactions. We do not review them here, but present a few results that are directly relevant to the theoretical issues raised in the preceding chapters. 

However, a closer inspection of the experimental data reveals several differences. For ion-transfer reactions the transfer coefficient a can take on any value between zero and one, and varies with temperature in many cases. For outer-sphere electron-transfer reactions the transfer coefficient is always close to 1/2, and is independent of temperature. The behavior of electron-transfer reactions could be explained by the theory presented in Chapter 6, but this theory - at least in the form we have presented it - does not apply to ion transfer. It can, in fact, be extended into a model that encompasses both types of reactions [7], though not proton-transfer reactions, which are special because of the strong interaction of the proton with water and because of its small mass. 

In the general case R denotes a set of coordinates, and Ui(R) and Uf (R) are potential energy surfaces with a high dimension. However, the essential features can be understood from the simplest case, which is that of a diatomic molecule that loses one electron. Then Ui(R) is the potential energy curve for the ground state of the molecule, and Uf(R) that of the ion (see Fig. 19.2). If the ion is stable, which will be true for outer-sphere electron-transfer reactions, Uf(R) has a stable minimum, and its general shape will be similar to that of Ui(R). We can then apply the harmonic approximation to both states, so that the nuclear Hamiltonians Hi and Hf that correspond to Ui and Uf are sums of harmonic oscillator terms. To simplify the mathematics further, we make two additional assumptions ... 

Fe3+X6...Fe2+X6, which is the reactant of the outer-sphere electron transfer reaction mentioned above when X = Y. Clearly the ground state involves a symmetric linear combination of a state with the electron on the right (as written) and one with the electron on the left. Thus we could create the localized states by using the SCRF method to calculate the symmetric and antisymmetric stationary states and taking plus and minus linear combinations. This is reasonable but does not take account of the fact that the orbitals for non-transferred electrons should be optimized for the case where the transferred electron is localized (in contrast to which, the SCRF orbitals are all optimized for the delocalized adiabatic structure). The role of solvent-induced charge localization has also been studied for ionic dissociation reactions [109],... 

Electrochemical reactions can be broken down into two groups outer-sphere electron-transfer reactions and inner-sphere electron transfer reactions. Outer-sphere reactions are reactions that only involve electron transfer. There is no adsorption and no breaking or forming of chemical bonds. Because of their simplicity, numerous studies have been performed, many entirely theoretical.18-25 By definition, though, electrode reactions are not outer-sphere reactions. However, if charge transfer is rate limiting for an electrode reaction, it typically takes a form similar to that of an outer-sphere reaction, which is described later in this section. 

Continuing the study of simple outer-sphere electron transfer reactions,... 

The stage is set in the first chapter, with the depiction of a typical electrochemical experiment and application to the determination of the thermodynamic and kinetic characteristics of outer-sphere electron transfer reaction, with no further chemical steps in the reaction mechanism. In this chapter as well as in the others, we describe both the experimental data and the methods by which they can be gathered. 

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