For outer-sphere electron transfer

FIGURE 34.4 Dependence of electrochemical rate constant on the electrode potential for outer-sphere electron transfer. An exponential increase in the normal region changes for the plateau in the activationless region. 

Section 18.2). The latest generation of such catalysts (1 in Fig. 18.17) reproduces the key features of the site (i) the proximal imidazole ligation of the heme (ii) the trisi-midazole ligation of distal Cu (iii) the Fe-Cu separation and (iv) the distal phenol covalently attached to one of the imidazoles. As a result, binding of O2 to compound 1 in its reduced (Fe Cu ) state appears to result in rapid reduction of O2 to the level of oxides (—2 oxidation state) without the need for outer-sphere electron transfer steps [Collman et ah, 2007b]. This reactivity is analogous to that of the heme/Cu site of cytochrome c oxidase (see Section 18.2). 

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 ... 

In order to account for the foregoing kinetic behavior, we rely on the Marcus theory for outer-sphere electron transfer to provide the quantitative basis for establishing the free energy relationship (8), i.e.,... 

J.K. Kochi For outer-sphere electron transfer, the slope... 

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 ... 

Another strategy consists in the application of convolution in the same manner as depicted in Section 1.4.3 for outer-sphere electron transfers. The activation-driving force law is then obtained directly from the variation of the rate constant, k(E), with the electrode potential. An example of the successful application of this strategy is provided by the electrochemical reduction of alkyl peroxides7 ... 

Figure 3. Outer-sphere correlation of the rates of various reductions of Co([14]-aneNt)(OHg)Os2. Outer-sphere reductants (%) are Cofsepf, 1 Ru(NHs)e2, 2 and V2, 3. Potentially inner-sphere reductants (O) are Co([14]aneNk)(OHt) 2 f 4 Co([15]aneNJ(OHt)22, 5 and Fe2, 6. Values of AGab° and AGbbT appropriate for outer-sphere electron transfer have been used for both open and solid circles. The open square corresponds to use of the measured Kab for the reaction of Co([14]aneNk)(OH2)Ot2 with Co([14]aneNk)(OHt)t2 The solid line has been drawn with unit slope through the solid circles.

Another important aspect of the Marcus theory has also been systematically investigated with organic molecules, namely the quadratic, or at least the non-linear, character of the activation-driving force relationship for outer sphere electron transfer. In other words, does the transfer coefficient (symmetry factor) vary with the driving force, i.e. with the electrode... 

The extent to which the radicals react according to Eqs. 6 or 7 depends on the nature of Ri, Ra, and R3. If Ri = Rj = H and R3 = H through NO2, the ratio (6) (7) > 20. The addition reactions observed with these systems are characterized by strongly negative activation entropies, which can be rationalized in terms of immobilization of water molecules by the positive charge at C in the transition state [15]. That the transition state for addition has pronounced electron-transfer character concluded from the fact [15] that the rate constants for addition depend on the reduction potential of the nitrobenzene in a way describable by the Marcus relation for outer-sphere electron transfer. 

On the basis of the very negative activation entropies, the transition states for the addition are highly ionic, i.e. there is a large degree of electron transfer in the transition state as with the hydroxyalkyl radicals (Sect. 2.1.1). In support of this is the fact that the rate constants for addition depend on the reduction potentials of the nitrobenzenes, varied by the substituent R3 in a way describ-able by the Marcus equation for outer-sphere electron transfer [19]. 

When the above factors are put under control, the possibility of changing the ligand L in the pentacyano(L)ferrate complexes adds a further dimension for studying systematic reactivity changes, brought out by the controlled modification of the redox potentials of the Fe(II)-Fe(III) redox couples. In this way, the rates of electron transfer reactions between a series of [Fen(CN)5L]re complexes toward a common oxidant like [Coin(NH3)5(dmso)]3+ showed a variation in agreement with Marcus predictions for outer-sphere electron transfer processes, as demonstrated by linear plots of the rate constants versus the redox potentials (123). 

Indirect evidence concerning intramolecular electron transfer has also been obtained by the observation of low-energy charge transfer absorption bands in mixed-valence complexes (reaction 8)14 even for outer-sphere electron transfer within ion pairs (reaction 9).15 The theoretical work of Hush makes it possible to use the energies and integrated intensities of such bands to estimate rates of intramolecular electron transfer.16... 

The theoretical results obtained for outer-sphere electron transfer based on self-exchange reactions provide the essential background for discussing the interplay between theory and experiment in a variety of electron transfer processes. The next topic considered is outer-sphere electron transfer for net reactions where AG O and application of the Marcus cross reaction equation for correlating experimental data. A consideration of reactions for which AG is highly favorable leads to some peculiar features and the concept of electron transfer in the inverted region and, also, excited state decay. 

Marcus attempted to calculate the minimum energy reaction coordinate or reaction trajectory needed for electron transfer to occur. The reaction coordinate includes contributions from all of the trapping vibrations of the system including the solvent and is not simply the normal coordinate illustrated in Figure 1. In general, the reaction coordinate is a complex function of the coordinates of the series of normal modes that are involved in electron trapping. In this approach to the theory of electron transfer the rate constant for outer-sphere electron transfer is given by equation (18). 

An ideal photosensitizer must satisfy several stringent requirements (Balzani et. al., 1986) 1) stability towards thermal and photochemical decomposition reactions 2) sufficiently intense absorption bands in a suitable spectral region 3) high efficiency of population of the reactive excited state 4) long lifetime in the reactive excited state 5) suitable ground state and excited state potentials 6) reversible redox behavior 7) good kinetic factors for outer sphere electron transfer reactions. 

Several studies of bimetallic complexes in which the donor and acceptor are linked across aliphatic chains have demonstrated that these are generally weakly coupled systems. " Studies of complexes linked by l,2-bis(2,2 bipyridyl-4-yl)ethane (bb see Figure 5), indicate that these are good models of the precursor complexes for outer-sphere electron-transfer reactions of tris-bipyridyl complexes. A careful comparison of kinetic and spectroscopic data with computational studies has led to an estimate of //rp = 20cm for the [Fe(bb)3pe] + self-exchange electron transfer. In a related cross-reaction, the Ru/bpy MLCT excited state of [(bpy)2Ru(bb)Co(bpy)2] + is efficiently quenched by electron transfer to the cobalt center in several resolved steps, equations (57) and (58). ... 

The interfacial kinetics processes at semiconductor/liquid contacts for reactions with one-electron, outer-sphere, redox species can be understood in a conventional theoretical framework. The rate constant can be broken down into a term representing the attempt frequency, Vn, a term representing the electronic coupling between the electrons in the conduction band of the semiconductor and the redox acceptor state, k x, and a term representing the nuclear reorganization energy in the transition state from reactants to products, For outer-sphere electron transfer processes, the nuclear term is well-known to be ... 

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