Inner-sphere electron transfer theory

Inner-sphere electron transfers are characterized by (a) temperature-independent rate constants that are greatly higher and rather poorly correlated by Marcus theory (b) weak dependence on solvent polarity (c) low sensitivity to kinetic salt effects. This type of electron transfer does not produce ion radicals as observable species but deals with the preequilibrium formation of encountered complexes with the charge-transfer (inner-sphere) nature (see also Rosokha Kochi 2001). 

Inner-sphere (electron transfer) — is, historically, an - electron transfer between two metal centers sharing a ligand or atom in their respective coordination shells. The term was then extended to any case in which the interaction energy between the donor and acceptor centers in the -> transition state is significant (>20 kj mol-1). See also -> Marcus theory. 

The redox reactions of [MCbpyls] are classified into an outer-sphere electron-transfer reaction, in which the coordination environment of the centered metal is unchanged before and after the electron transfer. The rate for such an outer-sphere electron-transfer reaction is often fast as compared with the inner-sphere electron-transfer reactions accompanied with formation and dissociation of chemical bonds. The rate constant, k, for the outer-sphere electron-transfer reaction is given by Marcus theory [2, 21]. 

In this section I have tried to follow a pattern comparable to the one used in the relevant chapter of the Specialist Periodical Reports series though minor adjustments have been made where necessary. The major developments in theory are followed by an outline of the outer-sphere and inner-sphere electron transfer literature. Photoinduced electron transfer, which remains fashionable, and bioinorganic studies covering mainly the interactions of metalloproteins with small inorganic reagents complete the chapter. Coverage is as comprehensive as space will allow and I have continued the practice of tabulating all the relevant rate data at the end of the chapter. 

The Marcus theory model is derived for unimolecular electron transfer. It is applied to bimolecular reactions by assuming that the reactants weakly associate in a precursor complex within which ET occurs to give the successor complex. The cross relation analyses above have implicitly adopted this same model, but HAT precursor complexes are quite different then ET ones. This is because proton transfer occurs only over very short distances, so HAT precursor complexes have distinct conformations, rather than the weakly interacting encounter complexes of ET. In this way, HAT resembles proton transfer and inner-sphere electron transfer. Including the equilibria for precursor and successor complex formation expands equation (1.1) into equation (1.20). 

Figure 2.1 (Plate 2.1) shows a classification of the processes that we consider they aU involve interaction of the reactants both with the solvent and with the metal electrode. In simple outer sphere electron transfer, the reactant is separated from the electrode by at least one layer of solvent hence, the interaction with the metal is comparatively weak. This is the realm of the classical theories of Marcus [1956], Hush [1958], Levich [1970], and German and Dogonadze [1974]. Outer sphere transfer can also involve the breaking of a bond (Fig. 2. lb), although the reactant is not in direct contact with the metal. In inner sphere processes (Fig. 2. Ic, d) the reactant is in contact with the electrode depending on the electronic structure of the system, the electronic interaction can be weak or strong. Naturally, catalysis involves a strong...

In addition, the determination of metal-ligand bond distances in solution and their oxidation state dependence is critical to the application of electron transfer theories since such changes can contribute significantly to the energy of activation through the so-called inner-sphere reorganizational energy term. 

In the case of stepwise electron-transfer bond-breaking processes, the kinetics of the electron transfer can be analysed according to the Marcus-Hush theory of outer sphere electron transfer. This is a first reason why we will start by recalling the bases and main outcomes of this theory. It will also serve as a starting point for attempting to analyse inner sphere processes. Alkyl and aryl halides will serve as the main experimental examples because they are common reactants in substitution reactions and because, at the same time, a large body of rate data, both electrochemical and chemical, are available. A few additional experimental examples will also be discussed. 

The most striking application of electron transfer theory has been to the direct calculation of electron transfer rate constants for a series of metal complex couples.36 37 46 The results of several such calculations taken from ref. 37b are summarized in Table 2. The calculations were made based on intemuclear separations appropriate to the reactants in close contact except for the second entry for Fe(H20)j3+/2+, where at r = 5.25 A there is significant interpenetratidn of the inner coordination spheres. The Ke values are based on ab initio calculations of the extent of electronic coupling. k includes the total contributions to electron transfer from solvent and the trapping vibrations using the dielectric continuum result for A0. the quantum mechanical result for intramolecular vibrations, and known bond distance changes from measurements in the solid state or in solution. 

Two questions are inseparable how to optimize ion radical reactions, and how to facilitate electron transfer. As noted in the preceding chapters, electron transfers between donors and acceptors can proceed as outer-sphere or inner-sphere processes. In this connection, the routes to distinguish and regulate one and another process should be mentioned. The brief statement by Hubig, Rathore, and Kochi (1999) seems to be appropriate Outer-sphere electron transfers are characterized by (a) bimolecular rate constants that are temperature dependent and well correlated by Markus theory (b) no evidence for the formation of (discrete) encounter complexes (c) high dependence on solvent polarity (d) enhanced sensitivity to kinetic salt effects. 

However, the mechanisms of conventional redox reactions and electrochemical reactions maybe quite different. Within the formalism of electron transfer theory, the electron transfer reactions at electrodes are usually of the outer-sphere type, whereas those that involve inorganic ions are often of the inner-sphere type [11]. 

This chapter mainly focuses on the reactivity of 02 and its partially reduced forms. Over the past 5 years, oxygen isotope fractionation has been applied to a number of mechanistic problems. The experimental and computational methods developed to examine the relevant oxidation/reduction reactions are initially discussed. The use of oxygen equilibrium isotope effects as structural probes of transition metal 02 adducts will then be presented followed by a discussion of density function theory (DFT) calculations, which have been vital to their interpretation. Following this, studies of kinetic isotope effects upon defined outer-sphere and inner-sphere reactions will be described in the context of an electron transfer theory framework. The final sections will concentrate on implications for the reaction mechanisms of metalloenzymes that react with 02, 02 -, and H202 in order to illustrate the generality of the competitive isotope fractionation method. 

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