Electron outer-sphere transfer

Electron-transfer reactions are the simplest class of electrochemical reactions. They play a special role in that every electrochemical reaction involves at least one electron-transfer step. This is even true if the current across the electrochemical interface is carried by ions since, depending on the direction of the current, the ions must either be generated or discharged by an exchange of electrons with the surroundings. 

In aqueous solutions these reactions seem to proceed via an outer-sphere mechanism on most metals. Typically such reactions involve metal ions surrounded by inert ligands, which prevent adsorption. Note that the last example reacts via an outer-sphere pathway only if trace impurities of halide ions are carefully removed from the solution otherwise it is catalyzed by these ions. 

Electrochemical electron and ion transfer reactions are commonly interpreted by the phenomenological Butler-Volmer law, according to which the rate constant k for 

For outer sphere electron transfer reactions the Butler-Volmer law rests on solid experimental and theoretical evidence. An outer sphere electron transfer reaction is the simplest possible case of an electron transfer reaction, a reaction where only an electron is exchanged, no bonds are broken, the reactants are not specifically adsorbed, and catalysts play no role (see, e.g.. Ref. 2). Experimental investigations such as those by Curtiss et al. [206] have shown that the transfer coefficient of simple electron transfer reactions is independent of temperature. The theoretical basis is given by the theories of Marcus [207] and of Levich and Dogonadze [208] these theories also predict deviations at high overpotentials which were experimentally confirmed [209, 210]. 

The so-called solvent coordinate is usually chosen as the difference in the solute-solvent energy between the reactant and the product system. For many models, this difference is proportional to the electrostatic potential due to the water molecules at the location of the ion. The approximately parabolic solvent reorganization energy functions can be calculated from computer simulations using umbrella sampling techniques. 

Benjamin [217] calculated the solvent reorganization free energy functions for the electron transfer reaction of a monovalent ion near the interface between immiscible 

Rose and Benjamin [197] calculated the adiabatic free energy curves for several choices of overpotential rj and electronic coupling parameter T (Fig. 32) from 

The following reactions are examples of outer-sphere electron transfers  

It is reasonable to expect that electron transfer will occur at a very high rate when two reactants are relatively close to each other. Reactions (5.3.2) and (5.3.3) are very fast indeed. This can be explained by assuming that the o-phenanthroline ligand is a ligand in which electrons are strongly delocalized (like in a metallic wire resistor). 

Self-exchange Electon configuration (25 °C) Difference in M-L bond length/nm Ref. 

Marcus theory of outer-sphere electron transfer 

Electron-transfer reactions have been attracting interest of theoretical chemists for many years. An important contribution to the theory of outer-sphere electron transfer is that of R. A. Marcus.  

Electrode reactions can be divided into two major groups those in which only charge is transferred across the interface, and those in which both charge and mass are transferred. Outer-sphere charge transfer is a good example of the former, while metal deposition and dissolution is an example of the latter. 

A typical outer-sphere charge-transfer reaction is the ferricyanide-ferrocyanide redox couple 

This reaction occurs at the solution side of the interface, the electrode serves only as a source or sink for electrons. The important thing to note is that the close 

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A powerful application of outer-sphere electron transfer theory relates the ET rate between D and A to the rates of self exchange for the individual species. Self-exchange rates correspond to electron transfer in D/D (/cjj) and A/A (/c22)- These rates are related through the cross-relation to the D/A electron transfer reaction by the expression... 

Iron(II) ediylenediaminetetraacetic acid [15651 -72-6] Fe(EDTA) or A/,Ar-l,2-ethaiiediylbis[A[-(carboxymethyl)glyciQato]ferrate(2—), is a colorless, air-sensitive anion. It is a good reducing agent, having E° = —0.1171, and has been used as a probe of outer sphere electron-transfer mechanisms. It can be prepared by addition of an equivalent amount of the disodium salt, Na2H2EDTA, to a solution of iron(II) in hydrochloric acid. Diammonium [56174-59-5] and disodium [14729-89-6] salts of Fe(EDTA) 2— are known. 

Outer sphere electron transfer (e.g., [11-19,107,160-162]), ion transfer [10,109,163,164] and proton transfer [165] are among the reactions near electrodes and the hquid/liquid interface which have been studied by computer simulation. Much of this work has been reviewed recently [64,111,125,126] and will not be repeated here. All studies involve the calculation of a free energy profile as a function of a spatial or a collective solvent coordinate. 

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

However, metal ions in higher oxidation states are generally smaller than the same metal ion in lower oxidation states. In the above example, the Co(ii)-N bonds are longer than Co(iii)-N bonds. Consider what happens as the two reactants come together in their ground states and an outer-sphere electron transfer occurs. We expect the rate of electron transfer from one center to another to be very much faster than the rate of any nuclear motion. In other words, electron transfer is very much faster than any molecular vibrations, and the nuclei are essentially static during the electron transfer process (Fig. 9-6). 

The reduction ofsec-, and /-butyl bromide, of tnins-1,2-dibromocyclohexane and other vicinal dibromides by low oxidation state iron porphyrins has been used as a mechanistic probe for investigating specific details of electron transfer I .v. 5n2 mechanisms, redox catalysis v.v chemical catalysis and inner sphere v.v outer sphere electron transfer processes7 The reaction of reduced iron porphyrins with alkyl-containing supporting electrolytes used in electrochemistry has also been observed, in which the electrolyte (tetraalkyl ammonium ions) can act as the source of the R group in electrogenerated Fe(Por)R. ... 

Classification exclusively in terms of a few basic mechanisms is the ideal approach, but in a comprehensive review of this kind, one is presented with all reactions, and not merely the well-documented (and well-behaved) ones which are readily denoted as inner- or outer-sphere electron transfer, hydrogen atom transfer from coordinated solvent, ligand transfer, concerted electron transfer, etc. Such an approach has been made on a more limited scale. Turney has considered reactions in terms of the charges and complexing of oxidant and reductant but this approach leaves a large number to be coped with under further categories. 

The rate sequence is determined by the entropy term and correlates with the oxidation potential of the chelate complex, indicating an outer-sphere electron transfer. 

An irreversible outer sphere electron transfer is thought to be the most likely ratedetermining step in view of the lack of retardation by Fe(CN)6 and CN ions. 

These present an interesting dichotomy in their reductions by tm(l,10-phen-anthroline)iron(ri) (ferroin) °. That of CIO2 to CIOJ is rapid, is first-order in each component ki = 1.86 0.13 l.mole sec at 35 °C) and is independent of acidity. Ferriin is the immediate product and an outer sphere electron-transfer is proposed. The reduction of CIO2 is much slower, proceeding at the same rate as dissociation of ferroin at high chlorite concentrations and a major product is feriin dimer, possibly [(phen)2Fe-0-Fe(phen)2] . Clearly the reaction depends on ligand-displacement followed by an inner-sphere electron transfer. 

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... 

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. 

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... 

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 outer sphere electron transfer, the reactant is not adsorbed therefore, the interaction with the metal is not as strong as with the catal5d ic reactions discussed below. Hence, the details of the metal band structure are not important, and the couphng A(s) can be taken as constant. This is the so-called wide band approximation, because it corresponds to the interaction with a wide, structureless band on the metal. In this approximation, the function A(s) vanishes, and the reactant s density of states takes the form of a Lorentzian. The simation is illustrated in Fig. 2.3. 

In typical outer sphere electron transfer on metal electrodes, A is in the weakly adiabatic region and thus sufficiently large to ensure adiabaticity, but too small to lead to a noticeable reduction of the activation energy. In this case, the rate is determined by solvent reorganization, and is independent of the nature of the metal [Iwasita et al., 1985 Santos et al., 1986]. 

Zusman LD. 1980. Outer-sphere electron transfer in polar solvents. Chem Phys 49 295-304. 

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). 

Influence of surface oxidation, 12-28 Potential energy surface, 66-73 Reaction order, 21 -22 Tafel slope, 18-20, 276-277, 297 Oxygen tolerance, 618-620 Outer sphere electron transfer, 33-38... 

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