Spheres processes

In the case of other systems in which one or both of the reactants is labile, no such generalization can be made. The rates of these reactions are uninformative, and rate constants for outer-sphere reactions range from 10 to 10 sec b No information about mechanism is directly obtained from the rate constant or the rate equation. If the reaction involves two inert centers, and there is no evidence for the transfer of ligands in the redox reaction, it is probably an outer-sphere process. 

Finally, we consider the alternative mechanism for electron transfer reactions -the inner-sphere process in which a bridge is formed between the two metal centers. The J-electron configurations of the metal ions involved have a number of profound consequences for this reaction, both for the mechanism itself and for our investigation of the reaction. The key step involves the formation of a complex in which a ligand bridges the two metal centers involved in the redox process. For this to be a low energy process, at least one of the metal centers must be labile. 

As regards intimate mechanism, electron transfer reactions of metal complexes are of two basic types. These have become known as outer-sphere and inner-sphere (see Chapter 4, Volume 2). In principle, an outer-sphere process occurs with substitution-inert reactants whose coordination shells remain intact in... 

Comparison of equations (2.11) and (2.15) reveals q and r to be kikilk i and A 2//r i, respectively. This enables k to be calculated from qjr. In its simplest forms the structure of the reactive intermediate can be viewed as V(OH)Cr " (when n is 1) or as VOCr (when n is 2). Similar species which have been characterized or implied kinetically are CrOCr (ref. 33), Np02Cr (ref. 37), U02Cr (ref. 31), VOV " (ref. 34), U0Pu02 + (ref. 41), Pu02pe + (ref. 42) and FeOFe + (ref. 38). Predictions on the rate of the V(III)- -Cr(lI) system, based upon Marcus theory", have been made by Dulz and Sutin on the assumption that an outer-sphere process applies. The value arrived at by these authors is 60 times lower than the experimental value. 

Plots of k versus [Cr ] at fixed [CP] are linear and allow A , to be calculated from the slopes as 2.2x 10 l .mole . sec , at 25 °C and = 1.00 M. Product yields of Cr(H20)sCP and Cr(H20)g obtained experimentally were in excellent agreement with those calculated on the basis of the kinetic scheme. Dulz and Sutin conclude that two routes exist for the chloride-catalysed oxidation, Cr(H20)sCP being formed in both paths, viz. inner-sphere process... 

The Cr(II) reduction of H2O2 involves transfer of one oxygen atom from the peroxide into the coordination shell of the resulting hexaaquochromium(III)" It would seem that 0-0 fission is an inner-sphere process, viz. 

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...

Outer-Sphere Electron Transfer The minimal interpenetration of the coordination spheres of the reactants is inherent in any mechanistic formulation of the outer-sphere process for electron transfer. As such, steric effects provide a basic experimental criterion to establish this mechanism. Therefore we wish to employ the series of structurally related donors possessing the finely graded steric and polar properties described in the foregoing section for the study of both homogeneous and heterogeneous processes for electron transfer. 

The same steric dichotomy persists in the oxidation of alkyl radicals by tris-phenanthrolineiron(III), in which two competing processes occur -- viz., the oxidation to alkyl cations, previously identified as an outer-sphere process in eq 3,... 

For the series of -branched alkyl radicals, the second-order rate constant in eq 3 is relatively unaffected by steric effects [compare Figure 2 (right)] as expected for an outer-sphere process. In strong contrast, the rate constant kL for ligand substitution in eq 21 is adversely affected by increasing steric effects, as shown in Figure 17. 

In the context of the Marcus formulation, the lowering of the activation barrier in an inner-sphere process could arise from the reduction of the work term wp as a result of the strong interaction in the ionic products, e.g., [RitSn+ IrCU3 ] and [RitSn+TCNE ]. The electrostatic potential in such an ion pair is attractive and may cause the tetraalkyltin to achieve a quasi five-coordinate configuration in the precursor complex, reminiscent of a variety of trigonal bipyramidal structures already well-known for tin(IV) derivatives, i.e.,... 

J.K. Kochi I agree. The quantitative treatment of inner-sphere mechanisms is difficult from a purely theoretical point of view. The phenomemological approach describes the activation barrier for inner-sphere process quantitatively, but provides no theoretical basis, unfortunately. 

In contrast, with organometals there may be substantial reorganization changes in inner-sphere processes. With the tetraalkyl-tins, for example, it could involve a conversion of a tetrahedral structure to a trigonal bipyramidal structure, i.e.,... 

There are three points of significance of this result. One is that it provides strong support for the 10-step mechanism originally proposed for reaction 1. Another is that it facilitates a more robust fitting of the mechanism to the kinetic data obtained for that reaction. Thirdly, it confirms that reaction 2 has a rate constant that is four orders of magnitude greater than predicted by Marcus theory. It is concluded that reaction 2 is poorly modeled as an outer-sphere process and is better described as... 

Chemical reactivity of unfunctionalized organosilicon compounds, the tetraalkylsilanes, are generally very low. There has been virtually no method for the selective transformation of unfunctionalized tetraalkylsilanes into other compounds under mild conditions. The electrochemical reactivity of tetraalkylsilanes is also very low. Kochi et al. have reported the oxidation potentials of tetraalkyl group-14-metal compounds determined by cyclic voltammetry [2]. The oxidation potential (Ep) increases in the order of Pb < Sn < Ge < Si as shown in Table 1. The order of the oxidation potential is the same as that of the ionization potentials and the steric effect of the alkyl group is very small. Therefore, the electron transfer is suggested as proceeding by an outer-sphere process. However, it seems to be difficult to oxidize tetraalkylsilanes electro-chemically in a practical sense because the oxidation potentials are outside the electrochemical windows of the usual supporting electrolyte/solvent systems (>2.5 V). 

First, in considering the question of whether or not in a particular case we do have an outer-sphere process, we need to know accurately such quantities as bond distances. I have brought some data (shortly to be published) from Dr. J. K. Beattie s laboratory in Sydney, which show that in the 3+ 2+... 

One final point should be noted. Theoretical discussions of electron transfer processes have focused almost entirely on outer-sphere processes. When we have an inner-sphere mechanism, or sufficient electronic interaction in a dynamically trapped mixed-valence complex to produce a large separation between upper and lower potential surfaces, the usual weak-interaction approach has to be abandoned. Thus a detailed knowledge of a potential surface which is not describable as an intersection surface of perturbed harmonic surfaces, for example, is required. For this purpose, detailed calculations will be required. The theory of these processes will be linked more... 

Reverting to outer-sphere processes, one should bear in mind that the observed spread of reaction rates for these is very large iiideed—in fact, it is on the order of magnitude of the age of the universe in seconds So I think that Dr. Sutin is doing very well in explaining it. 

Finally, I refer back to the beginning of this paper, where the assumption of near-adiabaticity for electron transfers between ions of normal size in solution was mentioned. Almost all theoretical approaches which discuss the electron-phonon coupling in detail are, in fact, non-adiabatic, in which the perturbation Golden Rule approach to non-radiative transition is involved. What major differences will we expect from detailed calculations based on a truly adiabatic model—i.e., one in which only one potential surface is considered [Such an approach is, for example, essential for inner-sphere processes.] In work in my laboratory we have, as I have mentioned above,... 

DR. HUSH For myself, if I gave the impression of any feeling of self-satisfaction, it was certainly in the sense that I think we can say that there is a glimmer of light in the darkness. And in chemistry we must be grateful for the smallest spark. I have stressed also that our present theoretical approaches to rate calculations have been almost entirely confined to outer-sphere processes, and that the task of formulating reliable theories for inner-sphere transfers will be a formidable one. 

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. 

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