Inner-sphere processes

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. 

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...

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.,... 

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,... 

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 important single development in the understanding of the mechanisms of redox reactions has probably been the recognition and establishment of outer-sphere and inner-sphere processes. Outer-sphere electron transfer involves intact (although not completely undisturbed) coordination shells of the reactants. In inner-sphere redox reactions, there are marked changes in the coordination spheres of the reactants in the formation of the activated complex. 

The inertness of CrCP and the labilities of Cr and Co (in part responsible for the rapidity of the intermediate formation and the breakup steps) were thus cleverly exploited to provide unambiguous proof for the operation of the inner-sphere process. Since most redox... 

An [H + ] term in the rate law for reactions involving an aqua redox partner strongly suggests the participation of an hydroxo species and the operation of an inner-sphere redox reaction (Sec. 5.5(a)). Methods (a) and (b) are direct ones for characterizing inner-sphere processes, analyzing for products or intermediates which are kinetically-controlled. Method (c) is indirect. Other methods of distinguishing between the two basic mechanisms are also necessarily indirect. They are based on patterns of reactivity, often constructed from data for authentic inner-sphere and outer-sphere processes. They will be discussed in a later section. 

As might be foreseen, there are a (limited) number of systems where the energetics of the outer- and inner-sphere reactions are comparable and where therefore both are paths for the reaction. An interesting example of this behavior is the reaction of Cr(H20) with IrClg which has been studied by a number of groups and is now well understood. At 0°C, most of the reaction proceeds via an outer-sphere mechanism. The residual inner-sphere process utilizes a binuclear complex, which can undergo both Cr —Cl and Ir —Cl cleavage ... 

In general, the larger /Th/ d value corresponds to an outer-sphere process or an inner-sphere process which is not substitution controlled. 

It is tempting to relate the thermodynamics of electron-transfer between metal atoms or ions and organic substrates directly to the relevant ionization potentials and electron affinities. These quantities certainly play a role in ET-thermo-dynamics but the dominant factor in inner sphere processes in which the product of electron transfer is an ion pair is the electrostatic interaction between the product ions. Model calculations on the reduction of ethylene by alkali metal atoms, for instance [69], showed that the energy difference between the M C2H4 ground state and the electron-transfer state can be... 

Single-electron transferring across electrified interfaces are traditionally characterized as either outer- or inner-sphere processes according to whether or not they are accompanied in a concerted manner with the formation or the breaking of chemical bonds. Outer-sphere reactions therefore solely involve the reorganization of the outer solvent sphere after the electron transfer has occurred. There are only very few truly outer-sphere reactions known to date such as [23]... 

The reduction of Mel by Co(CN)53-, which occurs by the mechanism represented by reaction (10),19 is offered as a second example of a facile inner-sphere process. The outer sphere alternative, reaction (11), has a very high energy barrier because of the formation of the five-coordinate intermediate Coin(CN)52. Spin-paired complexes of Co111 have a strong preference to be six-... 

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. 

Another disadvantage of the small, hydrophilic agents is that they tumble very rapidly in the extracellular fluid. In water at 25 °C, for example, Gd-DTPA has a rotational correlation time (rR) of 58 ps as determined by the fitting of NMRD data [3], and 105 ps by EPR simulation in the VO++-DTPA analog [4]. This very rapid motion dominates the relaxivity of the PCA in the frequency range of typical clinical interest (42-63 MHz). The reasons for this dominance of rR can be traced to the fact that small Gd3+ chelates like Gd-DTPA have a relaxivity at clinical frequencies that is determined predominantly by an inner sphere process for Gd-DTPA at 50 MHz, Chen et al. calculate that the relaxivity in water is 43 % inner sphere, 25 % second sphere, and 32 % outer sphere [4]. In turn, the inner sphere contribution to relaxivity is often modeled by the Solomon-Bloem-bergen equations [5,6]... 

However, some authors consider that an e.t. reaction which takes place within a complex of two molecules qualifies as an inner sphere process [15], The distinction between inner- and outer-sphere e.t. reactions is then blurred, and only long-range e.t. between distant molecules or chromophores would be truly outersphere... 

In an inner sphere process, the coordination sphere of one complex is substitute by a ligand bound to the other complex which then acts as a bridge and may be transferred during the redox process. For example, isotopic labelling studies show that to oxidation of aqueous Cr2+ with [Co(III)(NH3)5C1]2+ proceeds via a bridges species Cr CI Co, the chlorine not exchanging with free labelled Cl in solution but remaining attached to the kinetically inert Cr(III) product. 

Kumar and Endicott673 have examined the one-electron oxidation-reduction of [Co([14]aneN4) (H20)(02)]2+ in aqueous solution. Reduction competes successfully with dimerization in this system and even mildly reducing metal ions such as Fe2+ react via an inner-sphere process. Presumably this pathway is preferred owing to the large free-energy changes associated with formation of the p-peroxo adducts. With Fe2+ the adduct is observable as a transient CoOOFe species, which decays to Fe3+ and unspecified cobalt products. 

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