Rate constant successor complex

While reduction of [Fe(CN)6]" by [ Ru(bipy)3] is diffusion controlled, " reduction by [ Os(5-Clphen)3] is slower and data comparisons lead to an estimate of the rate of electron transfer within the ion pairs of 1.6xl0 s . Unexpectedly, this value increases with increasing ionic strength. Reduction of [Fe(CN)e] by MV is diffusion controlled with a rate constant of 7.6 x 10 A/ s at 23 C. The reverse reaction involves rate-determining successor complex dissociation and is an order of magnitude slower than the rate of electron transfer derived from optical data. 

Intersection region, but small enough so that It may be neglected In calculating the height of the potential barrier (Hab Eth) Under these conditions the rate constant for the conversion of the precursor to the successor complex Is Independent of the magnitude of the electronic coupling and depends only on the nuclear factor... 

Of course the Co CNHj) breaks down rapidly in acid into Co + and 5NHJ. Precursor complex formation, intramolecular electron transfer, or successor complex dissociation may severally be rate limiting. The associated reaction profiles are shown in Fig. 5.1. A variety of rate laws can arise from different rate-determining steps. A second-order rate law is common, but the second-order rate constant is probably composite. For example, (Fig. 5.1 (b)) if the observed redox rate constant is less than the substitution rate constant, as it is for many reactions of Cr +, Eu +, Cu+, Fe + and other ions, and if little precursor complex is formed, then = k k2kz ). In addition, the breakdown of the successor complex would have to be rapid k > k 2). This situation may even give rise to negative (= A//° +... 

In these systems, the donor and acceptor diffuse together to give a precursor complex, D A, whose formation is described by the equilibrium constant Kp. Electron transfer, characterized by rate constant eTj occurs within the associated donor-acceptor pair, converting the precursor complex to successor complex D A. Subsequent separation of the oxidized donor (D+) and reduced acceptor (A ) from the successor complex is described by. s- The rate of m/ermolecular electron transfer depends not only on the factors that influence kpj but also on factors affecting the formation of the precursor complex [19]. More quantitatively, as described by Eq. 2, the expression for intermolecular electron transfer has the form of a consecutive reaction mechanism described by an observed rate constant (A obs) consisting of rate constants for diffusion (A ) and the activated electron transfer. 

The scheme in which the successor complex breakdown is the position of highest energy was first thought to have been shown by the reaction of [Fe(CN) with [Co(EDTA)p in which formation of a binuclear species l(EDTA)CoNCFe(CN)jP was observed, followed by appearance of the final products, (Co(EDTA)l and lFe(CN). However, by application of the principle of microscopic reversibility and consideration of the rate constants observed for the reverse process, Fe(CN) ] reduc-... 

Because the electronic factors become more favorable with decreasing separation of the two reactants, the most favorable configuration for electron transfer is one in which the two reactants are in contact. As a consequence, the first step in bimolecular electron-transfer reactions is the formation of a close-contact (or bridged) precursor complex from the separated reactants. The actual electron transfer occurs within the precursor complex to form a successor complex. This is followed by the dissociation of the successor complex to give the separated products. Provided that the formation of the precursor complex is not rate determining, the observed (second-order) rate constant for the electron transfer is equal to K k, where is the equilibrium constant for the formation of the precursor complex and k, is the first-order rate constant for electron transfer within the precursor complex. If the formation of the precursor complex is rate determining, then it is necessary to use a steady-state approximation for its concentration. 

Additional alterations in the work terms with the electrode material for outer-sphere reactions may arise from discreteness-of-charge effects or from differences in the nature of the reactant-solvent interactions in the bulk solution and at the reaction plane. Thus metals that strongly chemisorb inner-layer solvent (e.g., HjO at Pt) also may alter the solvent structure in the vicinity of the outer plane, thereby influencing k bs variations in the stability of the outer-sphere precursor (and successor) states. Such an effect has been invoked to explain the substantial decreases (up to ca. 10 -fold) in the rate constants for some transition-metal aquo couples seen when changing the electrode materiaf from Hg to more hydrophilic metals such as Pt. Much milder substrate effects are observed for the electroreduction of more weakly solvated ammine complexes . 

After electron transfer (transition along the reaction coordinate from D" — Am to E)(n + i)-.A(m-i) in Scheme 1.1), the successor complex dissociates to give the final products of the electron transfer, D(" 1 1 and A(m l). The distinction between the successor complex and final products is important because, as will be shown, the Marcus model describes rate constants as a function of the difference in energy between precursor and successor complexes, rather than between initial and final products. 

Encounter of excited sensitizer with the electron relay leads to the formation of a precursor complex. The electron transfer event occurs within this pair to yield a successor complex. The latter subsequently dissociates into free product ions or reacts back to the starting material. When the stationary state approximation is used the observed (bimolecular) rate constant for product formation can be related to the specific rates of the individual steps in Scheme I by ... 

The incorporation of the Franck-Condon restriction leads to the partitioning of an electron-transfer reaction into reactant (precursor complex) and product (successor complex) configurations. The steps in Equations (6.13) to (6.15) go from reactants to products K is the equilibrium constant for the formation of the precursor complex [Aqx, Bred], and is the forward electron-transfer rate to produce the successor complex [Area, Box]-... 

In principle, any of the steps in Scheme 2 can be rate limiting from the diffusion controlled formation of the association complex to the substitutional breakup of the successor complex. Because of the multiplicity of steps, a detailed interpretation of an experimentally observed rate constant can be extremely difficult. However, in some cases it has been possible to obtain direct or indirect information about the electron transfer step in an inner-sphere reaction using chemically prepared, ligand-bridged dimeric complexes. For example, reduction of the Co -Ru precursor to the product shown in equation (7) by Ru(NH3)6 + or Eu + occurs selectively at the Ru " site. The initial reduction to give Ru is followed by intramolecular electron transfer from Ru to Co which is irreversible since the Co site is rapidly lost by aquation. ... 

The rate constant k for the electron exchange process can be modeled in terms of Marcus theory. In this approach electron transfer is modeled in terms of precursor and successor complexes. This can be done by writing... 

In this reaction sequence the symbols oo, a-, and o represent the bulk solution state, the interfacial state, and the surface-bound state, respectively. The sequence, therefore consists of substrate diffusion to the interface, catalyst formation, precursor complex formation, precursor/successor complex transformation on the surface, successor complex dissociation to regenerate the surface-bound precatalyst and product formation, and finally product diffusion from the interfacial region to the solution bulk. We must be careful about units here ko is a heterogeneous rate constant measured in cms . Furthermore U e, Ac i, kz, k-2> and kz are all first-order rate constants, measured in s Finally... 

The simplest mechanism, and the one adopted in the papers mentioned, was that of bridge cleavage, i.e. successor-complex dissociation. Consequently, the observed first-order rate constants for the disappearance of dinuclear complex were denoted A , and at 25 °C 10 Are/s" = 22.1, 5,4, and 3.17 for Y = cydta, edta, and pdta respectively. 

A little consideration soon shows that Fig. 14.6 is likely to be somewhat idealized. It implies that the path from products to reactants is smooth and uneventful. There are no sticky spots. But consider the reaction between a cationic complex, [Ni(H20)6] for example, and an anion, C say, to give the complex ion [Ni(H20)5Cl]. Simple electrostatic considerations suggest that the ion pair [Ni(H20)6] Cl" may well have some stability, particularly in solvents with a relatively low dielectric constant. The reactants are sticky the ion pair is likely to exist until atomic positions and momenta are either such as to allow the reaction to proceed or the ion pair to dissociate. Such an intermediate, formed between the reactants but in advance of reaction between them, is called a precursor complex. Similarly, when the reaction is one which involves loss of an anionic species by the complex, a so-called successor complex may be an intermediate on the way to the final product. This pattern is shown in Fig. 14.7 which also includes the possibility of a reaction intermediate of some stability. Fig. 14.7 shows a situation which is complicated and would therefore have a complicated rate law. Most systems studied either are, or are assumed to be, rather simpler. 

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