Rate constant electronic coupling

Nonetheless, in Table 4 are summarized the results of a series of rate constant comparisons between calculated values using optical absorption data and experimental values.83 The experimental data are derived from self-exchange rate constants for couples which are structurally related to the mixed-valence dimers shown in the table. The experimental values cited are calculated values for electron transfer within the association complex between reactants as estimated from k kQ >JKA. values were calculated using equation (33) and it was assumed in the calculations that vet = 5 x 1012 s-1. Calculations of this kind have been extended to unsymmetrical dimers like (NHJ)5RuIII(pz)RuIICl(bipy)24+ 83 and even to outer-sphere ion-pairs like (4).88... 

Classical, semi-classical, and quantum mechanical procedures have been developed to rationalize and predict the rates of electron transfer. In summary, the observed rate of a self-exchange reaction can be calculated as a function of interatomic distances, force constants, electronic coupling matrix element, and solvent parameters. These model parameters are either calculated, estimated, or determined by experiment, in each case with a corresponding standard deviation. Error propagation immediately demonstrates that calculated rates have error ranges of roughly two orders of magnitude, independent of the level of sophistication in the numerical procedures. 

Rate constants for coupled homogeneous electron-transfer reactions may be measured by analysis of voltammograms. 

As will now be clear from the first Chapter, electrochemical processes can be rather complex. In addition to the electron transfer step, coupled homogeneous chemical reactions are frequently involved and surface processes such as adsorption must often be considered. Also, since electrode reactions are heterogeneous by nature, mass transport always plays an important and frequently dominant role. A complete analysis of any electrochemical process therefore requires the identification of all the individual steps and, where possible, their quantification. Such a description requires at least the determination of the standard rate constant, k, and the transfer coefficients, and ac, for the electron transfer step, or steps, the determination of the number of electrons involved and of the diffusion coefficients of the oxidised and reduced species (if they are soluble in either the solution or the electrode). It may also require the determination of the rate constants of coupled chemical reactions and of nucleation and growth processes, as well as the elucidation of adsorption isotherms. A complete description of this type is, however, only ever achieved for very simple systems, as it is generally only possible to obtain reliable quantitative data about the slowest step in the overall reaction scheme (or of two such steps if their rates are comparable). 

This chapter is concerned with measurements of kinetic parameters of heterogeneous electron transfer (ET) processes (i.e., standard heterogeneous rate constant k° and transfer coefficient a) and homogeneous rate constants of coupled chemical reactions. A typical electrochemical process comprises at least three consecutive steps diffusion of the reactant to the electrode surface, heterogeneous ET, and diffusion of the product into the bulk solution. The overall kinetics of such a multi-step process is determined by its slow step whose rate can be measured experimentally. The principles of such measurements can be seen from the simplified equivalence circuit of an electrochemical cell (Figure 15.1). 

In the strong-coupling limit at high temperatures the electron transfer rate constant is given by the Marcus formula [Marcus 1964]... 

The first step was found to be a fast pre-equilibrium (Scheme 12-8). The dependence of the measured azo coupling rate constants on the acidity function and the effect of electron-withdrawing substituents in the benzenediazo methyl ether resulting in reduced rate constants are consistent with a mechanism in which the slow step is a first-order dissociation of the protonated diazo ether to give the diazonium ion (Scheme 12-9). The azo coupling proper (Scheme 12-10) is faster than the dissociation, since the overall rate constant is found to be independent of the naphthol con-... 

CO oxidation reaction. The spectral changes in Cluster C are followed hy Cluster B reduction with a rate constant that is similar to the steady-state value. On the other hand, the rate of formation of the characteristic EPR signal for the CO adduct at Cluster A is much slower. Its rate constant matches that for acetyl-CoA synthesis, hut is several orders of magnitude slower than CO oxidation. Therefore, it was proposed that the following steps are involved in CO oxidation (1) CO hinds to Cluster C, (2) EPR spectral changes in Cluster C are accompanied hy oxidation of CO to CO2 hy Cluster C, (3) Cluster C reduces Cluster B, and (4) Cluster B couples to external electron acceptors (133). 

EPR studies on electron transfer systems where neighboring centers are coupled by spin-spin interactions can yield useful data for analyzing the electron transfer kinetics. In the framework of the Condon approximation, the electron transfer rate constant predicted by electron transfer theories can be expressed as the product of an electronic factor Tab by a nuclear factor that depends explicitly on temperature (258). On the one hand, since iron-sulfur clusters are spatially extended redox centers, the electronic factor strongly depends on how the various sites of the cluster are affected by the variation in the electronic structure between the oxidized and reduced forms. Theoret-... 

The usual Tafel evaluation yielded a transfer coefficient a = 0.52 and a rate constant k of 4x 10 cm s at the standard potential of the MV /MV couple. This k value corresponds to a moderately fast electrochemical reaction. In this electrode-kinetic treatment the changes in the rate of electron transfer with pH were attributed only to the changes in the overpotential. A more exact treatment should also take into account the electrostatic effect on the rate of reaction which also changes with pH. 

Cobalt(II) Complexes. Spin conversion rates greater than 10 s have been estimated for [Co(terpy)2](PFg)2 [29]. Although Ar 0.04 A is available for the [Co(terpy)2] complex [132] there is a large uncertainty concerning the magnitude of electronic coupling. Therefore, no attempt has been made to calculate the rate constant. 

Very few references are available on the determination of the rate constant for each step of electron charge transfer in the reaction M2+ + 2e -> M(s), i.e., M2+ + e -> M+, M+ + c" -> M(s). Earlier studies are mostly related to two-electron charge transfer reactions either at M2+/Hg(dme), M2+/metal amalgam, or redox couple/Pt interfaces. Even in these studies, the kinetic parameters have been determined assuming that one of the two steps of the reaction is much slower and is in overall control of the rate of reaction in both... 

The extent to which the ion-radical pair suffers a subsequent (irreversible) transformation (with rate constant k characteristic of highly reactive cation radicals and anion radicals) that is faster than the reverse or back electron transfer (/cBET) then represents the basis for the electron-transfer paradigm that drives the coupled EDA/CT equilibria forward onto products (P)20 (equation 8). 

An alternative electrochemical method has recently been used to obtain the standard potentials of a series of 31 PhO /PhO- redox couples (13). This method uses conventional cyclic voltammetry, and it is based on the CV s obtained on alkaline solutions of the phenols. The observed CV s are completely irreversible and simply show a wave corresponding to the one-electron oxidation of PhO-. The irreversibility is due to the rapid homogeneous decay of the PhO radicals produced, such that no reverse wave can be detected. It is well known that PhO radicals decay with second-order kinetics and rate constants close to the diffusion-controlled limit. If the mechanism of the electrochemical oxidation of PhO- consists of diffusion-limited transfer of the electron from PhO- to the electrode and the second-order decay of the PhO radicals, the following equation describes the scan-rate dependence of the peak potential ... 

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