Outer-sphere self-exchange reactions

The rate constant kex for an outer-sphere self-exchange reaction may be expressed in terms of its free energy of activation AG through the equation ... 

For simple outer-sphere self-exchange reactions of transition-metal complexes in both aqueous and polar organic solvents, is dominated by AVj and hence is expected to be negative, regardless of whether electron transfer is fully adiabatic. In cases in which this expectation is not realized, there is usually an identifiable departure from a simple outer-sphere mechanism attributable to inner-sphere pathways, cationic catalysis of anion-anion electron transfer, or structural distortions associated with spin multiplicity changes. Thus, AV can serve as a mechanistic criterion. 

For the weakly coupled limit, based on outer-sphere self-exchange reactions or ion-pair spectra (see Tables 1 and 2). Estimated metal-to-metal distance in contact ion pair.In water vs. S.H.E. except as indicated. Formally a Ru (NH3)5/Ru (NH3)5 (terminal/terminal) MMCT transition. There may not be a great deal of metal-metal charge-transfer character in this transition. Ru /pz MLCT/Ru H3)5 in [(Ru (NH3)5 2(pz[Ru XNH3)4]pz)] . In water vs. S.C.E. Formally, a central-to-terminal transition in [(Ru (NH3)5 2(pz[Ru (NH3)4]pz)]. This is necessarily a transition from the symmetric combination of Ru (NH3)5 and Ru (NH3)4 moieties in the ground state to an antisymmetric combination in the MMCT excited state." See the discussion of thr center-thr lectron systems in Section 7.11.4.1.1. Central metal... 

The rates of outer-sphere self-exchange reactions vary considerably as illustrated in Table 26.9. Clearly, the reactants must approach closely for the electron to migrate... 

The simplest type of redox reaction is the outer sphere self exchange reaction which can be represented in terms of contact between the outer electron clouds of the reacting complexes. When the contact occurs the electron jumps from an orbital on the reducing complex to an orbital on the oxidising complex. Fig. 6.1... 

The rates of outer-sphere self-exchange reactions vary considerably as illustrated in Table 26.9. Qearly, the reactants must approach closely for the electron to migrate from reductant to oxidant. This reductant-oxidant pair is called the encounter or precursor complex. When electron transfer occurs, there is an important restriction imposed upon it by the Franck Condon approximation (see Section 20.7). Consider a self-exchange reaction of the type ... 

Outer-sphere electron transfer reactions involving the [Co(NH3)6]3+/2+ couple have been thoroughly studied. A corrected [Co(NH3)6]3+/2+ self-exchange electron transfer rate (8 x 10-6M-1s-1 for the triflate salt) has also been reported,588 which is considerably faster than an earlier report. A variety of [Co(NH3)g]3+/2+ electron transfer cross reactions with simple coordination compounds,589 organic radicals,590,591 metalloproteins,592 and positronium particles (electron/ positron pairs)593 as redox partners have been reported. 

This rules out, I would think completely, a dominant outer-sphere mechanism for that system, because the observed rate is just too fast to be compatible with this. The self-exchange reaction must almost certainly proceed most favourably via an inner-sphere mechanism. More data of this kind are evidently needed. 

Also, the observed rates probably refer to outer-sphere pathways, and the rate constants for the corresponding homogeneous self-exchange reactions are available or can be estimated from rate data for closely related cross reactions (15). These h ex... 

The theoretical results obtained for outer-sphere electron transfer based on self-exchange reactions provide the essential background for discussing the interplay between theory and experiment in a variety of electron transfer processes. The next topic considered is outer-sphere electron transfer for net reactions where AG O and application of the Marcus cross reaction equation for correlating experimental data. A consideration of reactions for which AG is highly favorable leads to some peculiar features and the concept of electron transfer in the inverted region and, also, excited state decay. 

The Marcus therory provides an appropriate formalism for calculating the rate constant of an outer-sphere redox reaction from a set of nonkinetic parameters1139"1425. The simplest possible process is a self-exchange reaction, where AG = 0. In an outer-sphere electron self-exchange reaction the electron is transferred within the precursor complex (Eq. 10.4). 

The simplest outer-sphere electron transfer reaction is the so-called self-exchange reaction, where the two reactants are converted one into the other by electron transfer. For example ... 

For the latter reason atom or group transfer may sometimes also take place in outer-sphere processes, and it has even been suggested that atom transfer can be part of an outer-sphere mechanism, if only for the case of hydrogen atom transfer. Such a case is the Fe(II)—Fe(III) self-exchange reaction in water where hydrogen bonding between two ligands in the transition state [2] would... 

Cyano metal complexes undergo a variety of oxidation-reduction reactions. One of the most studied is the fast self-exchange reaction of the [Fe(CN)4] /" anions information from this research was instrumental in establishing the outer-sphere mechanism (see Outer-sphere Reaction) for transition metal oxidation-reduction reactions (see Electrochemistry Applications in Inorganic Chemistry). The nature... 

Several studies of bimetallic complexes in which the donor and acceptor are linked across aliphatic chains have demonstrated that these are generally weakly coupled systems. " Studies of complexes linked by l,2-bis(2,2 bipyridyl-4-yl)ethane (bb see Figure 5), indicate that these are good models of the precursor complexes for outer-sphere electron-transfer reactions of tris-bipyridyl complexes. A careful comparison of kinetic and spectroscopic data with computational studies has led to an estimate of //rp = 20cm for the [Fe(bb)3pe] + self-exchange electron transfer. In a related cross-reaction, the Ru/bpy MLCT excited state of [(bpy)2Ru(bb)Co(bpy)2] + is efficiently quenched by electron transfer to the cobalt center in several resolved steps, equations (57) and (58). ... 

Another useful linear relationship is based on electrochemical data and is obtained by recourse to the fact that AG° = —nFE°. For a series of outer-sphere electron transfer reactions that meet the criteria discussed in context with Equation 1.14, a plot of In k versus E° will have a slope of 0.5(nF/RT), and a plot of log k versus E° will have a slope of 0.5(nF)/2.303RTor 8.5 V-1 for n = 1 at 25°C.5 All the above methods can be used to obtain a common (approximate) value of X for a series of similar reactions. For single reactions of interest, however, X values can often be measured directly by electron self-exchange. 

Rate constants for outer-sphere electron transfer reactions that involve net changes in Gibbs free energy can be calculated using the Marcus cross-relation (Equations 1.24—1.26). It is referred to as a cross-relation because it is derived from expressions for two different self-exchange reactions. 

Many electron transfer reactions of inorganic radicals conform to the outer-sphere model and hence can be modeled with the Marcus theory of electron transfer.71 This model relies, in part, on the concept of self-exchange reactions, and the inference that self-exchange reactions can be defined for radicals. For many years, it was simply... 

The accepted method of testing for an outer-sphere mechanism is to apply Marcus-Hush theory which relates kinetic and thermodynamic data for two self-exchange reactions with data for the cross-reaction between the selfexchange partners, e.g. reactions 25.53-25.55. 

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