Homogeneous reactions, intrinsic barriers

The first attempt to describe the dynamics of dissociative electron transfer started with the derivation from existing thermochemical data of the standard potential for the dissociative electron transfer reaction, rx r.+x-,12 14 with application of the Butler-Volmer law for electrochemical reactions12 and of the Marcus quadratic equation for a series of homogeneous reactions.1314 Application of the Marcus-Hush model to dissociative electron transfers had little basis in electron transfer theory (the same is true for applications to proton transfer or SN2 reactions). Thus, there was no real justification for the application of the Marcus equation and the contribution of bond breaking to the intrinsic barrier was not established. 

In the following sections, we shall explore the applicability of such relationships to experimental data for some simple outer-sphere reactions involving transition-metal complexes. In keeping with the distinction between intrinsic and thermodynamic barriers [eq 7], exchange reactions will be considered first, followed by a comparison of driving force effects for related electrochemical and homogeneous reactions. 

In the homogeneous case, the derivation of an activation-driving force relationship and of an expression of the intrinsic barrier is less straightforward. It is interesting in this connection to relate the kinetics of crossexchange reactions (31) to those of the two self-exchange reactions (also called identity or isotopic reactions) [(32) and (33)]. 

It seems clear that for reactions of carbocations with nucleophiles or bases in which the structure of the carbocation is varied, we can expect compensating changes in intrinsic barrier and thermodynamic driving force to lead to relationships between rate and equilibrium constants which have the form of extended linear plots of log k against log K. However, this will be strictly true only for structurally homogeneous groups of cations. There is ample evidence that for wider structural variations, for example, between benzyl, benzhydryl, and trityl cations, there are variations in intrinsic barrier particularly reflecting steric effects which lead to dispersion between families of cations. 

For many electrochemical reactions, values of E, and hence k are unknown so that the intrinsic barrier cannot be obtained experimentally. For example, the reductions of substitutionally inert Co(III)-amine complexes to the corresponding Co(II) species are accompanied by rapid following steps to form [CofOHj) ] . Nevertheless, rate-potential data still can be obtained for such systems which are directly related to corresponding homogeneous redox reactions in thejollowing two ways. 

First, the variation in the intrinsic barriers, AG, for related electrochemical reactions can be expected to be closely similar to those for the same series of homogeneous reactions using a fixed coreactant. If the comparison is made at a fixed electrode potential, E, the (often unknown) driving-force terms cancel provided that the free-energy profiles are symmetrical (the symmetry factor a. = 0.5) so that ... 

Relationships having the same form as eq 14 can also be written for the enthalpic and entropic contributions to the intrinsic free energy barriers (10). Provided that the reactions are adiabatic and the conventional collision model applies, eq 14 can be written in the familiar form relating the rate constants of electrochemical exchange and homogeneous self-exchange reactions (13) ... 

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