Marcus equation activation parameters

By measuring the temperature dependence of kex, activation parameters (Aff and AS ) could be calculated and were reported. However, I am not sure how to physically interpret these numbers. The temperature dependence of rate can be fit to other expressions, and here it is fit to the Marcus equation for nonadiabatic electron transfer in the case of degenerate electron transfer (e.g., AG° = 0)... 

TABLE 4.1 Activation Parameters and Fits to the Marcus Equation for Fe(G bpy)32+/3+ Self-Exchange"... 

The parameter A reflects the intrinsic reaction barrier . It coincides with the free activation energy for degenerate conversions (A = AG at AG° = 0). If the quadratic term in the Marcus equation is neglected it takes the form... 

Activation Parameters.— Negative heats of activation have previously been reported for some outer-sphere reactions, - and it has been suggested that some special factor, not covered by the simple Marcus theory, might need to be invoked to explain them. (It will be recalled that negative heats of activation of some inner-sphere reactions have been rationalized in terms of the energetics of formation of precursor complexes.) Marcus and Sutin point out, however, that negative AH values are theoretically predicted, under certain conditions. On differentiating equation (1) with respect to temperature, they obtain... 

With the model of Equation (19) and with a reasonable estimate of the free energies A(fn and AG°3 we can start to evaluate the apparent activation barrier. Before doing so, we must clarify several points (i) A Marcus type relationship and the corresponding LFERs are only valid for a two-state system (1 —>2), i.e., for a reaction with a single step. However, we have a three-state process that involves a two-step mechanism (1 ->2->3). Fitting such a system to a Marcus type formula can lead to nonphysical parameters (e.g., too small of a value for X). (ii) In order to use the HAW approach in a three-state system (or in a four-state system) we must consider the elementary rate constants and then consider the preequilibrium concentrations. 

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