Proton transfer encounter theories

As applied to proton transfers, the theory takes the form of equations 1.7 and 1.8, where kdiff is the diffusion-controlled encounter rate. AG is the free energy of activation defined by equation 1.8, AG° being the standard equilibrium free energy change and AG the intrinsic barrier , the free energy of activation when AG° = 0, a constant of the particular type of reaction. 

To summarize, the proton transfer reaction can be broken into three distinct parts Diffusion of the reactants to within the radius of the ionic atmosphere accelerated diffusion to within the encounter distance and subsequent conversion of the encoimter complex to products. For reactions in which the equilibrium is rapidly established within the encounter complex, the rate equations are dominated by the diffusion process. This results in the loss of information about the dynamics of the encounter complex. For such a reaction some information can be obtained about the ionic radius by varying the ionic strength and using an electrostatic theory (such as is done for Deby-Hiickel activity coefficients) to calculate the effect of shielding by the ions. ... 

The Marcus theory model is derived for unimolecular electron transfer. It is applied to bimolecular reactions by assuming that the reactants weakly associate in a precursor complex within which ET occurs to give the successor complex. The cross relation analyses above have implicitly adopted this same model, but HAT precursor complexes are quite different then ET ones. This is because proton transfer occurs only over very short distances, so HAT precursor complexes have distinct conformations, rather than the weakly interacting encounter complexes of ET. In this way, HAT resembles proton transfer and inner-sphere electron transfer. Including the equilibria for precursor and successor complex formation expands equation (1.1) into equation (1.20). 

It can be seen from the table that the predictions of the Debye-Smoluchowski theory are as follows, (i) The formation and dissociation of an encounter-complex involving uncharged species is always a very rapid process, (ii) In solvents of high dielectric constant, such as water, charges have little effect on the rates, but in media of low dielectric constant both rate and equilibrium constants are drastically affected, (iii) In aprotic solvents of intermediate dielectric constant, the diffusion apart of ions is a slow process, and may be rate-limiting in an overall proton-transfer reaction, (iv) In media of low dielectric constant, free ions are not formed at the usual concentrations. In what follows, several of these predictions are used and tested in the interpretation of experimental data. 

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