Test of Quantitative Relationships

At this point, it is useful to inquire into any quantitative relationship between the H-bond energies in Fig. 6.13 and the proton affinities of the two partners. Numerous experimental studies have indicated a strong correlation between these two quantities . The relationship usually tested is a linear one where the H-bond enthalpy varies as 

A number of concepts have been proposed over the years to explain the linearity of this relationship, and deviations therefrom. Probably the most popular is due to R. A. Marcus whose original ideas were developed for electron transfer and then extended to proton transfer reactions . These ideas apply primarily to the height of the barrier for these reactions and how it is influenced by the exothermicity of the overall reaction. But one can certainly imagine how flipping the energy profde upside down could allow the same notions to apply to the depth of energy minima. 

In fact, the idea of applying Marcus theory to systematize the well depths of H-bonded complexes has been described in the literature on a number of occasions ° . The concepts behind this approach are summarized in Fig. 6.14 which fills out the energy profiles for some of the reactions in Fig. 6.13. The symmetric system, that in which the proton affinities of A and are identical, is taken as a base point, and the depth of the energy well, AE, is denoted an intrinsic well depth. As B is changed to a stronger base Bj, the increase in its proton affinity is described by APA and the new proton transfer profile is represented by the dashed curve in Fig. 6.14. 

The Marcus formulation relates the new well depth (AE,) to the depth in the unperturbed, (that is, symmetric) system, AE, and the change in basicity of B, 5PA  

This equation is derived from a number of simplifying assumptions . In summary, it is presumed that each profile in Fig. 6.14 can be constructed by a pair of inverted parabolas. The energy of the total system is taken to be that of the first parabola, but then switches 

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