Relationship proton affinity difference

The second relationship is of particular interest because extended compilations of pa are accessible in the form of PA (proton affinities in the gas phase) and (acid-base dissociation constants in aqueous solution). With this in mind, the proton-affinity difference becomes... 

It should be stated parenthetically that the Marcus formulation is not the only one that could in principle reproduce the patterns of H-bond energy changes precipitated by proton affinity changes. There are other extant theories - that differ from the Marcus equation chiefly in the last term, a rather unimportant one in many cases as the relationship is very nearly linear anyway. 

One can rationalize a simple relationship between the strength of an ionic H-bond (A—H B) on one hand and the difference in proton affinity between the two partners A and E on the other. The Marcus formulation provides a convenient framework for predicting the El-bond energy of an arbitrary system based on knowledge of the interaction energy in a symmetric system (A=B), and the difference in proton affinity between the two partners. This model has proven successful in a series of interoxygen and internitrogen H-bonds. 

The relationship between proton affinity and Sn (lone pair orbital energy) implies that tautomeric pairs differ in their intrinsic basicities, and hence their aqueous pAf values can be estimated (e.g., 4-methylimidazole, 7.63 5-methylimidazole, 7.41 cf. 4(5)-methylimidazole, 7.52) <83JCS(P2)1869>. Somewhat higher values have been reported elsewhere <89CHE423>. 

Through high-level ealeulations. it was shown that there is a linear relationship between the strength of O—H-. -O hydrogen bonds and the difference in proton affinity. APA, of the donor and the aeeeptor (there is also a eorrelation between O-. -O distance and strength). Singlewell or low-barrier double-well hydrogen bonds tend to arise when APA 0 (this is corroborated by IR studies). 

The basic strengths of many amines have been measured in mixed solvents, particularly in mixtures of water with an alcohol. In such media a certain degree of solvent sorting occurs, with the result that the solvation layers around the various species tend to differ in composition from the bulk of the solution, thereby confusing the position still further. In spite of these complications, however, the p/Ca values for different amines in these hydroxylic media differ numerically from, but are closely parallel with, their values in water. The parallelism arises doubtless because of the variation of AH°, which depends predominantly on the relative proton affinities of the base and solvent. The actual numerical values, however, have not quite the same significance as for aqueous solutions, since the relationship piCa + P b = 14 no longer holds. 

It bears one last reiteration that there is no question that the strength of a typical H-bond is in fact directly related to the difference in pKg between the two participating groups [151]. This relationship has been known from some time, based on gas-phase data concerning proton affinities, which demonstrates that the H-bond enthalpy peaks when the proton affinities of the partners are close in value to one another [152-158]. A more recent test in nonaqueous conditions confirmed a linear correlation between the H-bond energy and the diminution of ApKa. However, in accord with quantum calculations [19], no special stabilization was noted when ApKa achieved a value of zero nor is there even a change in slope in the latter relationship observed at this point [159,160]. 

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