PA/pKa equalization and the prediction of the hydrogen-bond strength. A synergism of classical thermodynamics and structural crystallography

The PA/pK(a) equalization principle, that is the idea that H-bond strengths can be rationalized in terms of matching between acid-base properties of the H-bond donor and acceptor moieties, is more than forty years old but has never been verified in its generality for lack of suitable data. Its definitive verification has now become possible, at least in principle, because of the availability of ever more extended compilations of thermodynamic acid-base indicators (proton affinities, PAs, in the gas phase and pK(a)(H2O)s in aqueous solutions) and of two readily accessible and comprehensive sources of H-bond strengths (the NIST database, reporting gas-phase dissociation energies of hundreds of H-bonded complexes, and the Cambridge Structural Database, CSD, including the crystal structures and H-bond geometries of thousands of chemical compounds). The combination of two acid-base indicators (PA and pK(a)) with two datasets (gas-phase energies and solid-state geometries) provides four types of possible correlations between H-bond strengths and donor-acceptor acid-base properties, each one potentially leading to the full assessment of the equalization principle for the complete set of known H-bonds. This does not occur in practice and it is shown in the text that a number of constraints of both physical and thermodynamic nature arise which severely limit the application of each type of correlation to partial subsets (classes) of H-bonds and, sometimes, to none. The main practical consequences are that; (i) resonance-assisted H-bonds (RAHBs) cannot be interpreted by means of any acid-base indicator; (ii) gas-phase dissociation enthalpies can be used for the H-bonds which are charged associations of two acids, [A...H...A'](-), or two bases, [B...H...B'](+), but not for those which are acid-base associations, A-H... B, and constitute the class by far most numerous of H-bonds; and (iii) only the correlation between H-bond strengths deriving from crystal geometries and Delta pK(a)s, the pK(a) differences between H-bond donor and acceptor groups, can deal with these three classes of bonds at the same time and has, therefore, the chance to become the method of election for a quick and reasonably accurate prediction of H-bond strengths based on thermodynamic acid-base indicators.