Predicting Hydrogen-Bond Strengths by Structural and Thermodynamic Databases

The PA/pKa equalization principle [1,2], that is the idea that H-bond strengths depend on the matching of the donor and acceptor acid-base properties, is more than forty years old but has never been verified in its generality for lack of suitable data. Its definitive verification is now 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 [3] and pKa(H2O)’s in aqueous solutions [4]) and of two comprehensive sources of H-bond strengths (the NIST database, reporting gas-phase dissociation energies for hundreds of H-bonded complexes [3], and the Cambridge Structural Database, CSD, including the crystal structures and H-bond geometries of thousands of chemical compounds [5,6]). The combination of two acid-base indicators (PA and pKa) with two datasets (gas-phase energies and solid-state geometries) provides four possible correlations between H-bond strengths and donor-acceptor acid-base properties, each one potentially leading to the full assessment of the equalization principle. This does not occur in practice because a number of constraints of thermodynamic nature 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 (CAHBs) 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 by far most numerous class of H-bonds; and (iii) only correlations between H-bond strengths deriving from crystal geometries and DpKa values, i.e. pKa differences between H-bond donor and acceptor groups, can deal with these three classes of bonds at the same time and have, 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. The present communication, beside discussing the more theoretical thermodynamic aspects of the problem, will treat in detail the difficulties encountered in the practical comparison of acid-base parameters with geometrical and thermodynamic H-bond-strength indicators. The final aim is to develop an easy computer-based procedure able to provide reasonable energy estimates for all the H-bonds whose geometries become known from structural crystallography studies.