Covalent versus electrostatic nature of the strong hydrogen bond:: Discrimination among single, double, and asymmetric single-well hydrogen bonds by variable-temperature X-ray crystallographic methods in β-diketone enol RAHB systems

beta-Diketone enols are known to form intramolecular ...O=C-C=C-OH... resonance-assisted hydrogen bonds (RAHBs) with O...O distances as short as 2.39-2.44 Angstrom. However, even the most accurate diffraction studies have not been able to assess with certainty whether these very strong hydrogen bonds (H-bonds) are to be described as proton-centered O...H...O bonds in a single-well (SW) potential or as the dynamic or static mixing of two O-H...O reversible arrow OH...O tautomers in a double-well (DW) one. This contribution reexamines the problem and shows that diffraction methods are fairly able to assess the SW or DW nature of the H-bond formed and, in the second case, its dynamic or static nature, provided a Bayesian approach is used which associates a number of experimental techniques (X-ray crystallography at variable temperature, difference Fourier maps, least-squares refinement of proton populations, Hirshfeld's rigid-bond test) with a reasonable prior, that is the full set of possible proton-transfer (PT) pathways for the OH...O system derived from theoretical calculations, The method is first applied to three beta-diketone enols, whose crystal structures were determined in the interval of temperatures 100-295 K and then generalized to the interpretation of a much wider set of beta-diketone enol structures derived from the literature, making it possible to establish a general relationship between chemical structure (symmetric or dissymmetric substitution, steric compression or stretching, increased T-bond delocalizability), H-bond strength, and the shape of the PT-barrier. Final results are interpreted in terms of simplified VB theory and state-correlation (or avoided-crossing) diagrams.