The Nature of Solid-State N−H···O/O−H···N Tautomeric Competition in Resonant Systems. Intramolecular Proton Transfer in Low-Barrier Hydrogen Bonds Formed by the ···OC−CN−NH··· ⇄ ···HO−CC−NN··· Ketohydrazone−Azoenol System. A Variable-Temperature X-ray Crystallographic and DFT Computational Study

The tautomeric ···OC−CN−NH··· ⇄ ···HO−CC−NN··· ketohydrazone−azoenol system
may form strong N−H···O/O−H···N intramolecular resonance-assisted H-bonds (RAHBs) which are
sometimes of the low-barrier H-bond type (LBHB) with dynamic exchange of the proton in the solid state.
The problem of the N−H···O/O−H···N competition in these compounds is studied here through variable-temperature (100, 150, 200, and 295 K) crystal-structure determination of pF = 1-(4-F-phenylazo)2-naphthol
and oF = 1-(2-F-phenylazo)2-naphthol, two molecules that, on the ground of previous studies (Gilli, P;
Bertolasi, V.; Ferretti, V.; Gilli, G. J. Am. Chem. Soc. 2000, 122, 10405), were expected to represent an
almost perfect balance of the two tautomers. According to predictions, the two molecules form remarkably
strong bonds (d(N···O) = 2.53−2.55 Å) of double-minimum or LBHB type with dynamic N−H···O/
O−H···N exchange in the solid state. The enthalpy differences between the two minima, as measured by
van't Hoff methods from the X-ray-determined proton populations, are very small and amount to ΔH° =
−0.120 and ΔH° = −0.156 kcal mol-1 in favor of the N−H···O form for pF and oF, respectively. Successive
emulation of pF by DFT methods at the B3LYP/6-31+G(d,p)//B3LYP/6-31+G(d,p) level has shown that
both energetic and geometric experimental aspects can be almost perfectly reproduced. Generalization of
these results was sought by performing DFT calculations at the same level of theory along the complete
proton-transfer (PT) pathway for five test molecules designed in such a way that the RAHB formed changes
smoothly from weak N−H···O to strong O−H···N through very strong N−H···O/O−H···N bond of LBHB
type. A systematic correlation analysis of H-bond energies, H-bond and π-conjugated fragment geometries,
and H-bond Bader's AIM topological properties performed along the PT-pathways leads to the following
conclusions:  (a) any X−H···Y H-bonded system is fully characterized by its intrinsic PT-barrier, that is, the
symmetric barrier occurring when the proton affinities of X and Y are identical; (b) the intrinsic X−H···Y
bond associated with the symmetric barrier is the strongest possible bond in that system and will be single-minimum (single-well, no-barrier) or double-minimum (double-well, low-barrier) according to whether the
intrinsic PT-barrier is lower or slightly higher than the zero-point vibrational level of the proton; (c) with
reference to the intrinsic H-bond, the effect of chemical substitution can only be that of making more and
more dissymmetric the PT-barrier, while the two H-bonds split in a higher-energy bond which is stronger
because closer to the transition-state structure and in a lower-energy one (the stable form) which is weaker
because farther from it; (d) complete dissymmetrization of the PT-barrier will increasingly weaken the more
stable H-bond until the formation of an extreme dissymmetric single-minimum or dissymmetric single-well
H-bond.