Variable-Temperature X-ray Crystallographic and DFT Computational Study of the NH···O/N···HO Tautomeric Competition in 1-(Arylazo)-2-naphthols. Outline of a Transiton-State Hydrogen-Bond Theory

Phenyl-substituted 1-arylazo-2-naphthols (AAN) display ···HNNCCO··· ⇌ ···NNCCOH··· ketohydrazone−azoenol tautomerism and can form intramolecular resonance-assisted H-bonds
from pure NH···O to pure N···HO through tautomeric and dynamically disordered NH···O ⇌
N···HO bonds according to the electronic properties of their substituents. Three compounds of this series
(m-OCH3-AAN = mOM; p-Cl-AAN = pCl; and p-NMe2-AAN = pNM2) have been studied by X-ray
crystallography at four temperatures (100−295 K), showing that the remarkably short H-bonds formed
(2.53 ≤ d(N···O) ≤ 2.55 Å) are a pure NH···O in mOM, a dynamically disordered mixture in pCl
(NH···O:N···H−O = 69:31 at 100 K), and a statically disordered mixture in pNM2 (NH···O:N···HO =
21:79 at 100 K). These compounds, integrated by the p-H-, p-NO2-, p-F-, and p-O--substituted derivatives,
have been emulated by DFT methods (B3LYP/6-31+G(d,p) level) with full geometry optimization of the
stationary points along the proton-transfer (PT) pathway:  NH···O and N···HO ground states and
N···H···O transition state. Analysis of DFT-calculated energies and geometries by the methods of the rate-equilibrium Marcus theory shows that all H-bond features (stability and tautomerism, as well as position
and height of the PT barrier) can be coherently interpreted in the frame of the transition-state (or activated-complex) theory by considering the bond as a chemical reaction NH···O ⇌ N···H···O ⇌ N···HO which
is bimolecular in both directions and proceeds via the N···H···O PT transition state (the activated complex).