**1. Introduction**

The concept of hydrogen bonding has evolved considerably over its century of history [1,2]. The anomalous properties of water prompted the first suspicion of an attractive interaction between a hydrogen atom in one water molecule with the oxygen of another (HOH ... OH2). Similar phenomena involving N and F were soon recognized as well. H bonding has been recognized as a primarily electrostatic phenomenon expressed by its effect on vibrational frequencies (most often red-shifting the OH stretch), molecular structure (short X ... HY distances, where X and Y are electronegative atoms F, O, N etc.), and characteristic NMR parameters (owing to charge shifts) to mention the most prominent. The concept of H bonding has been expanded from its original context so to include a number of surprising interactions, involving atoms other than oxygen, fluorine, and nitrogen [3,4]; "strong" H-bonding [5]; and "anomalous" (blue-shifting) H bonding [6]. Further expansion of the concept also has been recognized [7].

The computational modeling of hydrogen bonding was reviewed in 1997 [8] and 1999 [9], in 2006 [10], and in 2009 [11]. The definition of hydrogen bonding has been formalized by IUPAC [12]. IUPAC's criteria for recognition of H bonding in a structure X-H ... YZ include: origins of bonding (largely electrostatic, but also including contributions from charge transfer and dispersion); polarization of the XH bond; geometry of the structure (XH . . . Y near linearity); distortions from reference structures (extension of the XH bond, with impact on vibrational frequencies); effects on NMR spectra including deshielding of H and coupling of X to Y. In the language of the Atoms in Molecules theory [13], a hydrogen bond is associated with presence of a bond path H ... Y including a bond critical point (BCP) between H and Y. We discuss this criterion below.

Recent collections of studies of intramolecular H bonding include the Molecules special issue from 2017 edited by S. Scheiner [14] and a follow-up 2019 special issue of Molecules edited by G. Sanchez [15]. The current special issue gives primary attention to computational studies. Interest in evaluating the strength of H bonds continues [16,17] and is an important part of this special issue of Molecules.

Intramolecular hydrogen bonding has a significant effect specifically on conformational preference in systems of importance in biochemistry, as various types of H bonding can occur in various conformations and isomers. The intramolecular H bonds in histidine have been described by Yannacome, Sethlo, and Kraka (YSK) [18]. To enhance insight into the relative strength of H bonds in context these authors brought together descriptors from Bader's theory of atoms in molecules (AIM) and the reduced density gradient from analysis of noncovalent interactions (NCI), both of which are described below. According to YSK two local measures of bond strength, the density at a BCP and the local stretching force constant are related by a power law. An analogous l link between a local stretching force constant (and hence that density) and bond energy seems eminently reasonable [19,20]. One particularly simple connection, between bond strength and the potential energy density at a Bond Critical Point, has been proposed [21]. However there is a conceptual issue in relating a strictly local property (such as the density at a specific point) to what is not a strictly local property, the energy associated with molecular rearrangement, especially dissociation.

The IUPAC AIM bond path and critical point criteria [12] for the existence of a hydrogen bond is subject to interpretation. Sometimes a path and its critical point seem much at variance with intuitive notions of bonding [22–26]. Bader recognized this awkward conflict, [27] and a proposal that these topological entities be called "line" CPs has been offered. [28] The issue is particularly troubled for weak interactions, which vary in directionality depending on the extent of electrostatic character [29].

In this work we study acetoacetamide and variants of its tautomer 1-amino-1- hydroxyacetone. Bauer and Wilcox addressed the issue of relative stability of the similar but simpler systems malonaldehyde and acetyl acetone [30], concluding that the enol form was the more stable. Intramolecular hydrogen bonding in many hydroxycarbonyl systems has been studied by Afonin and Vashchenko [31]. All the systems they reported have =O ... HO- interactions. The keto-enol isomerization of many substituted diketones has been studied by Belova et al. [32] In the unsubstituted system propane-1,3-dione which we can call (H, H), the enol form was favored in internal energy by 14.6 kJ/mol; ΔG = 6.2 kJ/mol according to the CBS-4 thermochemical scheme [33]. That scheme favors the enol of the (CH3, CH3) species acetylacetone by a Gibbs energy of 11.0 kJ/mol [26]. MP2 and B3LYP calculations by Belova et al. [32] favor the enol form by ca. 10 kJ/mol. Their systems include (R1, R2) = (NH2, CH3) of central interest here. The DFT model B3LYP/aug-cc-pVTZ placed a keto form above an enol form by 13 kJ/mol; the O ... O distance in the enol was found to be 2.55 Å and the O ... H distance was 1.638 Å in the enol. The enol form was evidently the structure we label TWO; see below. The authors addressed the issue of H-bond strength in their systems, recognizing the long-established link between H bonding and the OH stretching frequency shift to the red relative to the value for a OH group not involved in H bonding. Strong correlations between O ... O shortening, O ... H shortening and OH lengthening are noted.
