**3. Discussion**

We have described the intramolecular interactions of conformations of acetoacetamide and isomers of its tautomer 2-oxopropanolamine by accurate *ab intio* calculations of relative energies and analysis of their density by AIM and NCI theories. Recasting the vibrational modes by the Cremer-Kraka local modes analysis allow reliable assignments of relative strengths of hydrogen bonds XH ... Y with (X, Y) including (O, O), (O, N), (N, C), and (O, C) (Figure 8). Rank ordering of bond strength by measures bond order n, electron density *ρ* and potential energy density V, and also local force constants k produce an agreed sequence of bond strengths. In specific, ordering according to a bond energy BE estimate based on the potential energy density at the bond critical point agrees with ranking based on local force constants.

**Figure 8.** (**a**) Linear correlation between the local force constants *kLOCAL* and the Espinosa binding energy (BE) defined as BE = −V/2 where V is the potential energy density evaluated by QTAIM at the H bond's Critical Point. (**b**) Correlation diagram with a power law fit. The rank order of H bond strengths agrees with the ordering predicted by *kLOCAL* and other measures, including the Kraka bond order *n* and the density itself at the BCPs. A linear fit is imperfect, but illustrates a strong relation between variables.

All measures agree that the H bond strength decreases in magnitude in the order shown in Figure 9, which shows the values of the local force constants for H bonds.

**Figure 9.** Local force constants (millidynes/Angstrom) for hydrogen bonds.

We expect that the analysis can be extended to many molecules of biological importance and to the description of other kinds of noncovalent interactions.

## **4. Materials and Methods**

We employed extrapolation techniques to arrive at accurate relative energies. The Atoms in Molecules analysis of the computed density, and its extension to the reduced gradient description of non-covalent interactions allowed one perspective on the relative strength of our system's hydrogen bonds. An alternative view is provided by analysis of the vibrational spectrum and its canonical (normal) modes. Recovery of local vibrational modes and their associated frequencies allows more direct discussion properties of the hydrogen bonds.
