## 4 Conclusions  
The unique intramolecular hydrogen-bonding network of 3-hydroxyflavone (3-HF) was analyzed relative to unsubstituted flavone (0-HF) and other mono-hydroxyflavones (n-HFs). Using the density functional theory (B3 PW91/cc-pVTZ) in dimethyl sulfoxide (DMSO), 3-HF was found to be 1.85 kJ/mol more stable than the least stable (8-HF), but 33.13 kJ/mol less stable than the most stable (5-HF). This is consistent with earlier studies. Geometrically, 3-HF is unique, as its hydroxyl group resides in the \(\gamma\)-pyrone C-ring, unlike other n-HFs, where the hydroxyl groups are in the phenyl A- or B-rings. This positioning allows 3-HF to form an intramolecular hydrogen-bonding network connecting both the B-ring and the A-/C-rings. Although 3-HF is slightly non-planar, with a dihedral angle of 15.4\({}^{\circ}\), this structure enhances the rigidity due to its extended hydrogen-bonding network. These unique properties are further reflected in the \({}^{13}\)C-NMR chemical shift patterns, which are distinct from other n-HFs.  
Contrary to previous studies suggesting that \({}^{13}\)C-NMR shifts depend on the flavone's ring structure, these findings indicate that the shifts are predominantly influenced by the electronic environment of carbons within C-O bonds. The natural bond orbital (NBO)  
\begin{table}
\begin{tabular}{c||c|c|c|c|c} \hline C1s & 18a (C2) & 17a (C4) & 16a (C3) & 15a (C9) & 14a (C1\({}^{\prime}\)) & 15a (C10) \\ \hline
3-HF & & & & & \\ \hline C1s & 17a (C4) & 16a (C2) & 15a (C9) & 14a (C1\({}^{\prime}\)) & 13a (C10) & 12a (C2) \\ \hline
0-HF & & & & & \\ \hline \end{tabular}
\end{table}
Table 4: DFT-calculated carbon core electron density distributions of flavone (0-HF) and mono-hydroxylavones (3-HF) in DMSO solvent \({}^{\star}\).  
analysis revealed that all the carbon atoms in the \(\gamma\)-pyrone C-ring of 3-HF, except C10, carry positive charges, with C1 in the B-ring also exhibiting higher-energy C1s orbitals. These quantum mechanical effects uniquely define the electronic properties of 3-HF, which may be challenging to predict with machine learning due to their dependence on quantum phenomena. In conclusion, 3-HF's distinct geometry, electronic structure, and \({}^{13}\)C-NMR pattern underscore the significant role of its C3 hydroxyl group, and quantum mechanical approaches can accurately capture the nuanced behaviors of such systems, offering insights that complement empirical methods.  
The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/app15115928/s1](https://www.mdpi.com/article/10.3390/app15115928/s1)]([https://www.mdpi.com/article/10.3390/app15115928/s1](https://www.mdpi.com/article/10.3390/app15115928/s1)), References [9; 10; 20; 21] are cited in the Supplementary Materials.  
F.W.: conceptualization, methodology, validation, investigation, resources, formal analysis, writing--original draft, review and editing, and project administration. V.V.: data curation, calculation, and review and editing. F.W.: wrote the main manuscript text and prepared the figures. V.V.: conducted the calculations. All authors reviewed the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The data are contained within the article and Supplementary Materials.  
The authors thank the supercomputing facilities provided by the Swinburne University of Technology Supercomputing Facilities (OzSTAR and Ngargu Tindebeek (which means \"Knowledge of the Void\" in the Moondani Toombadool language)).  
The authors declare no conflicts of interest in this research.