## 3 Results and Discussion  
### Stability of Mono-Substituted Flavones (n-Hydroxylavones)  
The structure of 3-HF (C\({}_{15}\)H\({}_{10}\)O\({}_{3}\)) consists of a phenyl benzopyrone skeleton with fifteen carbon atoms, in which two benzene rings (A and B) are linked through a \(\gamma\)-pyrone ring C, as shown in Figure 1, together with its nomenclature. All the hydrogens of the ten C-H bonds of the unsubstituted flavone (0-HF, C\({}_{15}\)H\({}_{10}\)O\({}_{2}\)) can be replaced by a hydroxyl group (-OH) as mono-hydroxyflavones. As a result, in addition to the unsubstituted flavone (0-HF), there are seven unique mono-hydroxyflavones, 3-HF, 5-HF, 6-HF, 7-HF, 8-HF, 2\({}^{\prime}\)/6\({}^{\prime}\)-HF, 3\({}^{\prime}\)/5\({}^{\prime}\)-HF, and 4\({}^{\prime}\)-HF. Here, 5-HF was the most stable mono-hydroxyflavone in the gas phase, in agreement with an earlier study [10], and it was also the most stable mono-hydroxyflavone in DMSO solvent obtained from the present study. 3-HF is unique because its -OH group replaces a single hydrogen atom on the \(\gamma\)-pyrone C-ring. Among the intramolecular hydrogen bonds (HBs) formed, the one within the \(\gamma\)-pyrone C-ring was the most significant, as highlighted in the structure shown at the bottom right of Figure 1.  
The stability and electronic properties of mono-substituted hydroxyflavones (n-HFs) have been systematically calculated using DFT calculations. The ground electronic states of mono-substituted flavones (n-HF where n=0 for unsubstituted flavone, n = 2-8 for n-hydroxylavones) were optimized in DMSO solvent. Due to the symmetry and the rotations around the C2-C1\({}^{\prime}\) single bond at room temperature, the mono-substituted flavones on the phenyl B-ring would be practically the same in the measurements, although they are theoretically not identical [13]. For example, the 2\({}^{\prime}\)-HF and 6\({}^{\prime}\)-HF and the 3\({}^{\prime}\)-HF and 5\({}^{\prime}\)-HF  
Figure 1: **(a)** The structures of the flavone (0-HF: C\({}_{15}\)H\({}_{10}\)O\({}_{2}\)) and its derivatives by single substitutions for R, R\({}^{\prime}\) = -OH and H in rings A, B, and C (all eight Hs can be substituted by -OH). **(b)** The optimized structure of 3-hydroxyflavones (3-HF: C\({}_{15}\)H\({}_{10}\)O\({}_{3}\)) in three-dimensional (3D) space. The possible intramolecular hydrogen bonding is marked on the optimized 3D structure of 3-HF. pairs are hardly distinguished by room-temperature NMR measurements. As a result, we only studied 2\({}^{\prime}\)-HF (for 6\({}^{\prime}\)-HF) and 3\({}^{\prime}\)-HF (for 5\({}^{\prime}\)-HF). It was noted that the 2\({}^{\prime}\)-HF/6\({}^{\prime}\)-HF pair could be more different from the 3\({}^{\prime}\)-HF/5\({}^{\prime}\)-HF pair, as the former on the B-ring may engage with intramolecular interactions with the C-ring, forming certain hydrogen-bond networks, theoretically [10]. Figure 2 compares the stability of the n-HF compounds, such as the total energies and dipole moments. Here, the unsubstituted flavone is presented as a reference. The total electronic energies of these eight n-HFs provide insights into their relative stability, which follows the following order: 5-HF > 4\({}^{\prime}\)-HF \(\approx\) 7-HF > 3\({}^{\prime}\)-HF > 6-HF > 2\({}^{\prime}\)-HF > 3-HF > 8-HF. The most stable n-HF was 5-HF, with the hydroxyl group substitution in the benzopyrone system (specifically in the A- and C-rings). In contrast, 8-HF, which was the least stable, also resides in the same benzopyrone framework (opposite the C5 position (para) in the A-ring). This trend indicates that the stability of n-HFs is influenced by the position of the hydroxyl (-OH) substitution and the ability to form hydrogen bonds within the molecular framework. Notably, the differences in the total electronic energy between conformers are relatively small, especially for the n-HFs where hydroxyl rotation does not significantly affect intramolecular hydrogen bonding, as observed for 6-HF, 7-HF, 3\({}^{\prime}\)-HF, and 4\({}^{\prime}\)-HF.