## 3 Results and Discussion
### C-NMR Chemical Shifts Indicating Intermolecular Interactions of n-Hydroxylflavones  
Table 3 reports the calculated \({}^{13}\)C-NMR chemical shifts (\(\delta_{\rm C}\)) of the flavones. The accuracy of the calculated \(\delta_{\rm C}\) for n-HFs can be evaluated by comparing the root mean square deviation (RMSD) values between the calculated and experimental data [6] for each isomer. The RMSD values of the eight compounds ranged from 0.85 ppm (0-HF) to 1.56 ppm (5-HF). Note that the \"experimental\" \(\delta_{\rm C}\)s for 8-HF are the estimated averaged data from reference [17], as there are no available NMR measurements for this compound to our knowledge. As a result, it is no surprise that the error for this 8-HF was as large as 2.15 ppm. Other RMSD values for the n-HFs where a hydroxyl group replaced the Hs on the benzopyrone (A- and C-) rings exhibited smaller variations. The simulated individual H-NMR spectra of all the n-HFs are given in Figure S2 in the Supplementary Materials, which provides direct visualization of the patterns. The real RMSD values for carbons in the phenyl B-ring are likely smaller than the tabulated values. A significant factor contributing to this discrepancy is the rotational flexibility of the C2-C1\({}^{\prime}\) single bond. At room temperature, this bond allows for dynamic averaging of the chemical environments of carbons C2\({}^{\prime}\)/C6 and C3\({}^{\prime}\)/C5 in ring B [13]. Experimental NMR captures this averaged state, whereas computational models treat these environments as distinct [13]. Consequently, this difference inflates the RMSD values, suggesting larger deviations than may actually exist under experimental conditions. For example, the mono-substituted n-HFs on the B-ring exhibited both the smallest RMSD values, such as 0.92 ppm for 4\({}^{\prime}\)-HF and 0.98 ppm for 3\({}^{\prime}\)-HF, and the largest RMSD value of 2.13 ppm for 2\({}^{\prime}\)-HF. The notable RMSD for 2\({}^{\prime}\)-HF, which was significantly higher than those of 3\({}^{\prime}\)-HF and 4\({}^{\prime}\)-HF, can be attributed to the dynamic averaging of the carbon chemical shifts, \(\delta_{\rm C}\), in the experimental measurements. Specifically, the \(\delta_{\rm C}\) for 2\({}^{\prime}\)-HF reflects an averaged state between 2\({}^{\prime}\)-HF and its isomer, 6\({}^{\prime}\)-HF, due to the \"free\" flip of the phenyl B-ring, while the computational calculations accounted only for 2\({}^{\prime}\)-HF. As illustrated in Figure 1, the structural differences between the 2\({}^{\prime}\)-HF and 6\({}^{\prime}\)-HF isomers were more pronounced compared to those of the 3\({}^{\prime}\)-HF and 5\({}^{\prime}\)-HF isomers. In contrast, 4\({}^{\prime}\)-HF, located at the para \begin{table}
\begin{tabular}{c c|c c||c|c} \hline
**C-Site** & \(\delta_{\rm{Cal}}\) & \(\delta_{\rm{Expt}}\) [6] & \(\Delta_{\rm{Cal-expt}}\) & \(\delta_{\rm{Expt}}\) [7] & \(\Delta_{\rm{Cal-expt}}\) \\ \hline
2 & 164.81 & 162.6 & 2.21 & 162.4 & 2.41 \\
3 & 106.42 & 107.0 & \(-\)0.58 & 106.8 & \(-\)0.38 \\
4 & 177.43 & 177.1 & 0.33 & 177.0 & 0.43 \\
5 & 125.58 & 124.7 & 0.88 & 124.7 & 0.88 \\
6 & 125.28 & 125.3 & \(-\)0.02 & 125.3 & \(-\)0.02 \\
7 & 134.40 & 134.3 & 0.10 & 134.1 & 0.30 \\
8 & 118.13 & 118.7 & \(-\)0.57 & 118.3 & \(-\)0.17 \\
9 & 156.67 & 155.7 & 0.97 & 155.5 & 1.17 \\
10 & 123.36 & 123.3 & 0.06 & 123.2 & 0.16 \\
1\({}^{\prime}\) & 132.10 & 131.0 & 1.10 & 131.0 & 1.10 \\
2\({}^{\prime}\) & 126.66 & 126.4 & 0.26 & 126.2 & 0.46 \\
3\({}^{\prime}\) & 129.38 & 129.1 & 0.28 & 128.9 & 0.48 \\
4\({}^{\prime}\) & 132.76 & 131.7 & 1.06 & 131.6 & 1.16 \\
5\({}^{\prime}\) & 129.27 & 129.1 & 0.17 & 128.9 & 0.37 \\
6\({}^{\prime}\) & 127.36 & 126.4 & 0.96 & 126.2 & 1.16 \\ \hline RMSD & & & 0.85 & & 0.93 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of the DFT (B3 PW91/cc-pTVZ)-calculated \({}^{13}\)C-NMR chemical shifts of flavone in DMSO solvent with experimental measurements (ppm) (Color is for readiness).