## 3 Results and Discussion
### Computational Calculations
#### 3.4.1 The [CuII(\(\beta\)-CD)]\({}^{2+}\) Complex  
For geometric optimization of the [CuII(\(\beta\)-CD)]\({}^{2+}\) complex through DFT calculation, the copper ion was put in four different initial places, namely the center of the large rim edge, the edge of the large rim, the center of the small rim, and the edge of the small rim. The optimization can only proceed when the copper ion lies in the small rim. Figure 4 shows the top and side views of the initial and optimized structures when the ion placed at the center or the edge of the small rim. DFT calculation indicates that the copper ion was stabilized by three electron-donating oxygens of the 6-hydroxyl group localized on the primary rim edge while keeping the ion inside the cavity structure. The optimized Cu-O bond lengths range from 2.04 to 2.40 A. Furthermore, it is also shown that the structure of \(\beta\)-CD can be affected in various degrees by adding the copper ion. When the copper ion is in the center, the conformation of \(\beta\)-CD become more distorted after optimization (Figure 4A,B), induced by the strong attraction from the ion. In contrast, when the copper ion is initially placed close to the edge of the rim (Figure 4C,D), the \(\beta\)-CD maintains a more \"natural\" state with less compensation of the conformational change induced by the Cu coordination. DFT calculations suggest the optimized structure shown in Figure 4D as a more energy-favorable state, with the energy 13.3 kcal/mol lower than the optimized structure shown in Figure 4B. The more negative the energy is, the more stably the complex forms. This is reasonable because the distorted \(\beta\)-CD is energy-unfavorable, which could be compensated by the coordination of the ion to a certain extent for the energy-favorable state of the whole system. To satisfy the \(\beta\)-CD conformation requirement, copper ions can hardly be stabilized when the distance between them is too far, and that is the reason why the optimization failed when placing the ion at the large-rim side. In brief, the copper ion plays a bridge role to connect the \(\beta\)-CD and EZM in the complex because of its coordination ability. In previous studies, it is generally recognized that the large rim of \(\beta\)-CD containing secondary hydroxyl groups is the main binding site for guest inclusion [9; 20; 21], but one should also pay attention to the contribution from the small rim. It has been demonstrated that benzoic acid could insert into the carboxylic group at the small rim [22]. Another work also reveals that cations are likely to form a coordination bond at the small rim with \(\beta\)-CD when considering the distance between opposite oxygen atoms within the small rim is two-fold shorter when compared with the large rim. The author studied the complexes involving \(\beta\)-CD with Na\({}^{+}\), Mg\({}^{2+}\), Al\({}^{3+}\), Cu\({}^{+}\), and Zn\({}^{2+}\) using the DFT computational method and showed clearly that all these metal ions are located in the small rim in the optimized structure [23]. It is also reported many times that the size and shape of the entrance and cavity of \(\beta\)-CD will make proper changes for guest binding [24; 25]. [PERSON] et al. have determined that the methylation of the \(\beta\)-CD would affect the size of the cavity and the shape of the entrance [26]. \begin{table}
\begin{tabular}{c c c c} \hline  & [Cu(\(\textit{SR}\)-\(\textit{EZM}\))\({}_{2}\)(\(\beta\)-CD)]\({}^{2+}\) & [Cu(\(\textit{SR}\)-\(\textit{EZM}\))\({}_{2}\)(\(\beta\)-CD)]\({}^{2+}\) & **Difference Value** \\ \hline CE10 & 12.4\% & 8.2\% & 4.2\% \\ CE12 & 21.3\% & 13.1\% & 8.2\% \\ CE14 & 43.2\% & 23.6\% & 19.6\% \\ CE16 & 97.3\% & 46.7\% & 50.6\% \\ CE18 & 99.4\% & 99.2\% & 0.2\% \\ CE20 & 99.7\% & 99.6\% & 0.1\% \\ \hline \end{tabular}
\end{table} 
Table 1: The difference of the fragment ions abundance of [Cu(\(\textit{EZM}\))\({}_{2}\)(\(\beta\)-CD)]\({}^{2+}\) ternary complexes at different collision energy. Similarly, the copper ion also exhibits a significant effect on the rim parameters.