## 3 Results and Discussion
### Computational Calculations
#### 3.4.2 The Complex of [Cu\({}^{\rm II}\)(\(\beta\)-CD)(EZM)]\({}^{2+}\)  
With a basic understanding of how the copper ion acts with the \(\beta\)-CD, we explore the combination mode of the drug molecule and [Cu\({}^{\rm II}\)(\(\beta\)-CD)]\({}^{2+}\) system. One EZM molecule was randomly placed in the vicinity of the above-mentioned optimized [Cu\({}^{\rm II}\)(\(\beta\)-CD)]\({}^{2+}\) structure to form [Cu\({}^{\rm II}\)(\(\beta\)-CD)(EZM)]\({}^{2+}\) complex. The structures of the optimized [Cu\({}^{\rm II}\)(\(\beta\) \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \(\mathbf{R_{L}}\) (Max) & \(\mathbf{R_{L}}\) (Min) & \(\triangle\mathbf{R_{L}}\) & \(\mathbf{R_{s}}\) (Max) & \(\mathbf{R_{s}}\) (Min) & \(\triangle\mathbf{R_{s}}\) \\ \hline \(\beta\)-CD & 11.11 & 10.25 & 0.86 & 13.03 & 8.62 & 4.41 \\ \(\beta\)-CD+Cu & 10.09 & 9.82 & 0.27 & 11.40 & 10.22 & 1.18 \\ \(\beta\)-CD+Cu+\(SRS\) & 13.91 & 12.44 & 1.47 & 10.94 & 8.78 & 2.61 \\ \(\beta\)-CD+Cu+\(SRS\) & 13.02 & 12.27 & 0.75 & 14.18 & 5.83 & 8.35 \\ \(\beta\)-CD+Cu+\(2 SRS\) & 12.41 & 12.27 & 0.14 & 12.50 & 8.79 & 3.71 \\ \(\beta\)-CD+Cu+\(2 RSR\) & 13.32 & 12.90 & 0.42 & 14.23 & 6.27 & 7.96 \\ \hline \end{tabular}
\end{table} 
Table 2: Various Structural Parameters Calculated from Optimized Structures (Å). Figure 5: Definitions of parameters for the rim of the \(\beta\)-CD. (**A**): A scheme showing the skeletal rim parameters. (**B**): Labels for the O\({}_{2}\), O\({}_{3}\), and C\({}_{6}\) atoms used in the discussion for measuring the skeletal rim parameters. A set of three distances measured for O\({}_{2}\) and O\({}_{3}\) in glucose 1 and glucose 4, 5 is shown in lines. They are used for measuring R\({}_{L}\) (max) and R\({}_{L}\) (min); for the small rim, C6 at opposite groups are measured. R\({}_{L}\) and R\({}_{S}\) refer to the value of the large rim and small rim, respectively. CD)(EZM)]\({}^{2+}\) complex are shown in Figure 6 and the corresponding binding free energy is calculated according to the following reactions. \[\text{EZM }+\left[\text{Cu}^{\text{II}}\text{(fi-CD)}\right]^{2+}\xrightarrow{ \Delta\text{C}_{1}}\left[\text{Cu}^{\text{II}}\text{(fi-CD)}\text{(EZM)}\right]^ {2+}\] (R1)  
\[\text{EZM }+\left[\text{Cu}^{\text{II}}\text{(fi-CD)}\text{(EZM)}\right]^{2+} \xrightarrow{\Delta\text{C}_{2}}\left[\text{Cu}^{\text{II}}\text{(fi-CD)}\text{( EZM)}_{2}\right]^{2+}\] (R2)  
Figure 6: Ball and stick model of optimized \(\beta\)-CD/Cu and one EZM molecule complex with side and bottom views and its energy. (**A**): \(RSR\)-EZM+\(\beta\)-CD+Cu 1; (**B**): \(RSR\)-EZM+\(\beta\)-CD+Cu 2; (**C**): \(SRS\)-EZM+\(\beta\)-CD+Cu 1; (**D**): \(SRS\)-EZM+\(\beta\)-CD+Cu 2; (**E**): Conformation comparison with (**C**) when \(SRS\)-EZM are replaced with \(RSR\)-EZM. The black arrows refer to the change of the binding pose from \(SRS\)-EZM to \(RSR\)-EZM. Color coding: copper, ice blue; fluorine, pink; nitrogen, dark blue; carbon, gray; oxygen, light red; hydrogen, white. The bond length (Å) was estimated for three O atoms. The H-bond was illustrated with dotted line in purple color and the H-bond length between the EZM and \(\beta\)-CD was estimated. For the \(RSR\)-EZM case, as shown in Figure 6A, the complex exhibits the lowest energy when the drug molecule was mainly stabilized by the edge of the large rim of \(\beta\)-CD. The Cu-O distances were 1.92 A, 1.92 A, and 2.74 A, all of which were derived from the interaction between the oxygens and the small rim of \(\beta\)-CD, leaving no space for the \(RSR\)-EZM molecule to enter from the small rim and coordinate with Cu. Meanwhile, the R\({}_{\rm L}\) (max) changed from 13.03 A to 14.17 A, providing other binding sites for the drug molecule where a H-bond forms between the oxygen on the drug and a hydrogen on the rim with a length of 1.75 A.  
Interestingly, there is another stabilizing pattern which contains two kinds of binding mode: the coordinate bond and the H-bond (Figure 6B).