## 1 Introduction
Although the metal ion can change the binding mode between analytes and \(\beta\)-CDs by affecting the size and shape of the cavity, the detailed mechanisms about a big ternary cluster (including \(\beta\)-CDs, metal ions and analytes) underlying the separation remain unknown. This results in the screening of the type and/or size of the cavities and ions, as well as their combinations and other relevant conditions still being based on trials instead of rational design, making the separation process tedious and expensive. For example, the influence of hydrogen bonding in the chiral recognition process is especially difficult to analyze due to the limitations of the experimental method [18]. Therefore, finding the binding mode and chiral recognition mechanism between the analyte and selector is of great significance for both fundamental studies and potential applications, like designing the chiral reference individually. To understand its selective mechanism in molecular details, there are several available methods, including nuclear magnetic resonance (NMR) [19] and computational methods [11], applied to predict ligand selectivity in more studies. Compared with NMR, the theoretical calculation methods, including quantum mechanics (QM), molecular dynamics (MD), molecular docking, and quantitative structure activity relationships (QSARs), have been used to optimize all the systems in gas phase efficiently. These methods are acknowledged to be valuable tools for the molecular recognition mechanism correlation and owns different features. Density functional theory calculations (DFT) were used to perform a full geometry optimization from quantum mechanics aspects, while MD can provide the time-dependent trajectory of the host and guest molecules, revealing their binding mode from molecular mechanics aspects. The combination of the two methods is often used in studies. However, most computational calculations about \(\beta\)-CD are limited to small systems, and it is necessary to extend their application for more complicated clusters. Our intention for this study is to propose a new chiral separation method by using \(\beta\)-CD/metal complex as the selector in MS and to find a \"modular, robust molecular modelling workflow\" for how to analyze the formation of \(\beta\)-CD/metal and enantiomer drugs in general as well as revealing the molecular recognition mechanisms, which is a fundamental study for choosing and designing chiral selector. Ezetimibe (EZM), a potent cholesterol absorption inhibitor, has been applied to cure diseases related to the overabundance of cholesterol in individual or combined therapies. There are three asymmetric carbon atoms in EZM, thus producing eight different enantiomers. The desired one is designated as 3(\(S\)), 4(\(R\))-1-(4- fluorophenyl)-[3-(4-fluorophenyl)-3(\(S\))-hydroxpropyl]-(4-hydroxyphenyl)-2-azetidinone (\(SRS\)-EZM), as shown in Figure 1, while the others are presented as a chiral impurity without pharmacological effects. HPLC is the common method to separate them with obvious disadvantages of low efficiency and high expense. It would therefore be valuable to develop a new technique capable of higher efficiency. We have reported that the entecavir enantiomers were discriminated using the tandem MS of metal coordination trimeric complexes and the MS method was compared with the HPLC method in the USP convention. The latter requires up to 11 min in gradient elution, while the MS method requires no more than 2 min [9]. In this study, we take EZM as an example for the effort of finding an effective way to analyze the enantiomers. CR method in MS was performed to achieve chiral separation and Cu is chosen to act with \(\beta\)-CD by trial. DFT and MD simulations were performed to understand their interaction details.