2.1.1. β-CD/PX Interaction: Complex Formation in a 1:1 Host–Guest Stoichiometry

At first, the PX conformation was studied, and then the β-CD reported by Raffaini [22] was considered for the interaction between piroxicam and β-CD in a 1:1 stoichiometry considering possible host–guest inclusion arrangements without assuming any a priori inclusion complexes. Using a simulation protocol adopted in the previous work [20,21], four different starting geometries between piroxicam and the primary and secondary rim of β-CD are considered in the 1:1 stoichiometry as reported in Figure 1.

**Figure 1.** Side view of the four initial non-optimized geometries studied for the interaction between PX and β-CD with the primary rim and with the secondary rim at the top and the bottom, indicated respectively as (**a**–**d**). The two molecules are colored by atoms. Color codes: C atoms are grey, O atoms are red, N atoms are blue, S atoms are yellow, and H atoms are white.

These four initial geometries were optimized and after the initial energy minimizations, favorable host–guest complexes were formed. The final optimized arrangements found after these MM calculations are shown in Figure 2.

**Figure 2.** Side view of the 1:1 host–guest complexes formed by PX with β-CD, in the initial optimized geometries found after the MM calculations, starting from the four geometries reported in Figure 1 indicated respectively as (**a**–**d**). The β-CDs are green, the PX molecule is colored by atoms. Color codes: C atoms are grey, O atoms are red, N atoms are blue, S atoms are yellow, and H atoms are omitted for clarity.

After these initial energy minimizations, starting from all the four different geometries, MD runs were performed in implicit water and the final conformations assumed by the system at the end of each MD run were analyzed. Two different inclusion complexes were found, the most and the less stable host–guest inclusion complexes in the 1:1 stoichiometry being reported in Figure 3, while Table 1 reports the potential energy, the calculated interaction energies, and the information about the intermolecular and β-CD intramolecular H-bonds for all four optimized geometries. In Figure S1, the two metastable geometries reported in Table 1 indicated as B and C D are shown. The animation of the MD runs is shown in Supplemtary Information SI.

**Figure 3.** The side view and the top view with intermolecular H-bonds (light blue dotted line) of the 1:1 host–guest complexes formed by PX with β-CD (**A**) in the most stable and (**C**) in the less stable optimized geometries found after the MM, MD calculations. The β-CD is green, the PX molecule is colored by atoms (color codes: C atoms are grey, O atoms are red, N atoms are blue, S atoms are yellow, and in the side view, H atoms are omitted for clarity). Below, the conformation of the optimized isolated PX is reported with the diagnostic hydrogen highlighted.


**Table 1.** Potential energy and interaction energy in kJ/mol calculated in the optimized geometries assumed at the end of the MD runs for the most and the less stable final geometries. Intermolecular β-CD/PX H-bonds and intramolecular β-CD H-bonds are reported.

As reported by Fronza et al. [17] using NMR experiments, two different inclusion complexes having different stability were found. The most stable geometry reported in Figure 3 (geometry A) displays the pyridyl aromatic part of PX included in the hydrophobic cavity of β-CD near the primary rim interacting with its hydrogens, while the second geometry of Figure 3 (geometry C) is less stable, and displays the pyridyl moiety included in the hydrophobic β-CD cavity facing the secondary rim interacting with the latter hydrogens. The most stable geometry has an interaction energy equal to −173.2 kJ/mol, while the other one is less stable by 10 kJ/mol; similar favorable interactions stabilize these host–guest complexes thanks to the hydrophobic interaction in the β-CD cavity and to the H-bonds at the primary and especially at the secondary rim. It is important to underline that these theoretical results are in good agreement with the NMR data reported by Fronza et al. [16] who proposed two different inclusion compounds. It is interesting to note that these two inclusion complexes are also found when β-CD are crosslinked in the PMA NS model as it will be reported later in Section 2.2. Guo et al. [18] proposed a partial inclusion due to the absence of a Nuclear Overhauser Effect NOE of H-2, H-3 guest hydrogens (see Figure 3, H-2 and H-3 are the hydrogens of the PX phenyl ring) and diagnostic hydrogen β-CD, suggesting that the dimension of β-CD is too small to host the whole PX. In fact, in the most stable geometry with a 1:1 stoichiometry reported in Figure 3 (geometry A), the hydrogens of the phenyl ring are far from the β-CD cavity; only in the less stable and less populated inclusion complex, the phenyl ring is in the midst of the hydrophobic cavity, relatively closer to H-5' protons, while the pyridyl moiety is exposed to the solvent far from the secondary rim (geometry C in Figure 3). Guo et al. reported the 2D-ROESY (Rotating-Frame Overhauser Effect Spectroscopy) spectrum. In this spectrum, strong sizable contacts between the guest H-6, H-7, and H-8 protons (the hydrogens of the pyridyl moiety) and the host H-3' and H-5' are shown, probably due to deeper insertion, indicating that both phenyl and pyridyl rings are in the β-CD cavity. For this reason, Guo also suggested the presence of a β-CD and PX complex in a 2:1 stoichiometry with CDs facing their secondary rims. It will be important to carry out new reliable NMR experiments for the determination of the structure of cyclodextrin inclusion complexes in a solution [31], in particular, off-resonance ROESY or T-ROESY (Transverse Rotating-frame Overhauser Enhancement Spectroscopy) experiments must be carried out in order to determine the structure of complexes in a solution. In this work, increasing the CD concentration, a theoretical study of host–guest complexes in a 2:1 stoichiometry was carried out as reported in the next Section.
