H Nouioua

T Abbaz

B Harkati

A K Gouasmia

D Villemin

Theoretical Investigation on Inclusion Complex of (s)-2-Isopropyl-1-(o-nitrophenyl) Sulfonyl) Aziridine with β-Cyclodextrin

Keywords: β-Cyclodextrin, AZ, DFT, NBO and NCI

Theoretical Investigation on Inclusion Complex of (s)-2-Isopropyl-1-(o-nitrophenyl) Sulfonyl) Aziridine with β-Cyclodextrin

H Nouioua, T Abbaz, B Harkati, A K Gouasmia, Didier Villemin

INTRODUCTION

Cyclodextrins (CDs) are cyclic oligosaccharides that can be obtained artificially by enzymatic conversion of amylose using the enzyme cyclodextrin glycosyltransferase (CGTase) of bacterial origin. The three most commonly used CDs are α-CD, β-CD, and γ-CD, which consist of 6, 7, and 8 subunits of D-glucopyranose, respectively [START_REF] Szejtli | Introduction and general overview of cyclodextrin chemistry[END_REF][START_REF] Szejtli | Past, present and futute of cyclodextrin research[END_REF] linked together by α-glycosidic bonds (1 → 4). Thus the cavity formed has non-polar carbonate and hydrophobic environment, while the outer part contains many hydroxyls *Corresponding author. E-mail: hadjer.nouioua@univtebessa.dz groups, which leads to the solubility of cyclodextrins in an aqueous medium. Due to the presence of mentioned nonpolar cavity, cyclodextrins are able to form inclusion complexes in an aqueous medium with a variety of hydrophobic host molecules; the formation of complex depends on a proper match between the size of the host molecule and the cyclodextrin molecule. In this article, β-CD (Fig. 1a) has been used as a host due to its non-toxicity to the human organism. It has been used frequently in the food, pharmaceutical, and cosmetic industries.

Aziridine is an interesting class due to its chemical reactivity. They are valuable natural and/or synthetic organic compounds that are widely used to access many

The present work aims to study the theoretical chemistry applied to organic systems such as host/guest inclusion complexes. In literature, different molecular modeling computational methods have been used to study the complexation of the host β-cyclodextrin molecule (β-CD) with the guest (S)-2-Isopropyl-1-(o-nitrophenyl) sulfonyl) aziridine molecule (AZ). Among such methods are semiempirical (PM3) and Density Functional Theory (DFT) calculations in gas and aqueous phases. The present paper focuses on complexation, interaction, deformation energies determination, besides geometries, electronic structure, and chemical reactivity to describe the changes of AZ during encapsulation in two phases and at two orientations. Long-range corrected hybrid functional (WB97X-D/6-31G (d) basis) was used and the results clearly indicate that the formed complex is energetically preferred in both phases. The orientation in which the guest molecule pointed toward the secondary hydroxyls of β-CD showed good compatibility with the experimental results. The Natural Population Analysis (NPA) charges obtained from NBO analysis were used in order to find out the possible coordination modes of the AZ compound with β-CD. Natural bond orbital analysis (NBO) and Non-covalent interaction (NCI) analysis were performed on the β-medicines and bioactive products [START_REF] Keniche | Synthesis of a novel class of phosphono aziridines as interesting antibacterial agents[END_REF][START_REF] Kurmich | WO 2009015067 A2 20090129[END_REF].

Molecular modeling is a technique that not only can represent the chemical properties and chemical reactions, but also to manipulate the structure of model compounds in two or three dimensions. Actually, there are a large number of theoretical methods used in the molecular modeling of supramolecular systems. Among these methods are molecular mechanics (MM), molecular dynamics (MD), semi-empirical methods, and DFT methods that are widely used for large systems to determine the graphical representation of the geometry or configuration of the atoms of a molecule and assessing the physical and chemical properties of the molecule. Molecular modeling associated to a graphical representation of the stereochemistry allows interpretation of physical and chemical phenomenon, suggesting new experiments, and thus analyzing the results in a more significant way than the traditionally used experiments. In fact, both approaches, pure theoretical and experiment, are complementary.

This work is composed of two parts: in the first part, the processes of AZ inclusion in the β-CD cavity are examined using the semi-empirical PM3 method for determining minimum energy structures. In the second part, the more stable complex, obtained through PM3 calculations, are improved by the density functional theory (DFT) using the functionals B3LYP [START_REF] Kim | Comparison of density functional and MP2 calculations on the water Monomer and dimer[END_REF][START_REF] Stephens | Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields[END_REF], WB97X-D [START_REF] Head-Gordon | Long-range corrected hybrid density functional with damped atom-atom dispersion corrections[END_REF], and B97D3 [START_REF] Grimme | Effect of the damping function in dispersion corrected density functional theory[END_REF]9], and 6-31G(d) basis set in gas and aqueous phases. In this part, complexation, interaction, and deformation energies, geometries, thermodynamic parameters, frontier molecular orbitals, the global indices of reactivity, the (NPA) atomic charges, and natural bond orbital (NBO) are calculated. We also systematically compare the chemical shifts deviations obtained from Gauge-Including Atomic Orbital calculations (GIAO) and corresponding experimental values of 1H NMR [START_REF] Keniche | NMR investigation of the complexation of (S)-2isopropyl-1-(o-nitrophenyl)sulfonyl)aziridine with βcyclodextrin[END_REF].

Finally, analysis of non-covalent interactions (NCI) as a robust approach for evaluating intermolecular interactions is considered.

COMPUTATIONAL DETAILS

Quantum mechanical calculations were performed using density functional theory (DFT) applying the functionals B3LYP [START_REF] Kim | Comparison of density functional and MP2 calculations on the water Monomer and dimer[END_REF][START_REF] Stephens | Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields[END_REF], WB97X-D [START_REF] Head-Gordon | Long-range corrected hybrid density functional with damped atom-atom dispersion corrections[END_REF], and B97D3 [START_REF] Grimme | Effect of the damping function in dispersion corrected density functional theory[END_REF]9], and the 6-31G(d) basis set in the gas and aqueous phases. Gaussian 09 [START_REF] Frisch | Revision C.01[END_REF] and MOPAC 2016 [START_REF] James | Stewart Computational Chemistry[END_REF] software were used. The initial structures of the guest AZ and the host β-CD were retrieved from PUBCHEM compound database [START_REF] Bolton | Integrated platform of small molecules and biological activities[END_REF] and Chem office3D Ultra (version10, Cambridge Software) [START_REF]Chem-Office 3D Ultra[END_REF], respectively The AZ/β-CD complex was generated by Hyperchem 7.5 [15] molecular modeling software. The AZ and β-CD structures were optimized by the semi-empirical PM3 method [START_REF] Stewart | Optimization of parameters for semiempirical methods I[END_REF]. Semi-empirical calculations were first performed using MOPAC 2016 [START_REF] James | Stewart Computational Chemistry[END_REF], and the visualization and treatment of results were done using Gauss view 5.0 [START_REF] Roy | Gauss view 5.0[END_REF]. The optimized host and guest structures are shown in Fig. 1.

The coordinate system used to define complexation process is shown in Fig. 2. To inclusion the guest AZ molecule inside the β-CD, methods described in the literature have been followed [START_REF] Liu | Use of quantum chemical methods to study cyclodextrin chemistry[END_REF][START_REF] De Sousa | A DFT investigation on the host/guest inclusion process of prilocaine into β-cyclodextrin[END_REF][START_REF] Rahim | Driving forces and electronic structure in β-cyclodextrin/3,3′diaminodiphenylsulphone complex[END_REF][START_REF] Djilani | Theoretical investigation to characterize the inclusion complex of α-lipoic acid and β-cyclodextrin[END_REF][START_REF] Guendouzi | Quantitative conformational stability host-guest complex of carvacrol and thymol with β-cyclodextrin: a theoretical investigation[END_REF]. The β-CD host is positioned at the XY plane and its center is defined as the origin of the systems coordinates. The secondary hydroxyl groups of β-CD are oriented in the positive direction of the Z axis, and then the mass center of the guest molecule AZ is placed at the XYZ reference center. The center of the β-CD host is located at the origin of the reference frame, O (0, 0.0) and β-CD is in fixed position. The guest to host is then moved along the Z axis from -5 to +5 A0 with 1 Å step. Figure 2 shows two directions for insertion of guest molecule into the β-CD host molecule. This allows us to see the effects of the two types of hydroxyls: Orientation A, in which the aromatic ring is oriented toward the secondary hydroxyls of β-CD, and Orientation B, in which the aromatic ring is oriented towards the basic hydroxyls of β-CD.

To define the host-guest interaction in the optimized geometries, several energetic expressions were used: complexation energy [START_REF] Nouar | Theoretical study of inclusion complexation of 3amino-5-nitrobenzisothiazole with β-cyclodextrin[END_REF], interaction energy [START_REF] Bouhadiba | Host-guest interaction between tyrosine and β-cyclodextrin: Molecular modeling and nuclear studies[END_REF][START_REF] Himri | Density functional theories study of the interactions between host β-cyclodextrin and guest 8-Anilinonaphthalene-1-sulfonate: Molecular structure, HOMO, LUMO, NBO, QTAIM and NMR analyses[END_REF], and deformation energy [START_REF] Nouar | Molecular modeling investigation of para-nitrobenzoic acid interaction in β-cyclodextrin[END_REF].

The complexation energy is defined as the difference between the energy of the complex and the energy of the individual components in their optimized geometries, Eq. ( 1).

ΔE complexation = E complex -[E β-CDfree + E AZ free ] (1)
Where E complex represents the energy of the complex, E β-CD represents the energy of β-CD before the complexation, and E AZ represents the energy of the AZ guest molecule before the complexation. Interaction energy represents the interaction between the host molecule and the guest molecule in the inclusion complex (Eq. ( 2)).

ΔE interaction = E complex -[E β-CDsp + E AZsp ] (2)
Where E complex represents the energy of the complex, E β-CD represents the energy of β-CD after the complexation, and E AZ represents the energy of the guest molecule after the complexation.

The last energy is the deformation energy of each host and guest component during the formation of the complex. It is defined as the difference between the energy of the fully optimized component compared to its energy in the complex (Eqs. (3) and ( 4)).

E deformation ( β-CD ) = E β-CD sp -E β-CD free (3)
E deformation ( AZ ) = E AZ sp -E AZ free (4)

RESULTS AND DISCUSSIONS Energies

The graphical presentation of the energy changes for the insertion of AZ in the β-CD are shown as two curves in Fig. 3. From these curves, it is observed that the minimum energy of the more stable structures falls at Z = -3 Å, and Z = -3 Å for the two orientations A and B, respectively. The corresponding complexation energies are: -16.260 kcal mol - 1 and -17.063 kcal mol -1 for orientations A and B, respectively. After that, the resulting complex was optimized at a high computational level using the following functionals: B3LYP/6-31G(d) and WB97X-D/6-31G(d) and B97D3/6-31G(d)) in gas and aqueous phases. The calculation of the different energy conditions for the two orientations were reported and compared in Table 1. From Table 1, it is observed that, in contrast to PM3 semiempirical calculations, the interaction energy is in favor of ) method. For the two methods, WB97X-D/6-31G(d) and B97D3/6-31G(d), the dispersion effect is an important factor to study the supramolecular systems; weak dispersion forces increase with increasing the number of atoms and the molecular weight [START_REF] De Sousa | A DFT investigation on the host/guest inclusion process of prilocaine into β-cyclodextrin[END_REF]. The effects of electron correlation play an important role on the nature of intermolecular interaction probably having a considerable contribution to dispersion forces [START_REF] De Sousa | A DFT investigation on the host/guest inclusion process of prilocaine into β-cyclodextrin[END_REF]. The solvent effect is indicated by energy difference between the gas and aqueous phases. The results of the deformation energies of the gas and aqueous phases calculated by the three functionals are shown in Table 1. From the results, the deformation energy of the β-CD molecule is always higher than that of the AZ molecule in both orientations, A and B. This confirms that the flexibility of the β-CD structure plays an important role in increasing the intermolecular interaction and affects the stability of the whole system upon complexation [START_REF] Himri | Density functional theories study of the interactions between host β-cyclodextrin and guest 8-Anilinonaphthalene-1-sulfonate: Molecular structure, HOMO, LUMO, NBO, QTAIM and NMR analyses[END_REF]. Especially, the primary hydroxyl groups of β-CD play an important role in the formation of bonds with AZ (see Fig. 5).

We also note that the deformation energy of the β-CD molecule calculated by the classic B3LYP method (9.52 kcal mol -1 ) is lower than that obtained using the WB97X-D/6-31G(d) (12.84 kcal mol -1 ) and B97D3/6-31G(d) (12.20 kcal mol -1 ) methods. This indicates that WB97X-D/6-31G(d) and B97D3/6-31G(d) predict better optimized geometries than the traditional B3LYP method.

To improve the accuracy of our theoretical results, from the computation of optimized geometries, the interaction energy was corrected considering the basic set superposition error (BSSE) [START_REF] Van Duijneveldt | State of the art in counterpoise theory[END_REF] using the counterpoise method [START_REF] Boys | The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors[END_REF] through (Eq. ( 5)).

ΔE interaction = E complex -[E β-CDsp + E AZsp ] + BSSE (5)
BSSE corrected energies are shown in brackets in Table 1.

Geometry Optimization

According to our results, most of the geometric parameters have approximately the same values in both the gas state and the aqueous state. This let us to provide a single interpretation in the gas axis. Tables 2 and3 report the geometrical parameters (bond lengths, bond angles, and dihedral angles) of the AZ and β-CD molecules before and after complexation, which are related to the most stable This means that the guest AZ in the orientation A must be profiled to fit the host β-CD cavity and form a more stable inclusion complex. This result was confirmed by deformation energies (see Table 1). On the other hand, the distances between the primary and secondary hydroxyls' oxygens of β-CD and AZ, before and after complexation, (Table 3) show significant distortion in the β-CD lumen compared to its initial geometry (see Fig. 5). In the orientation 5). This explains why the interaction energy of inclusion in the orientation A (-52.35 kcal mol -1 ) is less than that in the orientation B (-46.56 kcal mol -1 ) in both phases using all three functionals.

Thermodynamic Properties

Calculations of standard thermodynamic parameters were performed using harmonic vibrational analysis [29]. Calculations were performed in vacuum and water at 1 atm pressure and temperature of 298.15 K using WB97X-D/6-31G(d), and B97D3/6-31G(d) methods. The thermodynamic quantities of the AZ/β-CD complex, such as the enthalpy change (ΔH°), the thermal Gibbs free energy (ΔG°), and entropy contribution (ΔS°) are summarized in Table 4.

It was observed that the enthalpy values (ΔH°) are negative in both orientations, and these differences indicate that the inclusion process is enthalpically favorable. On the other hand, the enthalpy differences of the orientation A (ΔH° = -48.67 kcal mol -1 ) were more negative than that in orientation B (ΔH° = -42.89 kcal mol -1 ), which is attributed to stronger van der Waals interactions [START_REF] Himri | Density functional theories study of the interactions between host β-cyclodextrin and guest 8-Anilinonaphthalene-1-sulfonate: Molecular structure, HOMO, LUMO, NBO, QTAIM and NMR analyses[END_REF] between AZ and β-CD in deeper penetration of the guest molecule into the hydrophobic host. Values of ΔG° = -60.01 cal mol -1 K -1 are negative and this indicates that the process of AZ inclusion in β-CD is spontaneous at 1 atm and 298.15 K. when the system is well arranged, the results of our theoretical calculations ΔG° < 0 is in good agreements with the data in the literature [START_REF] Keniche | NMR investigation of the complexation of (S)-2isopropyl-1-(o-nitrophenyl)sulfonyl)aziridine with βcyclodextrin[END_REF]. We can also see that the entropy (ΔS°) has a negative change in both orientations. This indicates that the formation of the complex is an exothermic process resulting from enthalpy [START_REF] Rahim | Driving forces and electronic structure in β-cyclodextrin/3,3′diaminodiphenylsulphone complex[END_REF]. Due to steric barrier, the negative change of the entropy (ΔS°) caused by molecular geometrical shape that limits the free shift of β-CD cavity and rotation of AZ molecule [START_REF] Rahim | Driving forces and electronic structure in β-cyclodextrin/3,3′diaminodiphenylsulphone complex[END_REF].

Frontier Molecular Orbitals (FMOs)

The occupied HOMO and unoccupied LUMO frontier molecular orbitals [START_REF] Senthilraj | Molecular structure, vibrational spectra, HOMO, LUMO and NMR studies of methylphenylcyclopropenone based on density functional theories[END_REF] play an important role in understanding the effect of guest molecule encapsulation within the host. HOMO is the electron donor and LUMO is the electron acceptor [START_REF] Gümüş | Quantum chemical calculations on the geometrical, conformational, spectroscopic and nonlinear optical parameters of 5-(2-chloroethyl)-2,4-dichloro-6methylpyrimidine[END_REF][START_REF] Gümüş | Effects of donor-acceptor groups on the structural and electronic properties of4-(methoxymethyl)-6-methyl-5nitro-2-oxo-1,2-dihydropyridine-3-carbonitrile[END_REF]. Results for the energies of HOMO and LUMO, and ΔE (HOMO-LUMO) obtained by WB97X-D/6-31G(d) and B97D3/6-31G(d) methods in the gas and aqueous phases are shown in Table 4. The energy gap ΔE (HOMO-LUMO) is an important measure of stability. The higher chemical values of ΔE (HOMO-LUMO) indicate higher stability and lower reactivity [33][START_REF] Ramalingam | Spectroscopic (FT-IR/FTRaman) and computational (HF/DFT) investigation and HOMO/LUMO/MEP analysis on 2-amino-4chlorophenol[END_REF][START_REF] Karelson | Quantumchemical descriptors in QSAR/QSPR studies[END_REF]. The values of ΔE (HOMO-LUMO) obtained by the two methods in the gas and aqueous phases of the AZ/β-CD complex are -0.291 eV for orientation A and -0.297 eV for orientation B. This means that orientation A is more stable than orientation B. These results are in good agreement with the complexation energy results of the orientation A (41.66 kcal mol -1 ) and the orientation B (-37.85 kcal mol -1 ). The Frontier orbitals of AZ/β-CD in the two obtained phases were calculated by B97D3/6-31G(d). Results indicate that HOMO orbit is localized on the host, and the LUMO orbit is localized on the guest molecule, which means mutual interactions are generated between β-CD and AZ (see Fig. 6).

The Global Indices

The energy gap between HOMO and LUMO can be used in determining the global indices of the reactivity such as electronegativity (χ), electronic potential (μ), hardness (η), and global electrophilicity index (ω). Indices of the reactivity were calculated by the methods WB97X-D/6-31G(d) and B97D3/6-31G(d) in gas and aqueous phases using the following equations: two phases, and the two orientations. This demonstrates that the complexation of the AZ in the β-CD cavity is a spontaneous phenomenon. Using WB97X-D/6-31G(d) method in the gas and aqueous phases, the electronic chemical potential of the free AZ molecule was less than that of the free β-CD. This difference allows the charge transfer from the β-CD, with high electronic chemical potential (-0.10/-0.10 eV), to AZ, with low electronic chemical potential (-0.18/-019 eV) [START_REF] De Almeida | Experimental and theoretical investigation of epoxide quebrachitol derivatives through spectroscopic analysis[END_REF]. From the values in the Table 4, it is clear that the chemical hardness of AZ/β-CD is important in both orientations, confirming the charge transfer. From the results obtained for the total global electrophilicity index, we can conclude that the compound is electrophilic.

μ = (E HOMO + E LUMO )/2 (6) χ = -μ = (E HOMO + E LUMO )/2 (7) η = (E LUMO -E HOMO )/2 (8) ω = μ 2 /2η (9)

Atomic Charges

The charge distribution in the AZ/β-CD complex was analyzed using two population analysis methods: The Mulliken Population Analysis (MPA), and NPA; our goal was to compare them and assess their utility. Mulliken atomic charge analysis was performed to identify the partial atomic charges that o allow the qualitative understanding of the structures and reactivity of molecules. The charge distributions of atoms calculated by the NBO approach are presented in Table 5. WB97X-D/6-31G(d) and B97D3/6-31G(d) methods were used to study the free and encapsulated AZ in the gas phase and in different orientations. From these results, it can be seen that all the atomic charges of AZ were altered upon complexation with the host β-CD. The results showed that the positive charges were localized on hydrogen (H 171: 0.177/0.164) and sulfur atoms (S 162: 1.361/1.285). The negative charges were localized on oxygen (O 160: -0.356/-0.331) and carbon atoms (C 170: -0.155/-0.128). Nitrogen atoms can be either positive (N 158: 0.405/0.360), due to the presence of high electronegative oxygen atoms (O 159: -0.396/-0.368 and O 160: -0.356/-0.331) in the adjacent position, or negative (N 163: -0.577/-0.540), due to the attachment of the positively charged sulfur atom (S 162: 1.361/1.285). We can also see that in both orientations, the H atoms (H 166, Orientation A Orientation B Fig. 6. The Frontier orbitals HOMO and LUMO of the AZ/β-CD complex was obtained using the B97D3/6-31G(d) method in the gas phase.

H 167, H 171, H 174) of AZ interact with the internal part of β-CD increasing their atomic charges. A significant change in trend was obtained in orientation A: C 168 (-0.001/0.009-0.029/-0.02). The data shows that the charge transfer in the orientation A (0.036) is greater than in the orientation B (-0.049), so the AZ/β-CD complex is more stable in the orientation A than in the orientation B [START_REF] De Almeida | 1 H NMR analysis of Omethyl-inositol isomers: A joint experimental and theoretical study[END_REF]. A method of natural population analysis has been developed to calculate atomic charges and orbital populations of molecular wave functions in general atomic orbital basis sets [START_REF] Reed | Natural atomic orbitals and natural population analysis[END_REF]. For the AZ/β-CD complex, the net charges are calculated by Natural Population Analysis (NPA). The calculated natural atomic charge values were obtained from the Natural Bond Orbital Analysis (NBO) [START_REF] Parr | Absolute hardness: companion parameter to absolute electronegativity[END_REF] and are listed in Table 6. The natural population analysis is an alternative to conventional Mulliken population analysis, and seems to exhibit improved numerical stability to better describe the electron distributions in AZ/β-CD complex.

Natural Bond Orbital Analysis (NBO)

In order to determine intra-and intermolecular bounds and interactions [START_REF] Parr | Electronegativity, the density functional viewpoint[END_REF] between guest AZ and host β-CD, to identify, and quantify the different donor-acceptor interactions of the host/guest partners, we used the energy E (2) in Eq. [START_REF] Keniche | NMR investigation of the complexation of (S)-2isopropyl-1-(o-nitrophenyl)sulfonyl)aziridine with βcyclodextrin[END_REF]; if E (2) is larger, the interactions between donors and acceptor is intense [START_REF] Liu | Chargetransfer interaction: A driving force for cyclodextrin inclusion complexation[END_REF]. The delocalization of the electron density between occupied orbitals and unoccupied orbitals is related to the stabilizing donoracceptor interaction [START_REF] Abdelmalek | Computational study of inclusion complex formation between carvacrol and βcyclodextrin in vacuum and in water: Charge transfer, electronic transitions and NBO analysis[END_REF].

i j j i F i q E     ) , ( ) 2 ( (10)
Where q i is the donor orbital occupancy, ε i and ε j are diagonal elements, and F ij is the off diagonal NBO Fock matrix element. The donor-acceptor interactions and their corresponding E (2) energies are shown in Table 7. As shown in Table 7, WB97X-D method gives the best values of E (2) . For orientation A, an interaction between the free doublet (LP) of donor orbital of the oxygen atom (O 159) of AZ and the anti-binding acceptor orbital σ* (O 33-H 107) of β-CD positioned at 1.87 Å with a stabilization energy E (2) of 12.06/10.62 kcal mol -1 in the gas phase, another interaction is observed between the free doublet (LP) of donor orbital of oxygen atom (O 164) and anti-binding acceptor orbital σ * (O 44-H 117) positioned at 2.02 Å with a stabilization energy E (2) of 4.89/3.43kcal mol -1 . The same interaction was obtained between the free doublet (LP) of the donor orbital of oxygen atom (O 159) and the anti-binding acceptor orbital σ* (O 69-H 140) that was positioned at 1.91 Å. In orientation B, lower energy value of 6.68/6.21 kcal mol -1 was obtained compared to orientation A. Orientation A is strongly stabilized by the formation of hydrogen. Intermolecular hydrogen bonds exist in the geometrical structures of both orientations (Fig. 7).

From the results of NBO calculations, we can confirm that the intermolecular hydrogen interactions and charge transfer between occupied and unoccupied orbitals of host/ guest have major contribution to the stabilization of the complex. of the formed molecule and the orientation of the embedded guest molecule. To better explore the introducing guest particles into the lumen of the host molecule, we calculated the chemical shifts δ. In this part, variability in H NMR chemical transitions was studied using the Gauge-Including Atomic Orbital (GIAO) approach [START_REF] Zaboli | The analysis of electronic structures, adsorption properties, NBO, QTAIM and NMR parameters of the adsorbed hydrogen sulfide on various sites of the outer surface of aluminum phosphide nanotube: A DFT study[END_REF]. The B3LYP/6-31G(d) method was applied using single-point calculations on geometries optimized by WB97X-D/6-31G(d) and B97D3/6-31G(d). The method was found suitable for the theoretical Proton NMR spectroscopy of organic molecules [START_REF] Erdogdu | FT-Raman NMR Spectra and DFT Simulations of 4-(4fluoro phenyl)-1H-imidazole1[END_REF][START_REF] Yüksek | Synthesis and GIAO NMR calculations for some novel4-heteroarylidenamino-4,5-dihydro-1H-1,2,4triazol-5-one derivatives: Comparison of theoretical and experimental 1 H and 13 C-chemical shifts[END_REF]. NMR chemical shifts (δ) were calculated by subtracting the nuclear magnetic shielding tensors of protons in molecules of interest from those in tetramethyl silane (TMS) as a reference. Chemical shift (δ) was calculated by the equation: [START_REF] Frisch | Revision C.01[END_REF] Changes in the chemical shifts of the isolated AZ guests and their inclusion complexes are shown in Table 8 and Fig. 8.

H NMR Analysis

     TMS
The inclusion of AZ in the β-CD cavities was evidenced by the change in the chemical shifts of the last encapsulated protons with respect to the chemical shifts of the same protons in the free form. The values of the calculated and the basis of our theoretical results, the orientation A can be considered as the most convenient structure.

Non-covalent Interaction Analysis (NCI)

The non-covalent interaction analysis method provides a graphic visualization of regions in which non-covalent interactions such as hydrogen bonds, van der Waals interactions, and repulsive steric interactions [START_REF] Zahedi | Following the molecular mechanism of decarbonylation of unsaturated cyclic ketones using bonding evolution theory coupled with NCI analysis[END_REF][START_REF] Venkataramanan | Density functional theory study on the dihydrogen bond cooperativity in the growth behavior of dimethyl sulfoxide clusters[END_REF] produce in real space. Recently, the NCI analysis has been used to identify the weak interactions from the AIM analysis [START_REF] Venkataramanan | Nature of bonding and cooperativity in linear DMSO clusters: A DFT, AIM and NCI analysis[END_REF][START_REF] Venkataramanan | Intermolecular interactions in nucleobases and dimethyl sulfoxide/water molecules: A DFT, NBO, AIM and NCI analysis[END_REF]. In the 3D spatial visualization of NCI isosurface shown in Fig. 9, the color-coding scheme is as follows: Van der Waals interactions are indicated by a green spot, strong hydrogen bond interactions are represented by a blue spot, and the repulsive steric forces are visualized by the red spot. From the NCI isosurface (Fig. 9), we observed green spots between AZ and β-CD in the orientations A and B, indicating weak attraction due to the van der Waals interaction. We also observed some blue spots for hydrogen bond interactions between guest and host. There was also the appearance of weak van der Waals, and weak intramolecular hydrogen bond interactions in β-CD, between the primary and secondary hydroxyls, and steric repulsions in the aromatic rings of AZ and β-CD.

CONCLUSIONS

This theoretical work explored the detailed study of the inclusion complex of AZ/β-CD. The DFT functionals B3LYP, WB97X-D, and B97D3, and 6-31G(d) basis set were used in both gas and aqueous phases. Orientation A was more preferable than orientation B in both the gas and aqueous phases, which is in good agreement with the experimental results. The best results were obtained using WB97X-D and B97D3/6-31G(d). Geometry optimization calculations for the complex in the aqueous phase were almost similar to those in the gas phase. The analysis of the thermodynamic calculations indicated the negative valued for ΔG, ΔH, and ΔS, suggesting that the formation of AZ/β-CD inclusion complexes in vacuo is a spontaneous and enthalpy-driven process. The charge distribution calculated using NBO method indicated that when the guest molecule interacts with β-CD, its charge distribution changes. The NBO and NCI analysis showed that the driving forces for the formation of complexes were formation of intermolecular hydrogen bonds. Finally, the results of the RMN and GIAO calculations were in agreement with experiment.

Fig. 1 .

 1 Fig. 1. Molecular structures and atom numbering for β-CD (a) and AZ (b).

Fig. 2 .

 2 Fig. 2. Coordinate systems used to define the complexation process for both orientations.

Fig. 3 .

 3 Fig. 3. Complexation energies of the inclusion of AZ into β-CD optimized at different positions Z using (PM3 calculations).

Fig. 4 .

 4 Fig. 4. Geometrical structures of the most stable complexes obtained from B3LYP/6-31G(d) (a, b), WB97X-D/6-31G(d) (a', b') and B97D3/6-31G(d) (a", b") calculations for AZ/β-CD in gas phase.

Fig. 5 .

 5 Fig. 5. Geometric structures of the free β-CD (a) and the AZ/β-CD complex (b, c) in the orientations A and B calculated by the method WB97X-D/6-31G(d) in the gas phase.

1 H

 1 NMR spectroscopy is one of the most useful techniques for studying host-guest systems, as it provides very interesting microscopic information about the structure

Fig. 8 .Fig. 7 .

 87 Fig.8. Chemical shifts experimental[START_REF] Keniche | NMR investigation of the complexation of (S)-2isopropyl-1-(o-nitrophenyl)sulfonyl)aziridine with βcyclodextrin[END_REF] and calculated of free AZ protons and inclusion complexes AZ/β-CD by the GIAO approach, B3LYP/6-31G(d).

Table 1 .

 1 The Different Energies of β-CD/AZ in the Gas and Aqueous Phase were Calculated by

	Methods: B3LYP/6-31G(d), WB97X-D/6-31G(d), and B97D3/6-31G(d)
		Gas phase	Aqueous phase
		Orientation A	Orientation B	Orientation A	Orientation B
	B3LYP/6-31G(d)
	ΔE complexation	-19.60	-6.80	-11.37	-3.52
	ΔE interaction	-25.58 (-12.01)	-8.74 (0.31)	-14.82	-4.42
	E DEF(Host)	9.52	1.38	5.79	0.53
	E DEF(Guest)	-3.54	0.56	-2.34	0.36
	WB97X-D/6-31G(d)
	ΔE complexation	-41.06	-37.02	-31.85	-31.38
	ΔE interaction	-52.35 (-39.24)	-46.56 (-32.00)	-40.37	-38.67
	E DEF(Host)	12.84	6.74	9.05	4.53
	E DEF(Guest)	-1.53	2.80	-0.52	2.75
	B97D3/6-31G(d)
	ΔE complexation	-41.66	-37.85	-33.41	-33.89
	ΔE interaction	-52.15 (-36.65)	-47.22 (-30.38)	-40.86	-39.77
	E DEF(Host)	12.20	6.66	8.17	3.77
	E DEF(Guest)	-1.70	2.70	-0.71	2.10

Table 2 .

 2 Geometric Parameters (Bond Lengths, Bond Angles and Dihedral Angles) for AZ before and after

	Inclusion in β-CD Calculated with B3LYP/6-31G(d)/WB97X-D/6-31G(d)/B97D3/6-31G(d) in the
	Gas Phase
			Gas phase
		AZ free	Orientation A	Orientation B
	Bond lengths (Å)
	O 164-O 161	2.54/2.52/2.56	2.52/2.49/2.53	2.53/2.51/2.54
	O 164-S 162	1.45/1.44/1.46	1.47	/1.45/1.47	1.45/1.44/1.46
	S 162-O 161	1.46/1.45/1.47	1.47	/1.45/1.48	1.47/1.45/1.47
	N 163-C 165	1.45/1.45/1.46	1.48/1.47/1.48	1.46/1.45/1.47
	Bond angles (°)
	S 162-O 164-C 151	42.10/41.96/41.92	38.89/38.00/37.84	42.04/42.35/42.02
	S 162-O 164-O 161	29.75/29.49/29.39	31.01/31.28/31.04	30.32/30.23/30.24
	S 162-N 163-O 164	33.20/33.32/33.54	33.15/33.34/33.50	33.18/33.22/33.43
	S 162-N 163-O 161	34.01/34.20/33.87	30.83/30.68/30.16	33.24/33.16/32.53
	N 158-O 159-O 160	27.31/27.18/27.00	27.39/27.26/27.07	27.33/27.44/27.34
	Dihedral angles ( °)
	S 162-O 164-O 161-C 151	-41.76/-41.48/-41.14	-37.48/-36.13/-35.81	-41.61/-41.63/-41.15
	S 162-O 164-O 161-N 163	38.81/38.50/39.41	32.49/32.32/32.13	37.82/36.89/37.30
	S 162-N 163-O 164-O 161	29.42/29.12/29.08	26.27/26.35/25.65	29.16/28.66/28.37
	S 162-N 163-O 161-C 151	39.31/39.86/39.14	46.47/47.45/47.97	39.45/39.85/39.74
	N 158-O 159-O 160-C 152	-2.04/-2.42/-2.46	2.37/2.57/2.76	-2.09/-1.40/-1.40

Table 3 .

 3 The Selected Parameters for Free β-CD and In-complex Forms Calculated with

	B3LYP/6-

Table 2 ,

 2 the results for the orientation A indicate that the initial geometry of guest AZ is completely changed. This is while the difference in the geometric parameters before and after the complexation slightly changed for the orientation B. Initially, there was a slight change observed in the bond lengths of the AZ before (O 164-S 162: 1.45/1.44/1.46 Å) and after the complexation in the orientation A (O 164-S 162: 1.47/1.45/1.47 Å) and in the orientation B (O 164-S 162: 1.45/1.44/1.46 Å). The real change was observed through the difference between the bond angles and dihedral angles of the AZ molecule before and after the complexation. For orientation A, the difference between the S 162-O 164-O 161-N 163 dihedral angle (38.810/38.50°/ 39.41°) of the free AZ molecule and the dihedral angle

S 162-O 164-O 161-N 163 (32.49°/32.32°)/32.13°) of AZ in the complex is important. The mentioned difference is more obvious compared to the similar results of dihedral angle S 162-O 164-O 161-N 163 (37.820/36.890/37.30°) in the orientation B.

Table 4

 4

shows the global indices of reactivity. It is clear that the values of the electronic potential (μ) are negative in the

Table 4 .

 4 Thermodynamic

		Parameters, HOMO, LUMO, Δ(HOMO-LUMO) and Global Descriptions
	of the AZ, β-CD, and AZ/β-CD Complex Computed by Methods WB97X-D/6-31G(d)/
	B97D3/6-31G(d)) in the Gas and Aqueous Phases
	Gas phase
		β-CD free	AZ free	Orientation A	Orientation B
	ΔH° (kcal mol -1 )	-	-	-48.67/-48.35	-42.89/-44.71
	ΔG° (kcal mol -1 )	-	-	-30.70/-32.97	-24.80/-26.43
	ΔS° (cal mol -1 K -1 )	-	-	-60.01/-52.81	-60.54/-59.04
	HOMO	-0.32/-0.19	-0.35/-0.22	-0.32/-0.19	-0.33/-0.20
	LUMO	0.11/0.01	-0.02/-0.11	-0.02/-0.12	-0.03/-0.13
	ΔE (HOMO-LUMO)	-0.44/-0.20	-0.32/-0.11	-0.291/-0.06	-0.297/-0.07
	μ (eV)	-0.10/-0.09	-0.1868/-0.174	-0.175/-0.16	-0.1862/-0.171
	x (eV)	0.10/0.09	0.1868/0.174	0.175/0.16	0.1862/0.171
	η (eV)	0.22/0.10	0.16/0.05	0.145/0.032	0.148/0.036
	ω (eV)	0.02/0.04	0.106/0.27	0.105/0.39	0.11/0.40
	Aqueous phase
		β-CD free	AZ free	Orientation A	Orientation B
	ΔH° (kcal mol -1 )	-	-	-37.05/-39.25	-34.91/-36.29
	ΔG° (kcal mol -1 )	-	-	-21.60/-18.84	-19.65/-16.76
	ΔS° (cal mol -1 K -1 )	-	-	-51.64/-66.23	-50.95/-65.52
	HOMO	-0.33/-0.20	-0.35/-0.23	-0.33/-0.20	-0.33/-0.20
	LUMO	0.12/0.01	-0.02/-0.12	-0.03/-0.13	-0.04/-0.13
	Δ(HOMO-LUMO)	-0.46/-0.22	-0.32/-0.10	-0.295/-0.06	-0.290/-0.07
	μ (eV)	-0.10/-0.09	-0.19/-0.180	-0.182/-0.168	-0.188/-0.171
	x (eV)	0.10/0.09	0.19/0.180	0.182/0.168	0.188/0.171
	η (eV)	0.23/0.11	0.16/0.05	0.147/0.033	0.145/0.036
	ω (eV)	0.02/0.03	0.111/0.29	0.113/0.41	0.12/0.43

Table 5 .

 5 Variation of Mulliken Atomic Charges of AZ before and after

	Inclusion into β-CD Calculated by WB97X-D/6-31G(d) and
	B97D3/6-31G(d) in the Gas Phase
	N° = Atome	AZ free	Orientation A	Orientation B
	C 148	-0.173/-0.142 -0.174/-0.141	-0.162/-0.130
	C 149	-0.144/-0.111 -0.144/-0.111	-0.147/-0.126
	C 150	-0.188/-0.172 -0.138/-0.139	-0.191/-0.189
	C 151	-0.221/-0.194 -0.193/-0.173	-0.229/-0.205
	C 152	0.239/0.239	0.251/0.254	0.249/0.259
	C 153	-0.154/-0.122 -0.153/-0.122	-0.166/-0.137
	H 154	0.200/0.164	0.199/0.165	0.203/0.169
	H 155	0.198/0.162	0.200/0.166	0.191/0.171
	H 156	0.234/0.203	0.221/0.208	0.236/0.219
	H 157	0.223/0.184	0.220/0.183	0.228/0.196
	N 158	0.396/0.352	0.405/0.360	0.414/0.365
	O 159	-0.373/-0.344 -0.396/-0.368	-0.405/-0.379
	O 160	-0.367/-0.340 -0.356/-0.331	-0.352/-0.330
	O 161	-0.546/-0.508 -0.564/-0.531	-0.548/-0.512
	S 162	1.300/1.211	1.361/1.285	1.298/1.213
	N 163	-0.514/-0.482 -0.577/-0.540	-0.524/-0.493
	O 164	-0.512/-0.476 -0.561/-0.530	-0.513/-0.478
	C 165	-0.225/-0.205 -0.275/-0.270	-0.250/-0.263
	H 166	0.212/0.187	0.233/0.211	0.224/0.230
	H 167	0.191/0.178	0.216/0.213	0.182/0.174
	C 168	-0.001/0.009	-0.029/-0.02	-0.007/-0.013
	H 169	0.194/0.169	0.248/0.234	0.191/0.187
	C 170	-0.145/-0.116 -0.155/-0.128	-0.129/-0.105
	H 171	0.145/0.135	0.177/0.164	0.153/0.145
	C 172	-0.515/-0.478 -0.521/-0.504	-0.531/-0.536
	H 173	0.213/0.201	0.201/0.199	0.201/0.197
	H 174	0.160/0.143	0.162/0.145	0.191/0.184
	H 175	0.163/0.147	0.172/0.167	0.134/0.141
	C 176	-0.494/-0.456 -0.522/-0.505	-0.513/-0.493
	H 177	0.166/0.152	0.175/0.170	0.149/0.135
	H 178	0.171/0.154	0.168/0.151	0.220/0.209
	H 179	0.168/0.152	0.173/0.174	0.154/0.151
	Charge transfer	0.000/-0,004	0.036/0.056	-0.049/-0.045

Table 6 .

 6 Calculated Net Charges by Mulliken Population Method and Natural

	Population Analysis (NPA) of the AZ/β-CD Complex by WB97X-D/6-31G(d)
	in the Gas Phase
		Orientation A		Orientation B
	N° = Atome	Mulliken charges	NPA	Mulliken charges	NPA
	C 148	-0.174	-0.210	-0.162	-0.211
	C 149	-0.144	-0.212	-0.147	-0.218
	C 150	-0.138	-0.175	-0.191	-0.216
	C 151	-0.193	-0.307	-0.229	-0.329
	C 152	0.251	0.088	0.249	0.077
	C 153	-0.153	-0.223	-0.166	-0.218
	H 154	0.199	0.260	0.203	0.266
	H 155	0.200	0.261	0.191	0.255
	H 156	0.221	0.278	0.236	0.287
	H 157	0.220	0.275	0.228	0.281
	N 158	0.405	0.560	0.414	0.560
	O 159	-0.396	-0.405	-0.405	-0.417
	O 160	-0.356	-0.345	-0.352	-0.341
	O 161	-0.564	-0.978	-0.548	-0.973
	S 162	1.361	2.405	1.298	2.403
	N 163	-0.577	-0.761	-0.524	-0.735
	O 164	-0.561	-0.964	-0.513	-0.931
	C 165	-0.275	-0.268	-0.250	-0.261
	H 166	0.233	0.271	0.224	0.257
	H 167	0.216	0.240	0.182	0.226
	C 168	-0.029	-0.065	-0.007	-0.055
	H 169	0.248	0.283	0.191	0.251
	C 170	-0.155	-0.293	-0.129	-0.281
	H 171	0.177	0.260	0.153	0.249
	C 172	-0.521	-0.698	-0.531	-0.696
	H 173	0.201	0.251	0.201	0.253
	H 174	0.162	0.240	0.191	0.249
	H 175	0.172	0.233	0.134	0.207
	C 176	-0.522	-0.694	-0.513	-0.692
	H 177	0.175	0.234	0.149	0.223
	H 178	0.168	0.244	0.220	0.272
	H 179	0.173	0.236	0.154	0.228

Table 7 .

 7 Stabilization Energy E(2) (kcal mol -1 ) of the most Important Donor-acceptor Interactions

	Calculated by WB97X-D/6-31G(d) and B97D3/6-31G(d) in the Two Phases for the Two
	Orientations
	Orbital donor	Orbital acceptor	E (2) (kcal mol -1 )	E (2) (kcal mol -1 )	d
			WB97X-D/B97D3	WB97X-D/B97D3	(Å)
			Gas phase	Aqueous phase
	Orientation A
	σ(1) (O 161-S 162) σ*(1) (C 63-H 134)	0.61/0.47	0.61/0.36	2.34
	LP(2) (O 11)	σ*(1) (C 165-H 166)	3.76/2.37	4.12/2.01	2.30
	LP(1) (O 159)	σ*(1) (O 44-H 117)	3.01/1.48	2.87/1.64	2.19
	LP(2) (O 159)	σ*(1) (O 33-H 107)	12.06/10.62	13.84/11.73	1.87
	LP(1) (O 164)	σ*(1) (O 44-H 117)	4.89/3.43	5.33/3.44	2.02
	Total		24.33/18.37	26.77/19.18	-
	Orientation B
	LP(2) (O 16)	σ*(1) (C 149-H 155)	1.25/0.79	1.17/0.81	2.57
	LP(1) (O 62)	σ*(1) (O 165-H 166)	5.1/4.56	4.81/2.7	2.16
	LP(1) (O 159)	σ*(1) (O 69-H 140)	5.53/4.31	5.98/4.09	1.91
	LP(2) (O 159)	σ*(1) (O 69-H 140)	6.68/6.21	6.41/4.64	1.91
	Total		18.56/15.87	18.37/12.24	-

Table 8 .

 8 1 H NMR Chemical Shifts (ppm) of AZ before and after Complexation Calculated by GIAO

		Method at B3LYP/6-31G(d) Optimized with WB97X-D/6-31g(d) and B97D3/6-31G(d) in
		the Aqueous Phase
			Calculated	Experimental
	Protons	AZ free	AZ in complex	AZ incomplexe	AZ free	AZ in complex
			Orientation A	Orientation B
	H(157)	8.04/0.85	8.07/8.20	8.50/8.71	8.52	8.17
	H(15 4)	7.99/8.18	8.08/8.24	8.58/8.72	8.14	7.71
	H(155)	7.99/8.17	8.13/8.28	8.49/8.75	8.02	7.90
	H(156)	8.42/8.54	8.48/8.50	9.04/8.87	7.68	8.50
	H(166)	2.93/3.10	3.42/3.18	4.55/4.41	1.50	2.80
	H(167)	2.50/2.61	2.70/2.86	2.40/2.60	1.50	2.38
	H(169)	2.46/2.58	3.95/3.94	2.99/2.86	1.59	2.75
	H(171)	1.47/1.70	2.50/2.66	1.74/1.77	1,98	1.87
	H(173)	2.38/2.47	1.98/2.24	2.44/2.56	0.88	0.82
	H(17 4)	1.05/1.21	1.36/1.56	2.15/2.04	0.88	0.82
	H(17 5)	0.90/1.05	1.57/1.48	1.19/1.30	0.88	0.82
	H(177)	0.78/0.94	1.51/1.45	0.74/1.00	0.84	0.82
	H(178)	0.92/1.08	1.36/1.56	2.21/1.98	0.84	0.82
	H(179)	0.85/0.98	1.80/1.79	0.96/1.11	0.84	0.82