domain: chim phys spi

text:
B Gassoumi

F E Ben Mohamed

M E Castro

F J Melendez

A Karayel

L Nouar

F Madi

H Ghalla

S Özkınalı

V I Kovalenko

R Ben

Chaabane

H Ben Ouada

In silico exploration of O-H … X 2+ (X=Cu, Ag, Hg) interaction, targeted adsorption zone, charge density iso-surface, O-H proton analysis and topographic parameters theory for calix[6]arene and calix[8]arene as model

Keywords: Calix[n]arene, Targeted adsorption region, electron density, binding energy, O-H proton, QTAIM

In this work, the best adsorption targeted zones of the metal cations Ag 2+ , Cu 2+ and Hg 2+ at the surfaces or inside, outside the cavity of the calix[6] (CX[6]), calix[8]arene (CX[8]), NUBMOM (NUB-.) and LAYKUR (LAY-.) have been discussed. For X 2+ =Ag, Cu and Hg adsorbed onto the surface of CX[6,8], NUB-., and LAY-. and the morphologies of these

Introduction

The last thirty years have shown an important interest for the calix [n]arene chemistry due to their excellent interaction behavior of various chemical functions that permits to address very diverse fields of sensor application [START_REF] Aloui | Synthesis and Characterization of Positively Charged tris -Imidazolium Calix[6]arene Hosts for Anion Recognition[END_REF][2][START_REF] Temel | One novel calix[4]arene based QCM sensor for sensitive, selective and high performance-sensing of formaldehyde at room temperature[END_REF][4]. Even if they remain somewhat confidential, the opto-electronic applications of the calix [6,8]arenes molecules are constantly increasing in very different fields such as cation or anion recognition [START_REF] Tan | A Fluorescence Sensing Determination of 2,4,6-Trinitrophenol Based on Cationic Water-Soluble Pillar[6]arene Graphene Nanocomposite[END_REF][6][START_REF] Tan | Nanocomposite Based on Organic Framework-Loading Transition-Metal Co Ion and Cationic Pillar[6]arene and Its Application for Electrochemical Sensing of l-Ascorbic Acid[END_REF][8], cell transfection [START_REF] Bagnacani | Macrocyclic Nonviral Vectors: High Cell Transfection Efficiency and Low Toxicity in a Lower Rim Guanidinium Calix[4]arene[END_REF], biopharmaceutical field [START_REF] Ukhatskaya | Encapsulation of Drug Molecules into Calix[n]arene Nanobaskets. Role of Aminocalix[n]arenes in Biopharmaceutical Field[END_REF], but also recent amphiphilic species cumulating both transfective and antibacterial properties [START_REF] Gezelbash | Synthesis, antifungal and antibacterial activity of calix[4]arene-based 1,3,4-oxadiazole derivatives[END_REF][START_REF] Bahojb Noruzi | Synthesis, Crystal Structure, and Biological Activity of a Multidentate Calix[4]arene Ligand Doubly Functionalized by 2-Hydroxybenzeledene-Thiosemicarbazone[END_REF]. Problems related to detection of anion or cation guest are based on the false choice of the targeted zone, or on the ionophore type interaction [START_REF] Mahmoud | Design of Solid-contact Ion-selective Electrode with Graphene Transducer Layer for the Determination of Flavoxate Hydrochloride in Dosage Form and in Spiked Human Plasma[END_REF]. The majority of the publications in literature have used a CX [4] cage molecule because the existence of the O ... H cyclic network [14][15][16]. Even in literature, it is found that the majority of experimental work has generated almost all physical-chemical studies of the CX [6,8] synthesized molecules since several years ago instead of testing other conformations of these materials, However, there is not much effort to use other conformations of the same family [START_REF] Steinfeld | The Role of Lean Process Improvement in Implementation of Evidence-Based Practices in Behavioral Health Care[END_REF][18][START_REF] Alex | Supramolecular stacking in a high Z ′ calix[8]arene-porphyrin assembly[END_REF][START_REF] Zang | p-Phosphonic acid calix[8]arene mediated synthesis of ultra-large, ultrathin, single-crystal gold nanoplatelets[END_REF]. A look at the most of the work concerning to the interaction of the calix [6,8]arene molecule with the cation or anion in the last twenty years has been described [START_REF] Mlika | Calix[4]arene sensitive thin films for detecting sodium[END_REF][START_REF] Wu | Conformational Features and Anion-Binding Properties of Calix[4pyrrole: A Theoretical Study[END_REF][23][24][25][START_REF] Mousavi | Potentiometric Ag+ Sensors Based on Conducting Polymers: A Comparison between Poly(3,4-ethylenedioxythiophene) and Polypyrrole Doped with Sulfonated Calixarenes[END_REF][START_REF] Suwattanamala | Comparative Density Functional Theory Study on Thiacalix[4]arene Binding Modes for Zn2+ and Cu2+[END_REF][START_REF] Rozhenko | Conformational features of calix[4]arenes with alkali metal cations: A quantum chemical investigation with density functional theory[END_REF][START_REF] Dumazet-Bonnamour | Calixarenes for metal cations extraction[END_REF][START_REF] Rouis | Optical spectroscopy studies of the complexation of chromogenic azocalix[END_REF][START_REF] Ebdelli | Electrochemical impedance detection of Hg2+, Ni2+ and Eu3+ ions by a new azocalix[4]arene membrane[END_REF][START_REF] Echabaane | Electrical and electrochemical properties of the MEH-PPV and MEH-PPV doped calix[4]arene derivative layers for the detection of Cu2+ and Na+ ions[END_REF][33][START_REF] Rouis | Electrochemical analysis of a PPV derivative thin film doped with ß-ketoimine calix[4]arene in the dark and under illumination for the detection of Hg2+ ions[END_REF][35][START_REF] Mohan | Synthesis of calix[6]arene and transduction of its furfural derivative as sensor for Hg(II) ions[END_REF][START_REF] Rodríguez-Lavado | Elucidating sensing mechanisms of a pyrene excimer-based calix[4]arene for ratiometric detection of Hg( ii ) and Ag( i ) and chemosensor behaviour as INHIBITION or IMPLICATION logic gates[END_REF][38][START_REF] Yilmaz | Novel integrated sensing system of calixarene and rhodamine molecules for selective colorimetric and fluorometric detection of Hg2+ ions in living cells[END_REF].

Around of the supra-molecular chemistry, the calix [6,8]arene molecule has an advantage to be utilized as host molecules. The calix [8]arene can be incorporated in a "pinched" conformational structure comprising, a kind of circularly hydrogen bonded sequences containing four OH groups each. Similar to Calix [8]arenes, Calix [6]arene is assumed a "pinched" conformation in non-polar solvents, resulting in circular hydrogen bond sequences containing three OH groups [40]. Theoretically, the families of calix [6,8]arene include the following conformations (Available from the Cambridge Structural Database): CX [8]: VARHAY, LAYKUR, RALQAW, XUGJUG, and ARUXEQ and CX [6]: VARGUR and NUBMOM [START_REF] Gassoumi | Role of hydrogen bonding interactions within of the conformational preferences of calix[n = 4,6,8]arene: DFT and QTAIM analysis[END_REF]. These derivatives can enclose guest entities, which can be stabilized by the introduction of the specific functional groups [START_REF] Talotta | Calix[6]arene Threading with Weakly Interacting Tertiary Ammonium Axles: Generation of Chiral Pseudorotaxane Architectures[END_REF][START_REF] Inthasot | Selective EPR Detection of Primary Amines in Water with a Calix[6]azacryptand-Based Copper(II) Funnel Complex[END_REF][44]. In the literature, the majority of experimental work does not explain the adsorption phenomenon clearly [45,[START_REF] Abd El-Rahman | Spectrophotometric determination of choline in pharmaceutical formulations via host-guest complexation with a biomimetic calixarene receptor[END_REF]. In the other words, the different zones where the cation is located exactly. Moreover, the most physical interpretations discuss a mixed between two nono-composite [START_REF] Güngör | Efficient removal of carcinogenic azo dyes by novel pyrazine-2carboxylate substituted calix[4, 8]arene derivatives[END_REF]. Afterwards, the experimenters give arguments that the cation for example, Zn 2+ , Cu 2+ , Ag 2+ and Hg 2+ stabilizes inside the cavity, or is collected around of the environment of the functional group, but these results are not completely correct. The development of chemical codes strengthened the theoretical chemists to improve and search for target areas, areas of activation where the cation is easily deposited. These codes are evolved for the experimental reasoned studies to simply visualize the complicated physical phenomena in terms of experience. In this work, the target sites to capture the cations Cu 2+ , Ag 2+ and Hg 2+ by the CX [6,8] and their derivatives are determined. The H-bonding interactions between the cation and the studied molecules are analyzed. The hydrogen bonds are always present in the studied region to have an effective stability of the activation sites. The vibrational properties have shown that the system is dynamically stable, from the cation effect on the hydrogen bonds in comparison with the free molecule. The optical interpretations prove that the presence of the cations Ag 2+ , Cu 2+ and Hg 2+ enrich the reactivity of relevant materials, the gap energy shift towards the red region in the presence of Ag 2+ and towards the blue region in the presence of the Cu 2+ cation. The 3D surfaces of Hirshfeld and molecular electrostatic potential (MEP) topography indicated the better absorption zone chosen by well-defined color codes. Finally, The high selectivity of the Ag 2+ , Cu 2+ and Hg 2+ cations in the chosen region is well supported by Bader's theory; QTAIM.

Bench marks

The CX [6,8] molecules have been specified by a cavity formed by six and eight phenols groups, which can be modified with a torsion angle between 0 and 180 ° for obtaining different conformations (CX [8]:VARHAY, LAYKUR, RALQAW, XUGJUG, and ARUXEQ and CX [6]:VARGUR and NUBMOM) [START_REF]Initial structures taken from CSD: Cambridge Structural Database[END_REF]. In this study, the two most stable conformers were selected, in which these conformations have more or less similar structural forms. In addition, these molecules are characterized in a limited area between the upper rim and the cyclic structure formed by O .... H hydrogen bonds in the lower rim. These parameters have encouraged the experimenters to test the selectivity of the CX [6,8] to the special heavy metals (Zn 2+ , Cu 2+ , Ag 2+ , Hg 2+ , Mg 2+ ,etc…). The results of the CX [6,8]-heavy metal detection are the objective to ameliorate the optoelectronic behavior of the CX [6,8] isolates. The encapsulation of the specific cation for the conformations; CX [6], NUB-., CX [8]. and LAY-. has been calculated. The conclusion is that the sensitivity of the CX [6,8] molecule for a given cation is not within the cavity only but there are other targeted sites studied the first time here.

A deep study concerning to the adsorption mechanism of the CX [6,8] systems is carried out. These mechanisms can't be determined experimentally. The determination of the active sites in the molecules unlike to the classic work, it will be very important in the future. This information explains that the cage molecules are not limited to detect the chemical species inside the cavity, but, they are able to absorb the cations in different regions.

Computational and theoretical methodology

The present study analyzes the electronic, adsorption and energetic mechanism of the calix [6,8]arene conformers in interaction with the X 2+ (X= Ag, Cu and Hg) cations in each chose targeted zone. Using density functional theory (DFT) incorporating the GGA functional hybrid (B3LYP-D3) [START_REF] Meryem | Computational investigation of vanillin@βéta-cyclodextrin inclusion complex: Electronic and intermolecular analysis[END_REF], the direct or indirect conduction of the OH-bond was well simulated and symbolized other weak attempts to fix and stabilize the cation in its region.

These calculations have been applied with the B3LYP-D3/6-31G(d)-def2svp level basis set (see Table S1), the polarized functions have been added to all atoms. The Gaussian 09 program [START_REF]Gaussian[END_REF] was used to optimize the complexes presenting different structures in the presence of the cation in its targeted region. The Figures represented in this study were obtained using the Gabedit 2.5.0 interface [START_REF] Allouche | Gabedit-A graphical user interface for computational chemistry softwares[END_REF]. Normal vibrational modes assignments in various conformations were calculated for the stationary point structures which placed onto the local minima on the potential energy surface. The GaussView 5.0 program [52] has been used to visualize the displacements of the atoms around their equilibrium positions. The chemical shift O-H prediction parameters have been simulated by the gauge-independent atomic orbital (GIAO) method [START_REF] Wolinski | Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations[END_REF] using the nuclear magnetic shielding tensors of the tetramethylsilane molecule (as reference). The NMR spectra were calculated for the lowest energy conformations in the AN-.solvent. These chemicals shifts have been calculated using the self-consistent reaction field (SCRF) incorporated the PCM model [START_REF] Wolff | CrystalExplorer, version 3.1[END_REF]. Sensor performances of the studied compounds have been discussed using UV absorption spectrum and total DOS orbital analysis in AN-.solvent with theoretical calculations at CAM-B3LYP-D3 level of theory. The Hirshfeld surface analysis and the two-dimensional fingerprint plots were investigated using the Crystal Explorer17 program [START_REF] Mennucci | Polarizable Continuum Model (PCM) Calculations of Solvent Effects on Optical Rotations of Chiral Molecules[END_REF] to obtain the interaction in percentage of the Ag 2+ , Cu 2+ and Hg 2+ cations with the atoms of the CX [6,8], NUB-. and LAY-. complexes. From the MEPs, the electrophilic and nucleophilic reactive sites were predicted to compare the electron-rich regions around of the targeted adsorption region in each complex. The topological study of the molecular electron density by the theory of Atoms in Molecules (AIM) proposed by Bader [START_REF] Bader | A Bond Path: A Universal Indicator of Bonded Interactions[END_REF] is very useful for exploring the principal bond critical points (BCP) responsible for the high interactions between the guest and the host. These results were performed by the AIM2000 software [START_REF] Biegler-Konig | Software news and updates AIM 2000[END_REF]. The non-covalent interactions (NCI) via reduced density gradient (RDG) were obtained using the Multiwfn program [START_REF] Lu | Multiwfn: A multifunctional wavefunction analyzer[END_REF]. All the theoretical results were simulated by the DFT-D theory were compared with the available experimental data.

Optimization, stabilities, OH … X 2+ (X= Cu, Ag and Hg) interaction and electron density charge population.

The cooperativity between the hydrogen-bonds in the calix[n]arene molecules provide for the formation of inter or intra-molecular H-bonding. These interactions play a very important role in the most natural or synthetic receptors. The calix[n]arene molecules have a cavity limited by a cyclic network of O ... H bonds which is useful to form this type of bonds with the guests (cation or anion). The theoretical calculations of the different complexes of CX [6]-X 2+ (X= Ag, Cu and Hg) and CX [8]-X 2+ (X= Ag, Cu and Hg) give the most stable conformations shown in Figure 1 with the atomic numbering scheme. These stable conformations are obtained using the DFT/B3LYP-D3/6-31G(d)-def2svp level of theory. The selected structural parameters for the stable geometries (CX [6]-X 2+ and CX [8]-X 2+ ) were given in Tables S3 and S4 (See supplementary material). In the hydrogen bonds described the possible direction of exchange of electrons between the donor and the acceptor.

In Figure 1, for CX [6]-X 2+ and NUBMON-X 2+ , for the I pos1 complex, the bond H contribute to the stability of this complex. In addition, the results show that the Ag 2+ cation is located in the center of two anti-symmetric oxygen atoms with "pinched" conformation of the calix [6]arene (see I pos3 in Figure 1). In Figure 1 The experimental values [START_REF]Initial structures taken from CSD: Cambridge Structural Database[END_REF] of 3.42 and 3.68 Å, prove that the cation exerts a compressive force on the two phenol groups (See Figure 1). The orientation of the two carbon atoms linked to the cation and the carbon atom of the methylene groups in the same axis provides an angle equal to 85.31 °. This angle is equal to 92.5 ° before the addition of Ag 2+ . It can be deduced that the fixation of the adsorption of the NUBMOM molecule for Ag 2+ in this zone ensures the modification of the conformations and their symmetry. In the Figure I (II pos1 ) the cation can be complexed with two opposite oxygen atoms in stuck cone conformation. In II pos2 the cation can be complexed with adjacent two oxygen atoms collinear conformation. As seen in II pos2 , the calix [6]arene is to force into a conformation in which the aryl groups in the 1-and 4positions inward perpendicular to the aryl groups in the 2-, 3-, 5-and 6-positions. Comparing energetically these two conformations, the binding energy for II pos1 is equal to [6] with the cation Cu 2+ , four conformations have been found (see Figure 1). The active interaction-region of this cation with the systems has been visualized. In this case the three conformations have almost the same order of energy binding stability (Figure 3). There is a slight variation of III pos2 of order E b = 0.01kcal/mol. This is reason why is important to discover the region of the interactions between the Cu 2+ cation and the CX [6] molecule. For the III pos1 complex, see Figure 1, the Cu 2+ cation stabilizes at the center of the cavity by forming three bonds π . ). However, similarly to silver (II) cation, in their complex the cupper (II) cation make square planar geometry complex with dsp 2 hybridization. This situation shows that the copper cation is planarly located in the calix [6]arene core. Also, it is observed that there is a conservation of the symmetry group (C 1 ).

Table S3 shows the H-bonding reconstructed during the addition of Cu 2+ cation. and the experimental values [START_REF]Initial structures taken from CSD: Cambridge Structural Database[END_REF] which are around of 2.61 and 2.64 Å is adequate. This is a clear idea which explained that there is a good consistency between these two studies. The S3). For the first conformation, In this part, the discussion about the interaction of the CX [8] and LAYKUR molecules with the metals-cation Ag 2+ , Cu 2+ and Hg 2+ is present. From Figure 2, the centro-symmetrically Ag 2+ cation interaction with the CX [8] and LAYKUR molecules presents a conservation of the structural properties, citing as an example, the conformation I pos1 (CX [8]) and the II pos1 S4). The mathematical calculations show that the projection of the Cu 2+ cation by a perpendicular axis toward to the targeted phenol group demonstrates that this cation attaches to the center of the gravity of this group. This result is not by chance, but there is a resultant of force which ensures the fixation of this cation in this place. These forces are of the electrostatic type formed by the two electrons gives up by the cation. If the cooperativity of hydrogen bonds have been discussed in the presence of the Hg 2+ cation, we have assigned to determine the adsorption of the CX [8] molecule for this cation in the endo or exo-cavity positions. In Figure 2, it is seen that the Hg 2+ cation forms exo-in V pos1 and VI pos2 , and endo complex in From the V pos1 and V pos2 , the results are equal to 0.98 and 1.75 Å, while, the experimental values are similar as the theoretical ones. The two electrons takes up by the Hg 2+ cation remains free in the space, that is to say does not have any structural system disturbance in this case. For the system VI pos1 , the deviation of the Hg 2+ cation by contribution the two oxygen atoms O 1 and O 3 in the same plane are specified by the angles with value of 39.27 °. The cation is stabilized by an electrostatic force which fixes it in the same plane of the hydrogen band HB1. The complex VI pos2 is described by the same physical interpretations as the previous ones. The interaction of cation Hg 2+ with the charged phenol group areas reinforces the molecule to modify its structure. The axis of symmetry and the structural properties remain preserved. Similarly, the Hg 2+ cation added to the structure has a role of moderator of the stability for the compounds but has no effect on the structural properties. These explanations can be useful to experimenters to inject a cation into an organ system with the preservation of the physical parameters.

V

H C O Ag Hg Cu

Calculation and assignments of vibrational frequencies

The theoretical results are compared with the experimental values for the free CX [6] and CX [8] molecules [START_REF] Furer | DFT study of hydrogen bonding and IR spectra of calix[6]arene[END_REF][START_REF] Furer | FT-IR and FT-Raman study of hydrogen bonding in p-alkylcalix[8]arenes[END_REF]. GHz for the III pos1 complexes. This frequency is related to the O … H symmetric band.

Moreover, the same frequency bands are observed for the III pos2-4 complexes. These rays are of low intensity. For the III pos1-4 , it is shown that there are three frequency bands varying from 92.10 3 to 97.10 [6] system conserved the normalized modes already existing for the free CX [6] molecule. Regarding the NUBMOM-Ag 2+ system, despite the total disruption of the system, the cation takes the place of the oxygen atom, forming a hydrogen bond with it, but the frequency bands are conserved. In this system it is observed the appearance of a low intensity phonon frequency located beyond 112. cation (see Figure 4).

The superposition of the infrared spectra of CX [8]-X 2+ complexes are shown in Figure 4. In this present case, the interaction of the Ag 2+ and Cu 2+ cation with the CX [8] molecule ensures a burst of a single hydrogen absorption band for the free CX [8] to form three IR absorption bands. According to the literature the single frequency is located at 91.10 3 GHz (O-H free).

These metal cations generated three peaks in the vicinity of 105.10 3 , 102.10 3 and 996.10 2 GHz, respectively. These infrared absorption peaks correspond to the free O-H, O…H antisym. and O-H sym. However, the guest Hg 2+ interacts with the molecule in question with a conservation of the hydrogen bonding by increasing its intensity. It has been demonstrated

that the peak shifted in comparison with the literature by 10 4 GHz (Figure 4). This stretching band is corresponding to the vibration of all the cyclically O-H sym. The evidence shows that the cations Hg 2+ and Cu 2+ keep the law of normal modes of vibration. As an interpretation it is noted that the zone varies between 106.10 2 and 54.10 GHz (see Figure 4). These bands are named in consideration of the vibrational modes of phonons by O-H sym., O…H anti-sym, and OH free. The remark noted here is the significant shift and high intensity of these bands in comparison of the peak with that of free CX [8] molecule. In addition, for NUBMOM-Ag 2+ and NUBMOM-Cu 2+ , a high intensity peak is located in the vicinity of 48. The infrared model shows that these metal cations have a significant effect on the hydrogen absorption band frequencies of CX [8] and CX [6], excluding the Hg 2+ cation which is sometimes kept the band that already exist but removed and shift the frequencies probably.

The calculations will trigger studies of integrated electronic cards involving these digital models for improved WLAN/WPAN 60 GHz to 10 5 GHz, standard CMOS technology and the Vivaldi antennae…etc. and LAYKUR-X 2+ complexes.

CX[6]-X 2+ NUBMOM-X 2+

Quantum chemical prediction of O-H proton.

The Gauge-Independent Atomic Orbital (GIAO) [START_REF] Imane | Investigation of intermolecular interactions in inclusion complexes of pyroquilon with cucurbit[n]urils (n = 7,8) using DFT-D3 correction dispersion[END_REF] method was used to calculate the O-H chemical shifts, δ. In the previous cases, the chemical shift δ i is determined as δ = σ TMS -σ, where σ is the computed value of the isotropic shielding relative to σ ref value for tetramethylsilane (TMS). The value of the σ OH (B3LYP-D3) is equal to 31.9918 ppm for hydrogen atoms. The statistical treatment of the O-H proton was calculated and the results are summarized in Tables S5 and S6 in the gas phase and the acetonitrile (AN) as solvent. Also, the physical interpretation results will be extracted from the histograms in Figure 5 and Tables S5 andS6.

The O-H chemical shift for the CX [6]-Ag 2+ structure (Table S5) showed multiple signals in the range between 6.76 ppm and 9.93 ppm in the gas phase. An expanded version is shown in the Figure 5 to clarify that the signals with O-H proton above of 10 ppm were not observed in the prediction. This results are presented in the CX [6] before adding of the Ag 2+ cation. The NUBMOM-Ag 2+ complex present three signals varying from 1.43 to 7.81 ppm. It is shown that the proton of O-H moves easily in the acetonitrile solvent than in gas phase. The nitrogen atom (CH 3 CN) in acetonitrile takes the proton in the OH group and performs exchange.

Despite the difference is not high but it is quite measurable. That the reason why the discussion is oriented to the complexes in the acetonitrile solvent. From Figure 5, it is shown that the signal of the O-H proton decreases when the Ag 2+ cation is approached (see NUB-.Ag 2+ in Figure 5). For the NUB-.X 2+ complex, the clustered electrons surrounding of the O- has a δ H value equal to 5.44 ppm. From Figure 5 and Table S6, it is observed that this low value is due to the interaction of the H 4 atom with that of the oxygen atom that is interacting with the Cu 2+ cation. The cation of Hg 2+ interacts with the CX [8] molecule with total conservation of the hydrogen bonds, this is explained by the high signals for the LAYKUR-Hg 2+ complex. In the most cases, it is shown that when the signal detected in the targeted area, it appears weak, so when the signal is located far from the cation environment, forming a hydrogen interaction with the other OH bonds, it appears high. Therefore, it is deduced that the cation absorbs all signals entering in its target area.

H

Sensor performance: Absorption spectroscopy and total DOS frontier orbital studies

Figure 6 depicts the UV-visible absorption spectra and the total DOS orbital [START_REF] Zhu | Adsorption of CO2, O2, NO and CO on s-triazine-based g-C3N4 surface[END_REF] of CX [6]-X 2+ and NUBMOM-X 2+ in the AN-.solvent. In comparison with the last publication [START_REF] Mohan | Synthesis of calix[6]arene and transduction of its furfural derivative as sensor for Hg(II) ions[END_REF], the presence of the Ag 2+ cation shifts towards red the absorption spectrum from 2.18 eV to 3.5 eV (with a proportionality between the wavelength (nm) and the energy in eV of E(eV)=1240/λ (nm)). The total DOS orbital analysis shows that the cation Ag 2+ widens the forbidden band towards the value 2.78 eV. In addition, the material becomes harder and it has an increase in electronic activity to go from the fundamental state to a less stable excited state. It The presence of this type of cation provides an absorption peak in the zone of 3.24 eV. This band could be due to an interaction of Ag 2+ and CX [6] via the functionalized oxygen atoms of the receptor. These results indicated the good selectivity toward Ag 2+ metal cation by CX [6] conformation type. The NUBMOM-Ag 2+ compound has three peaks located in the vicinity of 1.74, 2.52 and 3.96 eV, respectively. Moreover, the recent one is the shift of energy of 1.76 eV in comparison with the complex CX[6]-Ag 2+ , which results in a highest conduction parameter of this material. The largest absorption band corresponds to the π-π* transition type.

Also, it is shown that there is a transfer of electrons from an intrinsic valence band state to the first excited state of the conduction band, this type of transition is n-π* transitions. The activation energy of these electrons appears in the UV-visible spectrum at 3.96 eV. Changes were demonstrated after the addition of the Ag 2+ cation to the total orbital spectrum. This proves a contraction of the gap energy towards a value equal to 2.12 eV. This conformation is more selective for the Ag 2+ cation than the reference molecule CX [6]. The complexation of the CX [6] for the Cu 2+ cation in this specific targeted area is shown in Figure 6. In this case the result is totally the opposite of the CX [6]-Ag 2+ cation. The UV-visible deduces that the shifted of the energy towards blue from 2.18 to 0.60 eV [START_REF] Mohan | Synthesis of calix[6]arene and transduction of its furfural derivative as sensor for Hg(II) ions[END_REF]. This new result marked as a very good result for this system in the optoelectronic applications instead several materials in the future. Upon addition of Cu 2+ cation to the receptor, the valence electrons passed to the conduction band by weak energy equal to 0.75 eV. The flow of electrons is of the transition ππ* type. According to Figure 6, there is almost an overlap between the two bands, which proves that the CX [6] molecule is very selective for the Cu 2+ cation. Using the total DOS alpha spectrum, it is deduced that the forbidden band is shifted by 0.62 eV, so this type of material may be the best to have a good performance sensor in the near future. The accumulation of unstable electrons in the intrinsic states of this host-guest favors an electronic transfer from this site to an excited state by n-π* transition type. The maximum energy band of these unstable electrons is located in the vicinity of 1.15 eV. The same remarks are dedicated for the UV-visible spectroscopy and the DOS spectrum for the NUBMOM-Cu 2+ complex. Likewise, this compound has a very high degree of selectivity for the Cu 2+ cation.

The receptor exhibited two high intensity absorption bands located around of 1.03 eV and 1.42 eV, respectively, after the complexation with the Hg 2+ cation in the chosen region. These bands result from the interaction of CX [6] with the Hg 2+ via the functionalized atoms of the receptor. Thus, changes were observed in the CX [6]-Hg 2+ absorption spectra, showing a blue shift in energy from 2.18 to 1.41eV [START_REF] Mohan | Synthesis of calix[6]arene and transduction of its furfural derivative as sensor for Hg(II) ions[END_REF], shifted almost by the half. These absorption bands are due to the n-π* transition. The spectrum of occupied orbital shows gap energy equal to 1.60 eV. This result underlined that this material will be classified as conductor compound.

The chosen area is very sensitive to the Hg 2+ cation. Also, it is noticed the appearance of a weak intensity peak located around of 4.02 eV. This absorption band is due to the charge transfer between the Hg 2+ cation and the close phenolic groups. Regarding the NUB.-Hg 2+ complex, instead of the appearance of two very close peaks of the CX[6]-Hg 2+ complex, there are two peaks convoluted in a single band located in the vicinity of 1. The optoelectronic properties and the total DOS analysis were studied in the AN-.solvent for the CX[8]-X 2+ and LAY.-X 2+ complexes (see Figure 6). The stability of the Ag 2+ cation in the cavity center of the CX [8] molecule induces two close absorption bands located in the vicinity of 3.36 and 3.18 eV. The high intensity band shifted from 400 to 369 nm (3.36 eV) in comparison with the result published recently by Ning Li et al. [18]. So this value is outside of blue color precisely in the UV area. In this case the electrons passed from an intrinsic state of the valence band to the conduction band, so the phenomena is known by n-π* transitions. The DOS orbital spectrum shows that the gap energy for this complex is equal to 2.14 eV. This complex is more conductive than that of CX [6]-Ag 2+ , therefore, the CX [8] molecule is more selective to the Ag 2+ cation than that with CX [6] compound. The interaction of the Ag 2+ cation by the LAYKUR molecule forms three absorption band located in the neighborhood of 3.29, 3.47 and 4.62 eV, respectively. The two most intense peaks are due to the accumulation of electrons in the center of the cavity surrounding the Ag 2+ cation. Also, a very important result that demonstrate that there is a blue shift from 400 nm (reported in literature) to 369 nm (3.36 eV) as the same by the host-guest CX [8]-Ag 2+ . The gap energy is shown in Figure 6 by the total DOS spectrum (alpha, DOS orbital), the result is beyond to 3.80 eV. This conformation (see Figure 2) is more selective to Ag 2+ cation than that CX [8] molecule. The interaction of the Cu 2+ cation in the choice to target region with the CX [8] molecule induces the formation of two intense bands corresponding to the electron π-π* transition between the cation and the two phenol group interacted with it. This indicated that the receptor is selective toward to Cu 2+ metal cation. In addition, the maximum energy is obtained approximately at 0.45 eV. This is a very low value which infers that there is almost an overlap between the conduction band and the valence band; hence the gap energy is equal to 0.43 eV. Therefore, a real revolution will happen in the conductor materials because the specific complexes may be the first in the future. The comparison of the absorption results between the CX [8]-Cu 2+ and LAY-.Cu 2+ complexes shows that almost the same absorption bands appear with a shift between the first two peaks by 0.16 and 0. 24 eV. The LAY-.Cu 2+ complex is more selective to the Cu 2+ than CX [8]. The surprising result is as follows, it is shown that the presence of the Hg 2+ in the center of the cavity of the CX [8] molecule removes the entire absorption band in the CX [8] free, that is to say the compound becomes transparent. This result shows that CX [8] is not selective to the Hg 2+ cation. Contrary, the interaction of the Hg 2+ cation with the LAYKUR molecule form two absorption bands located in the vicinity of 1.35 and 1.12 eV.

So, it can be concluded that there is an almost double shift towards the infrared (400 nm (CX [8] free to 911nm (LAY-.Hg 2+ )). The center of the cavity is the best area for the selectivity of this molecule. According to the DOS spectrum, the gap energy of these materials is equal to 0.87 eV. Finally, the degree of energy shift between the CX [6] and CX [8] free molecules and the systems interacting with X 2+ cations is shown in percent (see Figure 7).

Hirshfeld surface analyses

Based on electron distribution calculation in a crystalline form of the compounds by the Hirshfeld surface analysis [START_REF] Mary | Theoretical investigation on the reactive and interaction properties of sorafenib -DFT, AIM, spectroscopic and Hirshfeld analysis, docking and dynamics simulation[END_REF], which indicates the sum of spherical atom electron densities around of the targeted region, it was determined the interaction of the cations Ag 2+ , Cu compounds, the fingerprint plot show 96.5 and 87.6 % for Ag … H interactions. An H-bonding interaction covers 6.5 and 2.9 %, respectively, for the two compounds. These interactions are visualized by stains colored in red on the Hirshfeld surface. The fingerprint plots show that Cu … C contacts comprising the 7.4 % (LAY-.Cu 2+ ) and 5.9 % (CX [8]-Cu 2+ ) of the total Hirshfeld surface area for these specific systems. The contact of the Hg 2+ cation with the CX [6] and CX [8] compounds promotes the maximum population of electronic charges surrounding this cation, with very weak interactions with the host. This cation is encapsulated by these systems but with very weak interactions. Sometimes, it is not possible to visualize it especially for CX [8] and CX [6] compounds.

The Hirshfeld surface study showed that the Ag 2+ and Cu 2+ cations are stabilized by strong hydrogen bonds interactions in the targeted area, which infers the significant selectivity in these regions for the used cations.

CX[6]-X 2+ NUBMOM-X 2+

MEPs topography

The molecular electrostatic potential (MEP) maps (iso-surface value = 0.05 a.u) of CX [6],

NUB-.X 2+ CX[8]-X 2+ and LAY-.X 2+ complexes were given in Figure 9. These graphs represent the intra-molecular or intermolecular interaction between the cation and the targeted zone as the electron-rich region in acceptor or donor electrons. A careful observation of Figure 9 suggests that electron deficit region (blue color) appears surrounding the environment close to the cations Ag 2+ (CX [6]), Hg 2+ (CX [6]), Hg 2+ (NUB-.), Cu 2+ (CX [8])

and Hg 2+ (LAY-.), proving the electron deficit region is located in the targeted cation zone to facility the interaction between the cation and H-bonding. Otherwise, the interactions of the H-bonding of the cavity with the guest form a double donor-acceptor in the targeted region, which infers the good selectivity of the molecule to the specific guest; this is the best absorption zone. Also there are populations of weak electronic loads visualized on the MEP for the complexes CX [6]-Cu 2+ , NUB-.Cu 2+ , NUB-.Ag 2+ ,CX [8]-Ag 2+ and LAY-.Ag 2+ , which

shows that the high interaction forces between the cation and the atoms close to cavity or the phenol group weakens the concentration of the electrons surrounding cation. The nucleophilic reactivity (red color) appears localized in the environment of phenol groups almost for all the

QTAIM analyses

Recently, QTAIM [START_REF] Md | DFT and QTAIM investigations of the adsorption of chlormethine anticancer drug on the exterior surface of pristine and transition metal functionalized boron nitride fullerene[END_REF][START_REF] Stefanello | New 1-(Spiro[chroman-2,1′-cycloalkan]-4-yl)-1H-1,2,3-Triazoles: Synthesis, QTAIM/MEP analyses, and DNA/HSA-binding assays[END_REF] analysis has merged as a prevailing technique to determine results that are difficult to see for the experimenter for different forms based on the electron density in each molecular interaction. The understanding of a region of a system on the basis of the specific physical proprieties of each studied system passing from the system (e.g., a molecule) to the into subsystem (e.g., atoms) gives only by the QTAIM analysis. The results data are given on the basis of zero-flux in the electron density gradient field. Based on the topological parameters in each system, it is possible to classify the bond/interaction nature, chemical bond/interaction types and distinguish the bond or the interaction strengths.

This part includes a discussion on the QTAIM theory. In CX [6]-Ag 2+ complex, the value of electron density is varying between 0.4013 and 0.5370 a.u. (see Table S7). The Laplacian values are positive. The highest density BCP value is observed in BCP1. This result is confirmed by interaction energy E BCP1 equal to -588.11 kJ mol -1 . The NCI-RDG data show that the Ag 2+ cation is stabilized by forming two hydrogen-type interactions (blue color) with the two oxygen atoms in front (see Figure 10). This idea proves that this target zone is very selective for the Ag 2+ cation. It is evident that the presence of Cu 2+ cation at the cavity center of the CX [6] molecule is stabilized by forming five hydrogen bonding interactions (see Figure 10). 10, it is visualized these VdW interactions by a green spot. Thus, the topological parameters and the NCI-RDG plots confirm that the chosen target region area is very selective for Ag 2+ , Cu 2+ and Hg 2+ cations. Based on the Table S7 and Figure 10, it was found that the Ag 2+ cation destroys the standard hydrogen bond and takes its place, forming with it a rather important interaction of hydrogen bond (blue color). The Ag 2+ cation also reconstructs a weak van der Waals interaction (green color) with the carbon atom to be well stabilized. Moreover, the NUB-.Cu 2+ complex is specified by the existence of hydrogen bonding and VdW interaction formed between the cation and the neighboring atoms. These interactions are shown by blue and green spots. In this area, the electron density values are calculated at these BCPS. The results are varied between 0.1239 a.u. (BCP1) and 0.7488 a.u. (BCP3). The Laplacian values are positive. The highest ρ characterized by interaction energy in the neighborhood of -1144.71 kJ mol -1 . This result is well confirmed by a strong hydrogen bonding interaction between Cu 2+ cation and the oxygen atom (see Figure 10). The ratio |V(r)|/G(r)<1, the value is equal to 0.54 (BCP2). In addition, the ρ bcp parameter corresponding to the NUB-.Hg 2+ compound is varying from 0.1766 to 0.3272 a.u. The high interaction energy value is obtained for BCP2. The result is close to -388.31 kJ mol -1 . The NCI molecular graph shows that the Hg 2+ interacts with the chosen target area by two hydrogen bonding interaction and one VdW interactions. So this region is more selective to the Hg 2+ cation.

Obviously, the addition of cation to the cavity center of CX [8] molecule ensures the formation of almost eight hydrogen bonding interaction with the cyclic network of O-H groups (see Figure 10). The cation is stabilized by a resultant of eight forces of energy intensity equal to 700 kJ mol -1 . The cavity center of CX [8] is a good selectivity region of this cation type. The CX [8]-Cu 2+ indicates that the cation forms a weak van der Waals interaction type (green color) with the hydrogen atom. In this case, the |V(r)|/G(r) ratio (BCP2) is equal to 1.15. This result confirmed the law of Bianchi et al. The V BCP /G BCP ratio is in this specific bond regime (1<V BCP /G BCP < 2). This result is confirmed by a low electron density equal to 0.2251a.u (BCP2). In this BCP, a high energy is noted with value of -278.83 kJ mol -1 . In this case the cation forms two hydrogen bonds practically very weak and a VdW type interaction to be more stable. The QTAIM analysis indicate that the CX[8]-Hg 2+ complex like most of previous data, the Hg 2+ cation stabilizes in its region by forming VdW type interactions with the environment of the phenol groups in front. Precisely, it can be concluded that the CX [8] molecule is reactive for this type of cation in each chosen targeted zone. For the LAY-.Ag 2+ complex, it is obtained that the highest electron density value is noted for BCP2. The data visualized 0.4184 a.u. in this BCP. The BCP1 has a lower value than BCP2. The result is around to 0.3827 a.u. The greatest interaction energy value is equal to -551.33 kJ mol -1 . From Figure 10, the NCI results show that the Ag 2+ cation gets stuck on the surface of LAY-.

molecule by a hydrogen bonding interaction (blue color) with the oxygen atom and a mixed between H-bonding interaction and VdW type interaction (blue/green disc) with the surface of phenol group in front. As a conclusion, this targeted area is reactive, selective for the Ag 2+ cation. However, concerning the host-guest LAY-.Cu 2+ , almost the same interpretation as previous is made. The cation is fixed in its region by strong hydrogen bonding interactions and weak van der Waals interactions. The maximum energy is equal to -1006.93 kJ mol -1 . The calculations for LAY-.Hg 2+ indicate that the Hg 2+ cation formed four weak interactions of the type VdW for stabilized. The LAY-. is more selective to the Hg 2+ cation than that of CX [8] molecule. This result is confirmed by all the data. Hence, the CX [6], CX [8], LAY-. and NUB-. molecules are useful for the selective extraction of Ag 2+ , Cu 2+ and Hg 2+ inside, outside or on the surface to sensory processing.

A correlation between the QTAIM via NCI analysis established that the presence of the O … H interactions in each system facilitates the fixation, stuck and adsorption of the metal cations in the chosen target region.

QTAIM NCI plot CX[6]-Ag 2+

molecule. Moreover, a careful discussion of the O-H proton in the AN-.solvent explains that the O-H signal appears maximum if it is far from the environment of the added cation, it is very weak in the interaction zone, which proves that the cation decreases the O-H signal strength near its adsorption region. The sensor performance of the stable studied complexes has been discussed by the UV-visible and the total DOS orbital characterization. The newly obtained for the complexation of the CX [6], CX [8], NUB-. and LAY-. molecules by the Cu 2+ inside, outside or on the surface at the absorption level, it appears weak and shifted towards blue. On the contrary, the existence of Ag 2+ cation favors a red shifted peak. A detailed analysis of the electrophilic and nucleophilic sites have been studied by the Hirshfeld surface and MEPs topography to distinguish the attractive and repulsive interaction sites of the molecules to the Ag 2+ , Cu 2+ and Hg 2+ cations to demonstrate that CX [6], CX [8], NUB-. and LAY-. are able to select these cations inside, outside or on the surface. A correlation between QTAIM and the NCI analysis have been demonstrated that the Ag 2+ and Cu 2+ cations are stabilized by strong interactions of hydrogen bond with neighboring oxygen atoms and Van der Waals interaction with other neighboring atoms (C or H). It is specific, that the Hg 2+ cation fixed in the targeted area but it formed a weak Van der Waals interaction with the environment of the phenol group. This work provides a complete important stepping stone for understanding the effects of the binding mechanisms and adsorption of Ag 2+ , Cu 2+ and Hg 2+

metal cations at the level of the surfaces of the studied molecules, which will be a guide for the experimenters who will use these systems in the near future as a best trapping material of this cation for sensor applications.

Declarations

Figure1.

  Figure1. The most stable adsorption sites X 2+ (X=Ag, Cu and Hg) cation for the

Figure 1

 1 Figure 1 III pos2 , the Cu 2+ cation can form a couple of donor-acceptors with the phenol group. The interaction is identified like a π•••π interaction. The maximums of the electron densities are localized around the interactions Cu 2+ -C 4 , Cu 2+ -C 5 , O 1 -Cu 2+ and O 6 -Cu 2+ (HB1). These interactions are also compatible with complex formations in square planar geometry in experimental studies. The addition of the cation minimizes the axis of symmetry from C 2 to C 1 . About the structural parameters, the O 2 -H 3 (HB1) and O 9 -H 10 (HB2) have the following values 0.98 and 0.97 Å. In addition, the transfer of electrons between the atoms O8 ᷉ H 7҃ and O 1 ᷉ H 10 ensure the formation of the H-bonding interactions of the order of 1.67 and 1.82 Å. The comparison between the theoretical results of the O 1 … O 2 HB1 (2.74) and O 8 -O 9 HB2 (2.61 Å)

valence angles O 1 - 1 …

 11 Cu-O 6 , C 4 -Cu-C 5 and O 2 -Cu-C 5 show the degree of the compressive force exerted by the cation Cu 2+ on the phenol groups. The values are 125.57 °, 37.00 ° and 58.51 °, respectively. From the III pos3 , the strong interaction of the cation Cu 2+ with the atoms O 1 , O 2 and O 6 bundle this complex with a fairly relevant stability. The conformation III pos3 is characterized by the formation of four hydrogen bonds with cation Cu 2+ ; Cu 2+ -O 2 , Cu 2+ -O 6 , Cu 2+ -O 7 + and Cu 2+ -O 10 (HB1). It is seen that the electropositive cupper cation forms complex in the lower rim of the calixarene, which are the electron-rich due to hydroxyl groups, as expected. These hydrogen bonds interactions (HB1) result in the great stability of this hostguest. The symmetry is preserved after the addition of the cation. Also, it is observed the formation of the C-O .... π interactions. The physical interpretations of the structural parameters are almost similar to the previous conformation. Concerning to the III pos4 , the intermolecular π-π bonding interaction present in this compound shows the attraction of Cu 2+ cation by the atoms O 1 , C 3 and C 4 (HB1). The two lost electrons by Cu are captured by these atoms to stabilize this host-guest. As noted here, the electronic effect of Cu:2+ cation assures the increase of the electron density in this active region. Moreover, the symmetry is fixed in C 1 as before the addition of the cation. The values of O 98, 1.65 and 1.95 Å. The experimental hydrogen bonding interactions have values of 2.89, 2.91 and 1.81 Å. The addition of Cu 2+ cation disrupts the interactions of the hydrogen bonds (HB2). The cation promotes an electronic disturbance to attach itself to the targeted area (See Figure 1). The interaction O 7 -H 8 presents a value very close to the experimental value [48] equal to 0.98 Å. Therefore, it is known to have a force applied by the cation to the C 3 and C 4 atoms of phenol group. The bond lengths of the C 2 -C 3 and C 3 -C 4 are equal to 1.53 and 1.43A °. The experimental values [48] are equal to 1.51 and 1.39 Å. This result indicates that the cation imposes a compressive force on the benzene group, which ensures the modification of the carbon places. The angles in CX[6]-Cu 2+ (III pos4 ) are O 1 -Cu-C 3 (86.84 °), O 1 -Cu-C 4 (124.31 °) and C 3 -Cu-C 4 (124.31 °). These angles-interactions have a great interest in the stability of this host-guest. The interaction of NUBMOM-X 2+ visualize three conformations noted IV pos1 , IV pos2 , and IV pos3 (see Table

Figure 1 O 9 .

 19 Figure1shows that the cation generates π .... π interactions with the carbon C 3 , C 4 and the oxygen O 2 atoms. In this case the axis of symmetry is retained. The Cu 2+ cation breaks the hydrogen bond and forms with it a double π .... interaction for stabilizing the structure. The force exerted by the cation on the oxygen atom ensures the orientation of the phenol group

Figure 2 :

 2 Figure 2: The most stable adsorption sites X 2+ (X=Ag, Cu and Hg) cation for the

Figure 3 :

 3 Figure 3: The relative energy representations for the different studied host-guests (GM: Global Minimum, LM: Local Minimum, NUB-.: NUBMOM and LAY-.: LAYKUR).

  The high frequency vibration modes at 2050 (I pos2 ), 2667 (I pos1 ) and 2896 GHz (I pos3 ) are reported for the first time in the CX[6]-Ag 2+ complexes. These strong absorption stretching are correspond to independent of the C-H symmetric and asymmetrical stretching peaks mode to the three possibilities. It explains that the Ag 2+ cation forced the displacement of the O … H vibrations in comparison with the free CX[6] molecule from 3168 GHz (O … H anti-sym.) to these specifics values. The Ag 2+ cation is justified as a frequent moderator in a specific region. On the other hand, it is observed an appearance of two bands of medium intensity in the three conformations shifted approximately by 100 GHz. These typical phonon frequencies are corresponding to the cyclic O-H stretching vibrations. The system disorder provides couple relevant absorption located in the neighborhood of 3200 GHz for the I pos1,3 . The strange thing is the presence of the C-H vibration of phenol groups in these independents absorption frequency bands. The not acceptable points in this situation is the totally disturbed of the rule in the classification of frequencies in comparison to literature after the addition of the Ag 2+ cation in the CX[6] system. This cation ensures the exchange between the normal studied modes O … H and C-H according to the placement of cation. The visualization of the frequency bands for the CX[6]-Cu 2+ system shows that there is not a substantial difference between the absorption frequency bands O ... H, O-H and even C-H in the studied conformations. A high intensity absorption phonon band is noted located near to 10 5

Figure 4 .

 4 Figure 4. Three vibration models are proposed. Figure 4 shows that in the IV pos1 appears a frequency band of about 113.10 3 GHz corresponding to the O … H sym. and O-H at the same time. A direct visualization to the IV pos1 and IV pos2 complexes shows two close bands located in the vicinity of 107.10 3 GHz. These bands are named O-H free. The IV pos1 complex is characterized by a frequency phonon probably equal to 61.10 3 GHz. This strong absorption band corresponds to the C=C and C-H starching vibration of the phenol connected to the Cu 2+

  10 3 GHz. This frequency band of these complexes corresponds to the C=C assignments. The addition of the Hg 2+ cation to the cyclic O ... H system for the LAYKUR host has a direct effect only on the hydrogen band by forming instead of single peak free three frequency bands of fairly low intensity. This result is practically the only one in comparison with other studied systems. At high intensities are specified the infrared absorption bands of C=C, C ar. H and C met. H of the phenol groups.

Figure 4 :

 4 Figure 4: Calculated infrared spectra at 298 K, for CX[6]-X 2+ , NUBMOM-X 2+ , CX[8]-X 2+

Figure 5 :

 5 Figure 5: Descriptors computed for O-H proton deviations for each DFT functional using linear scaling factor for TMS absolute shielding.

CX[ 6 ]

 6 corresponds to the passage of an intrinsic electron from π state to π* state by 3.5 eV energy.

Figure 6 :

 6 Figure 6: UV-visible absorption spectroscopy and the Total DOS Orbitals analysis for the most stable targeted area cation.

Figure 7 :

 7 Figure 7: Comparison of energy shift between the CX[6], and CX[8] free and the stable studied complexes.

  2+ and Hg2+ with the H, C and O atoms in percentage, to define the majority of interactions formed between the cation and the specific atom in the targeted zone. The topography of each point on the Hirshfeld surface is described by two distances noted d e and d i . The first distance means the distance from a point on the surface to the nearest nucleus outside the surface and the second defines the distance between a point of the surface and the nearest nucleus inside the surface. The combination between di and de produces the fingerprint plot in 2D representation from 3D Hirshfeld surface. This theory can provide a summary of intermolecular contacts between the cation and others atoms. The fingerprint plots and the Hirshfeld surface maps are shown in Figure8. For CX[6]-X 2+ , the major interaction between the cation and neighboring molecule is between hydrogen atoms in Ag … H and Cu … H, this interaction covers 83.8 and 79.1 % of the surface. The strong hydrogen bond interactions between Ag … O/Cu … O are visualized by large spikes in the fingerprint plot. These specific interactions accounted for 6.6 and 4.5 %. This H-bonding interaction is also represented by bright red spots. From Figure8, the fingerprint plots show that Ag … C/Cu … C take up 9.2 and 11.4 %, respectively, of the total Hirshfeld surface. The contacts between the NUB-. molecule and the Ag 2+ , Cu 2+ cations promote H-interactions comprising 80 and 88.2 % of the total Hirshfeld surface area for these complexes. These interactions are specified by two small spikes on the sides of fingerprint plot. The remarkable result is that appears a minor Ag … O/Cu … O interaction comprising almost 6.6 and 4.5 % of all the interactions. These strong interactions are visualized by red spots in Hirshfeld surface (see Figure8). The fingerprint plots visualize that Ag … C and Cu … C contacts comprise 13.4 and 7.3 % of the total Hirshfeld surface area for the specific host-guests. Concerning the CX[8]-Ag 2+ and LAY-.Ag 2+

Figure 8 :

 8 Figure 8: Hirshfeld mapped surfaces and the fingerprint plots of the non-covalent interactions between the studied cation and the molecules in the specific region of the stable host-guests complexes.

Figure 9 :

 9 Figure 9: Molecular electrostatic potential (MEP) maps (iso-surface value= 0.05 a.u.) of the studied stable host-guests in front view or side view calculated at B3LYP-D3/6-31G(d)-def2svp level of theory. Negative, positive and neutral potential sites are represented by red, blue and yellow-green colors, respectively.

  52.71 kcal/mol and II pos2 has low energy around of 34.51 kcal/mol. Despite the O ... H bond is broken in the complex II pos1 , it is the most stable. This result shows that the classical studies which linked the great stability of conformations by the number of hydrogen bonding are not

	always obvious. The Table S3 shows the existence of the O ... H bonds (O 3	… H 4 , H 4 -O5 and O 6 -
	H 7 ) with values at 1.91 Å and 0.98 Å. The experimental values are 1.92 and 0.96 Å. The
	theoretical simulation values are in good agreement with the experimental values. Concerning
	the adsorption of the CX

  .. O 1 , π ... O 3 and π ... O 7 . The cation Cu 2+ can fixed in the center

	of the gravity of a triangle formed by three angles of the order of magnitude (113.71 ° (O 7 -Cu-
	O 1 ), 90.50 °( O 1 -Cu-O 3 ) and 137.67 °( O 3 -Cu-O 7 )

Table S3

 S3 recapitulates the interactions O 2 -H 3 , H 3 -O 4, O 6 -H 7, H 7 -O 8, O 8 -H 9 and H 9 -O 10 with the values 0.98, 2.03, 0.98, 1.91, 0.98, 1.71 Å, respectively. It is obvious to compare these values with those experimentally obtained; In this case, similar results were obtained before addingthe Hg 2+ cation. The addition of the Hg 2+ in the CX[6] or NUBMOM preserves all the Hbonding interaction. In this situation the cation is a " noble guest " for the structures. The weak deviation of the Hg 2+ cation about the phenol group is determined by the angle O 4 … Hg … C 5which is approximately to 27 °.

pos1 , see

  the cation and the target atom. Moreover, at the supra-molecular system III pos1 , it is shown that the Cu 2+ cation forms two π type interactions with the C 1 O 2 and C 3 O 4 groups to stabilize the structure. Due to the electropositivity of the Cu 2+ cation, we can deduced that an electron transfer and the taking of two unpaired electrons on the oxygen atoms at the lower rim in the calix[8]arene by the Cu 2+ cation. This result involved that the Figure2, clearly shows that the Cu 2+ cation bonds is located near the center of the phenol group forming five charge transfer band with this group. The flows of the charge transfer were visualized using the Gabedit program. About the physical interpretation, it was deduced that the electrons yielded by the Cu 2+ cation are not stable; it moves towards the C 6 , C 7 , C 8 , C 9 and C 10 carbon atoms with a very high speed, and

	O 5	… Cu … C 7 (134.68 °), O 5	… Cu … C 11 (77.33 °) and C 11	… Cu … C 7 (71.10 °) (Table
	are named by H 1 interactions which are equal to 1.96, 1.65 and 1.76 Å. The values given experimentally … O 2 , H 5 … O 6 , and H 7 … O 8 . Table S4 contains the calculated values of these (VARHAY) [48] are 2.30, 2.01 and 1.89 Å. So a fairly important modification is observed for the cooperativity of hydrogen bond interaction in each system. The breakup of the H … bonding ... Cu 2+ and C 3 O 4 … Cu 2+ . The energy parameter for this host-guest is higher than the two complexes known by IV pos1 and IV pos2 . As usual, the structural parameters are analyzed and compared with them experimentally obtained [48]. The O 2 … O 4 HB1, H 6 … O 7 HB2 and H 8 … O 9 HB2 are characterized by values equal to 3.70-2.69, 1.70-1.84 and 1.81-1.78 Å. The theoretical-experimental calculations give information for the reader that the Cu 2+ cation after destroying the two H they cannot be measured. Therefore, the electron populations are concentrated surrounding to the targeted phenol group. The symmetry group is C 1 . The H-binding distances H 2 … O 3 HB1 (1.83 Å), H 4 … O 5 HB1 (2.07 Å), O 12 -H 13 HB2 (0.99 Å) and H 13 … O 14 HB2 (1.64 Å) were interaction to form a π electron densities are very high surrounding to the groups C 1 O 2 calculated (Figure 2 and Table S4). The comparison of the results with the experimental

complex for LAYKUR. The first host-guest has a bond O 1 -H 2 and H 2 … O 3 of 0.99 A ° and 1.76 Å (see Table

S4

). The second is characterized by two symmetric interactions O 1 -H 2 and H 2 … O 3 , these have similar values as the precedent complex. The experimental values (VARHAY)

[START_REF]Initial structures taken from CSD: Cambridge Structural Database[END_REF]

are equal to 0.96 and 1.77 Å. The angles are close to 40°. The addition of the Hg 2+ cation has no effect on the structural parameters, in the same way the symmetry axis is preserved. A large electronic density is located in the center of the cavity. For II pos2 , this host-guest is specified by the extraction of the Ag 2+ cation between the oxygen atom O 2 and the carbon atom C 3 of the phenol group. In this situation, the cation forms two π … interactions with the two atoms. The two electrons given by the Ag:2+ cation are snatched by the carbon and oxygen. The two forces exerted by the bonds C 3 … Ag 2+ and O 2 … Ag 2+ reinforced the stability of each compound to take a good place in the energetic stability diagram (Figure

3

).

Energetically, the resulting binding energy of the related systems is ΔE= 144.33 kcal/mol. This stable complex remains less stable than I pos1 and II pos1 by a difference of about 10 kcal/mol. The H-bonding interactions which are responsible for the stability of this complex … interaction with the Ag 2+ cation ensure the stability of this host-guest.

The angle O 1 … Ag … O 3 is equal to 98.81 °. This angle is very important to stabilize to the cation in this active zone. Around of this angle environment there is a maximum electronic concentration between … bond interaction to take the most stable place which gives rise to modify all structural parameters, thus playing the role of moderator of stability. The forces formed by the Cu 2+ cation with C 1 O 2 and C 3 O 4 did not modify the Bond lengths of these groups, the values remained similar as the experimental results (see Table

S4

). The O 5 -H 6 and O 9 -H 10 interaction appears almost in the same value around of 0.99 Å. The greatest angle discussed is 150.51 ° (O 2 -Cu-O 4 ). This idea means that the Cu 2+ cation oriented towards the cavity exterior, the electron donor-acceptor torque flow is centrifuged. The complex IV pos1 is specified by the fixation of the Cu 2+ cation between two symmetric oxygen atoms (O 1 … Cu … O 7 ) which provided two symmetric systems HB1 and HB2. The majority of the H-bonding interactions are preserved. The electronic exchange flow is rectilinear passing from O 1 to O 7 . During the selection of the studied complexes of the same order of stability, a very surprising host-guest was found. This complex noted IV

values

[START_REF]Initial structures taken from CSD: Cambridge Structural Database[END_REF]

is 1.78, 1.78, 0.84 and 1.86 Å, respectively. There is a total disturbance of the hydrogen bonding interaction in two regions HB1 and HB2 during the addition of the Cu 2+ cation. The cation oriented in the direction of the phenol group is given by the angles

  3 GHz corresponding to a weak vibration of O-H cyclic groups. In this case the addition of the Cu 2+ cation preserves the O … H and the other type's vibrations as same of CX[4] free. The region assignments varying between 7.10 3 and 4.10 4 GHz correspond to the C ar .H, C met .H, C=C and C-H 2 vibrations. The infrared spectrum of two conformations for CX[6]-Hg 2+ divided into two parts, one part varies between 9.10 3 and 10 5 GHz was specified for the phonons of the O ... H (anti-sym.) and O-H(sym.) bands. A part is located between 8.10 3 and 49.10 3 GHz corresponding to the vibration of the C ar .H, C met .H, and C=C. The addition of the Hg 2+ cation in the CX

  3 GHz specified for the displacement of the phonons C=C, C-H 2 , C-H, C ar. H, and C met. H with a significant shift in comparison with that in the literature. The same interpretation has been noted for the cation Hg 2+ . The presence of Ag 2+ and Hg 2+ cations in the NUBMOM compound promotes a burst of the free H-bonding peak for the creation three infrared absorption bands located between 95.10 3 GHz and 11.10 4

  [START_REF] Temel | One novel calix[4]arene based QCM sensor for sensitive, selective and high performance-sensing of formaldehyde at room temperature[END_REF] have a maximum signal equal to 8.59 ppm. In contrary, the signal close to the Ag 2+ cation is characterized by a very low value equal to 2.68 ppm. This shift in the upper field indicates that the OH groups are non-hydrogen bonded. In other words, the Ag cation prevents the OH groups from making hydrogen bonding by taking electrons on the oxygen atoms in the formation of the complex. The maximum chemical shift detected by the O-H 6 (CX[6]-Ag 2+ ) and OH 3 (NUBMOM-X 2+ ) signals demonstrates that the cation weakens the chemical shifts around its environment. While, the hydrogen bonds proton located far from cation environment has a high δ OH value. These values observed in the lower field indicate the presence of hydrogen bonding. Moreover, the interaction of the proposed molecules with the 7 ensures the conservation of the proton signal OH 6 as when the CX[6] is free. It is important to notice that when the hydrogen bonds interactions are presented the signal will be important, if these interactions are disturbed by the Cu 2+ cation, it is concluded that the signal will be weak and shifted to upper field. This result is well explained by the signal OH 6 , the δ H value is equal to 13.57 ppm. A measure of the O-H signals after the addition of the metal cation Cu 2+ indicated that the chemical shifts are weak surrounding on the environment of the specific cation. The Cu 2+ cation disturbs the electronic concentrations of the O-H bonds, which prove a decrease in such proton signals. Concerning the host-guests CX[6]-Hg 2+ and NUBMOM-Hg 2+ , it is notable that the conservation of the cyclic hydrogen bond systems after the adsorption Hg 2+ cation causes quite significant signals. It is possible to say that these signals are very close to that free CX[6] in literature. On the contrary, the direct attack of the Hg 2+ cation added in the targeted zone for the second compound assumes a disruption of the system, hence the destruction of hydrogen bonds. The cyclic state of the cooperativity of the hydrogen bonds is destroyed likewise, this is why are shown different signals summarized in the TableS5. A case contrary to the previous ones is shown. It is deduced that when it is approached to the cation an important proton signal noted OH 3 (11.12 ppm) is found. If it is moved away from the cationic environment, a practically weak signal is found, for example δ OH9 =4.1 ppm. The strongest among these signals, at ~8.67-9.27 ppm are attributed to the signals of the OH symmetrical system in the CX[6]-Hg 2+ compounds. The interaction of the CX[8] molecule with the Ag 2+ , Cu 2+ , and Hg 2+ cations promotes an O-H signal, which varies between 8.09 to 9.92 ppm (see TableS6). The added of the Ag 2+ cation conserves the cyclic network of hydrogen bonds, so the signals are conserved equal to 8.09 ppm, therefore, this molecule is very sensitive to this type of cation. In contrast to the previous system, the Cu 2+ cation destroys the hydrogen system; hence O-H 8 bonds far from the targeted area with a high signal

	Cu 2+ cation results in a decrease in the chemical shifts towards 3.76-8.22 ppm (OH 2 -OH 4 ) for
	the CX[6]-Cu 2+ complex and from 5.1 to 9.61 ppm (OH 2 -OH 8 ) for the NUBMOM-X 2+

complex in comparison to the O-H chemical shift for CX

[6]

free reported in literature. For a more definite assignment of the studied signals, for CX

[6]

-Cu 2+ , it is shown a maximum signal for OH 6 located in the neighborhood of 10.11 ppm. For the other host-guest systems, it was obtained a frequency signal equal to 13.57 ppm. In this case, it is shown that the cooperativity of the hydrogen bonds between O-H 4 ... O-H 6 ... O-H are found. This assignment's value is around of 9.92 ppm. The no-destruction of the hydrogen bonds interactions for CX[8]-Hg 2+ involves high signals surrounding of 8 ppm. LAYKUR-Ag 2+ is characterized by O-H signals passing from 6.09 to 8.2 ppm (see Table S6). These values correspond to the chemical shifts of O-H 1 , O-H 5 and O-H 7 . Figure 5 shows that the electron concentrations are low when approaching to the Ag 2+ cation (O-H 1 signal). The cooperativity of the O-H 5 …O-H 7 …O 8 -H hydrogen bonds presented a signal almost at the same value equal to 8 ppm. For LAYKUR-Cu 2+ , the peaks with the highest chemical shifts, at 10.37 ppm can be assigned to the OH 13 signals (see Figure 5). A weak signal peak noted O-H 4

X=Ag X=Cu X=Ag X=Cu Ag … H, Ag … C and Ag … O interactions=83.8, 9.2, and 6.9 %. Ag … H, Ag … C and Ag … O interactions=79.1, 11.4, and 9.5 %. Ag … H, Ag … C and Ag … O interactions=80.0, 13.4, and 6.6 %. Ag … H, Ag … C and Ag … O interactions=88.2, 7.3 and, 4.5 %. CX[8]-X 2+ LAYKUR-X 2+ X=Ag X=Cu X=Ag X=Cu Ag … H, Ag … C and Ag … O interactions=96.5, 2.1, and 1.4 %. Ag … H, Ag … C and Ag … O interactions=87.6, 5.9, and 6.5 %. Ag … H, Ag … C and Ag … O interactions=89.8 7.4, and 2.8 %. Ag … H, Ag … C and Ag … O interactions=93.3, 3.8, and 2.9 %.

  TableS7clearly shows that BCP3 have the highest electron density value around of 0.6500 a.u. This BCP is characterized by high rapport of |V(r)|/G(r)(9.34). According to the above-described classification of Bianchi et al. (1 <V BCP /G BCP < 2), the ratio |V(r)|/G(r) ratio is outside of this intermediate bond regime, may be due to the great interaction between the cation and the oxygen atom. Likewise, the energy measured in this region is washed away.

	The E int (r) result is equal to -1240.02 kJ mol -1 . The lowest number of ρ(r) is located at 0.1845
	a.u (BCP2). Concerning to the complexation of the Hg 2+ cation and the CX[6] molecule, the
	ρ

bcp parameters in the range 0.1633-0.2005 a.u. with the corresponding positive Laplacian  2 ρ(r) parameters which predict the presence of hydrogen bonding. The NCI graphs show that the cation interacts with the environment of the closest phenol groups forming with it van der Waals interactions. From Figure

Acknowledgements

M.E.C. and F.J.M. thank the LaboratorioNacional de Supercómputo del Sureste de México (LNS-BUAP) of the CONACyT network of national laboratories for the computer resources and support provided.

Availability of data and material:

RMSD calculated, geometry optimization for the cone conformer (CX [6,8] ), Selected structural parameters of CX [6]-X 2+ , NUB-.X 2+ , CX [8]-X 2+ and LAY-.X 2+ , O-H proton

LAYKUR-X 2+

complexes but of unequal concentration. The maximum of the nucleophilic reactivity is characterized the phenol groups of the CX [8]-Ag 2+ and CX [8]-Hg 2+ complexes. It is clear that the phenol aromatic rings in the NUB.-Cu 2+ , CX [8]-Cu 2+ and LAY-.Cu 2+ are less electronrich compared with the other members of the complexes. A neutral zone appears (green color) around the Hg 2+ cation for the CX [8]-Hg 2+ complex. This result shows that there is almost no interaction between the cation and the target molecule. Thus, all the charges are concentrated behind the cation, as this is also indicated by the Hirshfeld surface.

The three-dimensional (3D) MEPs maps (see Figure 9) provide a good selectivity, reactivity and affinity between the guest and host in the chose targeted area.

Summary and conclusions

Dispersion-corrected density functional theory DFT-D3 was performed to calculate the studied systems in the presence of the metal cations Ag 2+ , Cu 2+ and Hg 2+ in the targeted area of the molecular receptor CX [6] CX [8], NUB-. and LAY-. The vibrational spectrum analysis confirms that the addition of metal cation to the CX [6] and CX [8] result a noteworthy frequency-shifted of characteristic of the O … H stretching vibration in comparison to the free

Conflicts of interest:

The authors declare that they have no conflict(s) of interest.

Authors contributions:

B. Gassoumi: wrote the paper, conceived and designed the analysis.

F.E. Ben Mohamed, M. E. Castro, F.J. Melendez, L. Nouar, F. Madi: performed a part of calculation and interpret some results.

A. Karayel, S. Özkınalı: analyzed and interpreted the data;

H. Ghalla: performed the AIM analysis.

R. Ben. Chaabane, V. I. Kovalenko, H. Ben Ouada: supervisor of the paper.