Computational Insight into the Nature and Strength of the π-Hole Type Chalcogen∙∙∙Chalcogen Interactions in the XO2∙∙∙CH3YCH3 Complexes (X = S, Se, Te; Y = O, S, Se, Te)

In recent years, the non-covalent interactions between chalcogen centers have aroused substantial research interest because of their potential applications in organocatalysis, materials science, drug design, biological systems, crystal engineering, and molecular recognition. However, studies on π-hole-type chalcogen∙∙∙chalcogen interactions are scarcely reported in the literature. Herein, the π-hole-type intermolecular chalcogen∙∙∙chalcogen interactions in the model complexes formed between XO2 (X = S, Se, Te) and CH3YCH3 (Y = O, S, Se, Te) were systematically studied by using quantum chemical computations. The model complexes are stabilized via one primary X∙∙∙Y chalcogen bond (ChB) and the secondary C−H∙∙∙O hydrogen bonds. The binding energies of the studied complexes are in the range of −21.6~−60.4 kJ/mol. The X∙∙∙Y distances are significantly smaller than the sum of the van der Waals radii of the corresponding two atoms. The X∙∙∙Y ChBs in all the studied complexes except for the SO2∙∙∙CH3OCH3 complex are strong in strength and display a partial covalent character revealed by conducting the quantum theory of atoms in molecules (QTAIM), a non-covalent interaction plot (NCIplot), and natural bond orbital (NBO) analyses. The symmetry-adapted perturbation theory (SAPT) analysis discloses that the X∙∙∙Y ChBs are primarily dominated by the electrostatic component.


Introduction
A chalcogen bond (ChB) [1][2][3][4] is an attractive non-covalent interaction (NCI) between an electron-deficient region related to a chalcogen atom (mainly S, Se, and Te) as Lewis acids and any electron-rich region (lone pairs, π-electrons, anions) as Lewis bases.These electron-deficient regions corresponding to the positive electrostatic potentials can be divided into two categories: σ-holes and π-holes [5][6][7][8][9].The former is generally located along the extension of the covalent σ-bond involving a chalcogen atom, while the latter is generally located perpendicular to the σ-framework of the molecular entity.Both σ-holes and π-holes are capable of interacting attractively with Lewis bases, and the formed NCIs are called the σ-hole interactions and π-hole interactions [6,7,[10][11][12][13], respectively.Previous studies disclose that the attractive nature of such interactions is mainly composed of electrostatic, dispersion, and charge transfer interactions [1,14].In analogy to the halogen bonds (HaBs) [15,16] which involve group VII element atoms (mainly Cl, Br, and I) as Lewis acid sites, the ChBs exhibit a strong directional nature as a result of the existence of the σ-hole.In addition, the ChBs also exhibit comparable strength to that of the HaBs or hydrogen bonds (HBs) [17] and in some cases even exceed that of the HBs [18,19].Additionally, it should be noted that the chalcogen atoms can serve not only as the ChB donors owing to the existence of an σ-hole [20][21][22][23] or π-hole [24][25][26] on the chalcogen atoms, but also as the ChB acceptors thanks to the presence of lone pairs of electrons on the chalcogen atoms as in chalcoethers [20,26].
Among the various ChBs, the non-covalent chalcogen•••chalcogen interactions have received substantial research interest in recent years because of their potential applications in organocatalysis [27][28][29][30], materials science [31], drug design [32], biological systems [33][34][35][36], crystal engineering [37][38][39], and molecular recognition [40,41].Experimental and theoretical studies concerning such interactions have suggested that both the chalcogen atom size and the substituents covalently attached to the chalcogen atom can affect the strength of the ChBs [37,42,43].Specifically, the ChB becomes stronger in strength as the ChB donor atom increases in size and progressively becomes weaker in strength as the ChB acceptor atom increases in size.Moreover, the strength of the ChB becomes greater as the electron-withdrawing capacity of the substituent covalently linked to the ChB donor atom and the electron-donating capacity of the substituent adjoined with the ChB acceptor atom increase.Gleiter and colleagues [42,43] theoretically studied the binary complexes of CH 3 YCH 3 and CH 3 YZ (Y = S, Se, Te; Z = CH 3 , CN), and symmetry-adapted perturbation theory (SAPT) analysis demonstrated that dispersion and induction forces are responsible for the formation of chalcogen•••chalcogen interactions.Additionally, statistical analyses of crystal structure surveys have also shown that there is a great number of chalcogen•••chalcogen interactions in small molecules, nucleic acids, proteins, and protein-ligand complexes [33,35,36,[44][45][46][47], further suggesting the importance of such chalcogen•••chalcogen interactions.
Currently, the vast majority of investigations concerning ChBs focus on the divalent chalcogen atoms as the ChB donors [18,[27][28][29][30][31][32][33][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50].However, the chalcogen atoms can also frequently participate in hypervalent bonding such as tetravalent bonding [21,[51][52][53].Taking the S atom as an example, it behaves as a tetravalent bond in both SF 4 and SO 2 .The former acts as a ChB donor to form the σ-hole interactions with Lewis bases [19,54], while the latter acts as a ChB donor to form the π-hole interactions with Lewis bases [24,26,55,56].Scheiner and coworkers theoretically studied the heterodimers of SF 4 and nitrogencontaining Lewis bases and revealed that the S•••N ChB are stronger in strength than that of a classical hydrogen bond [19].The same group also computationally studied the S•••O ChBs between SO 2 and a series of carbonyl-containing molecules, and the results show that the most stable isomer of each complex is mainly stabilized by one S•••O ChB as the primary interaction, supplemented by weak C−H•••O HBs [55].Recently, Feng and coworkers applied microwave spectroscopy and theoretical calculations to investigate the gas-phase binary complex of SO 2 with cyclohexanol and found that the two moieties within the four detected isomers are connected together via one dominant S•••O ChB and secondary weak C/O−H•••O=S HBs [56].Microwave spectroscopic investigation on the SO 2 •••CH 3 SCH 3 complex demonstrated that the S•••S ChB is the primary interaction with the determined distance of 2.947(3) Å [26].The SAPT analysis results indicate that the electrostatic interactions mainly dominate the attractive nature of both S•••O and S•••S ChBs in the two above-mentioned complexes [26,56].

Molecular Electrostatic Surface Potential (MESP)
For the sake of identifying the potential interaction sites in each monomer, the MESPs of the XO 2 (X = S, Se, Te) and CH 3 YCH 3 (Y = O, S, Se, Te) monomers were computed at the MP2/aug-cc-pVTZ(PP) level of theory.The MESP maps of these monomers are shown in Figure 1.For all the monomers, the positive potential corresponds to the redcolored region and the negative potential corresponds to the blue-colored region.For the XO 2 (X = S, Se, Te) monomers, the positive potential regions (π-holes) are located above the chalcogen atoms on both sides of the monomeric plane, exhibiting a perpendicular orientation to the molecular plane.The negative potential regions are located at the surfaces of two O atoms.The most positive electrostatic potential values (V S,max ) are 183.0,217.8, and 257.7 kJ/mol for the SO 2 , SeO 2 , and TeO 2 molecules, respectively.The V S,max values related to the chalcogen atom become more positive as the chalcogen atom increases in size.This can be primarily attributed to the fact that the polarizability of the X atom becomes larger, and its electronegativity becomes smaller as the size of the chalcogen atom increases.hydrogen bonds [57,58], chalcogen bonds [20,26], and pnictogen bonds [59].Additionally, the molecular electrostatic surface potential (MESP) [60], quantum theory of atoms in molecules (QTAIM) [61], non-covalent interaction plot (NCIplot) [62], natural bond orbital (NBO) [63], and symmetry-adapted perturbation theory (SAPT) [64] analyses were also conducted to gain a deeper understanding of the π-hole-type chalcogen•••chalcogen interactions.Simultaneously, we have also compared the strength and nature of such interactions with those of the σ-hole-type chalcogen•••chalcogen interactions within the CH3YCH3•••CH3YZ (Y = S, Se, Te; Z = CH3, CN) complexes [42,43].

Molecular Electrostatic Surface Potential (MESP)
For the sake of identifying the potential interaction sites in each monomer, the MESPs of the XO2 (X = S, Se, Te) and CH3YCH3 (Y = O, S, Se, Te) monomers were computed at the MP2/aug-cc-pVTZ(PP) level of theory.The MESP maps of these monomers are shown in Figure 1.For all the monomers, the positive potential corresponds to the red-colored region and the negative potential corresponds to the blue-colored region.For the XO2 (X = S, Se, Te) monomers, the positive potential regions (π-holes) are located above the chalcogen atoms on both sides of the monomeric plane, exhibiting a perpendicular orientation to the molecular plane.The negative potential regions are located at the surfaces of two O atoms.The most positive electrostatic potential values (VS,max) are 183.0,217.8, and 257.7 kJ/mol for the SO2, SeO2, and TeO2 molecules, respectively.The VS,max values related to the chalcogen atom become more positive as the chalcogen atom increases in size.This can be primarily attributed to the fact that the polarizability of the X atom becomes larger, and its electronegativity becomes smaller as the size of the chalcogen atom increases.

Geometrical Structures and Binding Energies of the Studied Complexes
Based on the interaction sites identified by the MESP analysis, the initial structures of the studied 12 complexes were obtained by changing the relative positions between XO 2 and CH 3 YCH 3 monomers.Figure 2 shows the geometrically optimized structures of these 12 complexes, and the corresponding Cartesian coordinates for each complex are provided in Tables S1-S3 in the Supplementary Materials.The binding energies (E B ) and the key geometrical parameters associated with the ChBs within these complexes are summarized in Table 1.One can clearly find that the complexes of CH 3 OCH 3 with XO 2 (X = S, Se, Te) possess C 1 symmetry and the remaining complexes have C s symmetry.Interestingly, it should be pointed out that the structures possessing C s symmetry for the XO 2 •••CH 3 OCH 3 (X = S, Se, Te) complexes are unstable, with imaginary frequencies.The distances (R ChB ) between two interacting chalcogen atoms in all these complexes vary from 2.603 Å to 3.210 Å (Table 1), which are obviously smaller than the sum (R sum,1 ) of van der Waals radii of the corresponding two atoms by 18.6% to 29.4% [65], thus suggesting the formation of a strong π-hole-type chalcogen•••chalcogen interaction.However, it should be also noted that these distances are bigger than the sum (R sum,2 ) of covalent radii of the two interacting chalcogen atoms by 18.0% to 56.8% [66].The π-hole-type X•••Y distances in this work are all significantly shorter than the σ-hole-type [42,43], suggesting that the π-hole-type X•••Y ChBs are stronger in strength than those of the σ-hole-type X•••Y ChBs.In addition, Obenchain and collaborators investigated the π-hole chalcogenbonded complex formed between SO 2 and CH 3 SCH 3 using high-resolution microwave spectroscopy in the gas phase and experimentally determined the intermolecular S•••S distance of 2.947(3) Å [26].This is in good accordance with the computed theoretical value of 2.920 Å, demonstrating the reliability of the theoretical method utilized in this paper.We also calculated the ratio (λ) between R ChB and R sum,1 to qualitatively evaluate the strength of the π-hole-type chalcogen•••chalcogen interactions.The calculated λ values range from 0.71 to 0.81 for all the studied complexes, further indicating that the relatively strong π-holetype chalcogen•••chalcogen interactions are formed in the studied complexes.The O•••H distances between one of the O atoms of XO 2 and one of the H atoms of CH 3 YCH 3 are determined to be in the range of 2.021-2.704Å (see Table S4).These O•••H distances in all the studied complexes except for the SO 2 •••CH 3 OCH 3 complex are significantly lower than the sum (2.62 Å) of van der Waals radii of the corresponding two atoms.The ∠C−H•••O angle has been determined to be in the range of 102.4-151.8• (see Table S4).It is important to point out that the O•••H distance gradually decreases and the ∠C−H•••O angle becomes bigger as the Y atomic radius increases for a given XO 2 (X = S, Se, or Te) subunit.This suggests that the strength of the C−H•••O HB becomes progressively stronger as the size of the Y atom increases.
One can see from Table 1 that the E B values of the studied complexes vary from −21.6 kJ/mol for the SO 2 •••CH 3 OCH 3 complex to −60.4 kJ/mol for the TeO 2 •••CH 3 TeCH 3 complex.For a given ChB acceptor, the E B in absolute value gradually increases with increases in the X atom size, which is very consistent with the above-mentioned MESP analysis results.For the same ChB donor, the E B value becomes more negative as the Y atomic radius increases.It is worth noting that there is a good linear correlation between the E B and the V S,max values (Figure S1) of XO 2 as well as the V S,min values (Figure S2) of CH 3 YCH 3 .In addition, a linear correlation is also found between the E B and the X•••Y distance (Figure S3).
It should be also noted that although there exist other isomers involving only hydrogen bonds for the studied model complexes on the potential energy surface, all these hydrogenbonded isomers are not true minima due to the existence of an imaginary vibrational frequency.This suggests that the π-hole-type chalcogen bonds play a crucial role in stabilizing the studied model complexes.Furthermore, this work mainly focuses on the π-hole-type chalcogen•••chalcogen interactions; thus, the discussion on these hydrogenbonded isomers has been omitted for simplicity.One can see from Table 1 that the EB values of the studied complexes vary from −21.6 kJ/mol for the SO2•••CH3OCH3 complex to −60.4 kJ/mol for the TeO2•••CH3TeCH3 complex.For a given ChB acceptor, the EB in absolute value gradually increases with increases in the X atom size, which is very consistent with the above-mentioned MESP analysis results.For the same ChB donor, the EB value becomes more negative as the Y atomic radius increases.It is worth noting that there is a good linear correlation between the EB and the VS,max values (Figure S1) of XO2 as well as the VS,min values (Figure S2) of CH3YCH3.In addition, a linear correlation is also found between the EB and the X•••Y distance (Figure S3).

Quantum Theory of Atoms in Molecules (QTAIM) Analysis
For the purpose of estimating the strength and nature of the π-hole-type chalcogen•••chalcogen interactions present in the studied complexes, we performed the QTAIM analysis on the basis of the optimized structures at the MP2/aug-cc-pVTZ(PP) level.One bond critical point (BCP) and bond path (BP) between the two interacting chalcogen atoms in each complex was identified (see Figure 3 2 lists the calculated topological parameters at the BCPs including the electron density (ρ(r)), Laplacian of electron density (∇ 2 ρ(r)), and total energy density (H(r)).The absolute ratio between local kinetic energy density (G(r)) and local potential energy density (V(r)) was also computed and is given in Table 2.One can see that the ρ(r) value varies from 0.0290 a.u for the SO 2 •••CH 3 OCH 3 complex to 0.0438 a.u for the TeO 2 •••CH 3 OCH 3 complex, and the corresponding ∇ 2 ρ(r) value varies between 0.0184 and 0.0911 a.u, suggesting the formation of a relatively strong interaction between two chalcogen atoms.In addition, the ρ(r) value gradually decreases in the order of Y = O > S > Se > Te for the same Lewis acids (XO 2 ).Similarly, for the same Lewis bases (CH 3 YCH 3 ), the ρ(r) value gradually becomes larger as the X atom increases in size.This is in good accordance with the above-mentioned MESP analysis results.The QTAIM analysis results reveal that the π-hole-type chalcogen•••chalcogen interactions in all the studied complexes are moderate strong closed-shell interactions owing to the positive ∇ 2 ρ(r) values.Apart from the SO 2 •••CH 3 OCH 3 complex, the H(r) values are all negative and the |G(r)/V(r)| values are less than 1, demonstrating that the natures of these chalcogen•••chalcogen interactions have partial covalent characters.The intermolecular interactions between XO2 and CH3YCH3 were also characterized

Non-Covalent Interaction Plot (NCIplot) Analysis
The intermolecular interactions between XO 2 and CH 3 YCH 3 were also characterized and visualized by performing the NCIplot analysis, which is based on the electron density and its derivatives.The NCIplot analysis results are graphically displayed in Figure 4, where the weak and strong attractive interactions are represented in green-colored and blue-colored regions, respectively, and the repulsive interactions correspond to the redcolored regions.One can see that one dark blue isofurface between the X atom and Y atom in each studied complex was found, indicating the existence of a strong attractive chalcogen•••chalcogen interaction.Additionally, two green(-blush) isosurfaces between the O and H atoms were also found in all the studied complexes, suggesting the presence of two weak attractive C−H•••O HBs.It should be noted that the attractive HBs in the XO 2 •••CH 3 OCH 3 (X = S, Se, Te) complexes are the weakest among these HBs.

Natural Bond Orbital (NBO) Analysis
To further understand the nature of the X•••Y ChBs in terms of orbital interactions and the corresponding second-order perturbation energy (E (2) ), which can qualitatively represent the strength of the X•••Y ChBs, NBO analysis has been implemented for the studied complexes.Table 3 summarizes the obtained E (2) values for orbital interactions associated with the X•••Y ChBs.The results disclose that the interactions between the lone pair (LP) of the Y atoms of CH 3 YCH 3 and π*(O=X, X = S, Se, Te) antibonding orbital of XO 2 are the largest contribution to the stabilization of these twelve complexes.One can note that the E (2) values for all the LP(Y)→π*(O=X) orbital interactions except for the LP(O)→π*(O=S) orbital interaction in the SO 2 •••CH 3 OCH 3 complex are relatively large.Indeed, the X•••Y ChB is so strong that the NBO judges it to be a covalent bond in the SeO 2 •••CH 3 TeCH 3 , TeO 2 •••CH 3 SeCH 3 , and TeO 2 •••CH 3 TeCH 3 complexes.In other words, the NBO considers these three complexes as one single molecular entity.For the same ChB donor, e.g., SO 2 , the E (2) value becomes larger as the Y atom becomes bigger in size.Similarly, for the same ChB acceptor, e.g., CH 3 OCH 3 , the E (2) value increases upon going from the S atom to the Te atom.The changing trend of the E (2) values is in qualitative accordance with that of the E B values and the NCIplot findings described above.In addition, Figure 5 also graphically displays the NBO analysis results for the three selected representative complexes.One can clearly see that there exists a large overlap between the LP orbital of the S atom of CH 3 SCH 3 and the π*(O=X) antibonding orbital of XO 2 (X = S, Se, Te), suggesting the existence of strong X•••S ChBs.

Natural Bond Orbital (NBO) Analysis
To further understand the nature of the X•••Y ChBs in terms of orbital interactions and the corresponding second-order perturbation energy (E (2) ), which can qualitatively represent the strength of the X•••Y ChBs, NBO analysis has been implemented for the studied complexes.Table 3 summarizes the obtained E (2) values for orbital interactions associated with the X•••Y ChBs.The results disclose that the interactions between the lone pair (LP) of the Y atoms of CH3YCH3 and π*(O=X, X = S, Se, Te) antibonding orbital of XO2 are the largest contribution to the stabilization of these twelve complexes.One can note that the E (2) values for all the LP(Y)→π*(O=X) orbital interactions except for the LP(O)→π*(O=S) orbital interaction in the SO2•••CH3OCH3 complex are relatively large.Indeed, the X•••Y

Symmetry-Adapted Perturbation Theory (SAPT) Analysis
We also carried out the SAPT analysis to gain an in-depth understanding of the intrinsic nature of the studied intermolecular interactions.This method can decompose the total interaction energies (Etotal) of the studied complexes into the three attractive components including electrostatics (Eelec), induction (Eind), and dispersion (Edisp) interactions and

Symmetry-Adapted Perturbation Theory (SAPT) Analysis
We also carried out the SAPT analysis to gain an in-depth understanding of the intrinsic nature of the studied intermolecular interactions.This method can decompose the total interaction energies (E total ) of the studied complexes into the three attractive components including electrostatics (E elec ), induction (E ind ), and dispersion (E disp ) interactions and one repulsive component of exchange-repulsion (E ex-re ) interaction.Table 4 collects the resulting energetical values for each component.It is evident that the electrostatic component is the largest contributor for the attraction of these interactions, which stabilize the studied complexes.The contribution of this component to the total attractive interaction energy varies between 41% and 51%.The dispersion component is dominant over the induction component in the SO 2 •••CH 3 OCH 3 complex, whilst the induction component is superior to the dispersion component for all the remaining complexes.It is estimated that these two components account for about 49-59% of the total attractive interaction energies.Conversely, the σ-hole-type chalcogen•••chalcogen interactions are mainly dominated by induction and dispersion components in the CH 3 XCN•••CH 3 YCH 3 (X = S, Se, Te; Y = O, S, Se, Te) complexes [42,43].The results of the SPAT analysis also indicate that the total interaction energies range from −31.3 kJ/mol for the SO 2 •••CH 3 OCH 3 complex to −129.8 kJ/mol for the TeO 2 •••CH 3 TeCH 3 complex.For the same Lewis acid, the E total value becomes more negative with increasing Y atom size.For the same Lewis base, the E total value also becomes more negative upon moving from X = S to Te atom.In addition, the changing trend of the total interaction energies obtained from the SAPT analysis has a linear correlation with that of the binding energies in Table 1 (Figure S4).Table 4.The energetical values of the attractive and repulsion components as well as total interaction energies for the studied complexes obtained by using the SAPT approach at the SAPT2+3/aug-cc-pVTZ(PP) level of calculation a .

Computational Methods
Full geometry optimizations of both monomers and complexes have been carried out via the MP2 method [67] in combination with the aug-cc-pVTZ basis set [68].The MP2/augcc-pVTZ level of theory has been frequently employed to investigate various chalcogenbonded complexes owing to its accuracy and reliability, which have been demonstrated in the past [24,25,48,49,54].The pseudopotential aug-cc-pVTZ-PP basis set [69] obtained from the EMSL new Basis Set Exchange (BSE) library [70] was employed for the Te atom to consider the relativistic effects.The same level was also utilized for conducting harmonic vibrational frequency calculations to verify that all the optimized geometrical structures are real minima with no imaginary frequencies.The binding energies (E B ) of the complexes were computed by applying the following equation: where E AB denotes the energy of the complex, and E A and E B represent the energy of the isolated optimized monomers.The counterpoise method [71] was utilized to correct the binding energies by removing the basis set superposition error (BSSE).The Gaussian 16 program [72] was used to execute all the computations described above.The Multiwfn program [73] was employed to compute the molecular electrostatic surface potentials (MESPs) of the monomers on the electron/Bohr 3 isosurface and the resulting MESP isosurfaces were visualized utilizing the VMD software (version 1.9.3) [74].The Bader's QTAIM analysis was performed at the MP2/aug-cc-pVTZ(PP) level of theory via the Multiwfn program to identity bond paths (BPs) and obtain their topological properties including the electron density (ρ(r)), Laplacian of electron density (∇ 2 ρ(r)), local kinetic energy density (G(r)), local potential energy density (V(r)), and total energy density (H(r)) at the bond critical points (BCPs).The Johnson's NCIplot approach was applied for characterizing the intermolecular interactions occurring in the studied complexes using the Multiwfn program, and the NCIplot analysis results were also visualized with the VMD program.The information on the charge transfer, orbital interactions, and second-order perturbation energy (E (2) ) in the studied complexes was obtained by performing the NBO analysis using the NBO 3.1 module embedded into Gaussian16 program at the B3LYP-D3(BJ)/def2-TZVP level.The SAPT2+3/aug-cc-pVTZ(PP) level [64] was chosen to perform the SAPT analysis in the PSI4 software (version 1.3.2) [75] for quantitatively understanding the nature of the studied intermolecular interactions.

Conclusions
In summary, we systematically studied the π-hole-type chalcogen•••chalcogen interactions in a series of model complexes of XO 2 (X = S, Se, Te  [42,43].The findings of the SAPT analysis indicate that electrostatic interactions are the largest contributor to the stabilization of the studied complexes, but the induction and dispersion interactions also play a key role in stabilizing the studied complexes.Hopefully, the findings obtained from this work will prove valuable to the scientific community engaged in crystal engineering, materials science, drug design, organocatalysis, molecular recognition, and biological systems.
Conversely, the negative potential regions are distributed around the chalcogen atoms for the CH 3 YCH 3 (Y = O, S, Se, Te) monomers, and the positive potential regions are located on the H atoms of each CH 3 group.The absolute value of the V S,min associated with the chalcogen atom decreases as the chalcogen atomic radius increases.The most negative potential values (V S,min ) are −143.9,−103.6,−99.2, and −91.4 kJ/mol for the CH 3 OCH 3 , CH 3 SCH 3 , CH 3 SeCH 3 , and CH 3 TeCH 3 molecules, respectively.Accordingly, we can predict that the intermolecular π-hole-type chalcogen•••chalcogen interactions between the X atom of XO 2 and the Y atom of CH 3 YCH 3 and the C−H•••O interactions between the O atoms of XO 2 and the H atoms of CH 3 YCH 3 can be formed.Int.J. Mol.Sci.2023, 24, x FOR PEER REVIEW 3 of 14 Conversely, the negative potential regions are distributed around the chalcogen atoms for the CH3YCH3 (Y = O, S, Se, Te) monomers, and the positive potential regions are located on the H atoms of each CH3 group.The absolute value of the VS,min associated with the chalcogen atom decreases as the chalcogen atomic radius increases.The most negative potential values (VS,min) are −143.9,−103.6,−99.2, and −91.4 kJ/mol for the CH3OCH3, CH3SCH3, CH3SeCH3, and CH3TeCH3 molecules, respectively.Accordingly, we can predict that the intermolecular π-hole-type chalcogen•••chalcogen interactions between the X atom of XO2 and the Y atom of CH3YCH3 and the C−H•••O interactions between the O atoms of XO2 and the H atoms of CH3YCH3 can be formed.

Figure 1 .
Figure 1.The MESP maps of the XO2 (X = S, Se, Te) and CH3YCH3 (Y = O, S, Se, Te) monomers.The red-colored region indicates the positive potential and the blue-colored region indicates the negative potential.The VS,max and VS,min values (in kJ/mol) denote the most positive potential and the most negative potential, respectively.

Figure 1 .
Figure 1.The MESP maps of the XO 2 (X = S, Se, Te) and CH 3 YCH 3 (Y = O, S, Se, Te) monomers.The red-colored region indicates the positive potential and the blue-colored region indicates the negative potential.The V S,max and V S,min values (in kJ/mol) denote the most positive potential and the most negative potential, respectively.

Figure 2 .
Figure 2. The optimized geometrical structures of the studied complexes.The chalcogen•••chalcogen distances are given in Å.The binding energies in kJ/mol are displayed using blue numbers.

Figure 2 .
Figure 2. The optimized geometrical structures of the studied complexes.The chalcogen•••chalcogen distances are given in Å.The binding energies in kJ/mol are displayed using blue numbers.
), demonstrating the formation of the π-holetype chalcogen•••chalcogen interaction.Interestingly, no BCPs and BPs associated with the C−H•••O HBs were found in the SO 2 •••CH 3 OCH 3 complex, and there only exists one BCP and BP associated with one C−H•••O HB in the SeO 2 •••CH 3 OCH 3 complex.However, for all the other complexes, two BCPs and BPs related to two C−H•••O HBs between each O atom of XO 2 and one H atom of each CH 3 group of CH 3 YCH 3 were identified.Table

14 Figure 3 .
Figure 3.The diagrams of the QTAIM analysis for the studied complexes.The orange and yellow dots represent the bond critical points (BCPs) and ring critical points (RCPs), respectively.The brown lines denote the bond paths.

Figure 3 .
Figure 3.The diagrams of the QTAIM analysis for the studied complexes.The orange and yellow dots represent the bond critical points (BCPs) and ring critical points (RCPs), respectively.The brown lines denote the bond paths.
Figure 4 also displays the scatter plots of the electronic reduced density gradient (RDG) vs. the sign(λ 2 )ρ for the twelve studied complexes.It is seen that the sign(λ 2 )ρ values associated with the X•••Y ChBs and the C−H•••O HBs are all negative, further confirming the presence of intermolecular attractive interactions.However, the sign(λ 2 )ρ values for the X•••Y ChBs are significantly more negative than those for the C−H•••O HBs, indicating the strengths of the X•••Y ChBs are obviously stronger than those of the C−H•••O HBs in all the studiedcomplexes.Furthermore, it is worth mentioning that for the given ChB acceptor, the sign(λ 2 )ρ value becomes more negative upon going from the S to Te, demonstrating that the X•••Y ChBs are stronger in strength in the order of X = S < Se < Te.This matches very well with the MESP and QTAIM analysis results.

X
•••Y ChBs and the C−H•••O HBs are all negative, further confirming the presence of intermolecular attractive interactions.However, the sign(λ 2 )ρ values for the X•••Y ChBs are significantly more negative than those for the C−H•••O HBs, indicating the strengths of the X•••Y ChBs are obviously stronger than those of the C−H•••O HBs in all the studied complexes.Furthermore, it is worth mentioning that for the given ChB acceptor, the sign(λ 2 )ρ value becomes more negative upon going from the S to Te, demonstrating that the X•••Y ChBs are stronger in strength in the order of X = S < Se < Te.This matches very well with the MESP and QTAIM analysis results.
(2) value (kJ/mol) related to the X•••Y ChBs in all the studied complexes a .lone pair, and BD* represents antibonding orbital.b The corresponding ChB is so strong that the NBO judges it to be a covalent bond.

Figure 5 .
Figure 5.The NBO plots of the donor-acceptor interaction for the three selected representative complexes.

Figure 5 .
Figure 5.The NBO plots of the donor-acceptor interaction for the three selected representative complexes.
) with CH 3 YCH 3 (Y = O, S, Se, Te) using ab initio calculations in conjunction with QTAIM, NCIplot, NBO, and SAPT methodologies in this work.The binding energies range from −21.55 kJ/mol for the SO 2 •••CH 3 OCH 3 complex to −61.38 kJ/mol for the TeO 2 •••CH 3 TeCH 3 complex.The X•••Y distance varies between 2.526 Å and 3.210 Å, which is obviously less than the sum of the van der Waals radii of the corresponding two chalcogen atoms.The QTAIM analysis results suggest that all the X•••Y ChBs are closed-shell interactions, and simultaneously, the X•••Y ChBs possess some degree of covalent character in all the studied complexes, except for the SO 2 •••CH 3 OCH 3 complex.The strengths of the X•••Y ChBs are clearly stronger than those of the C−H•••O HBs, revealed by performing the NCIplot and NBO analyses.In addition, the π-hole-type X•••Y ChBs are stronger in strength than those of the σ-hole-type X•••Y ChBs in the CH 3 XCN•••CH 3 YCH 3 (X = S, Se, Te; Y = O, S, Se, Te) complexes

Table 1 .
The binding energies (EB, kJ/mol) and geometrical parameters associated with the ChBs for the studied complexes.

Table 1 .
[66]binding energies (E R sum,1 denotes the sum of the van der Waals radii of the corresponding two chalcogen atoms, and the van der Waals radii of the O, S, Se, and Te atoms are 1.52, 1.80, 1.90, and 2.06 Å, respectively[65].bλdenotes the ratio of R ChB and R sum,1 .cRsum,2denotes the sum of the covalent radii of the corresponding two chalcogen atoms, and the covalent radii of the O, S, Se, and Te atoms are 0.63, 1.03, 1.16, and 1.36 Å, respectively[66].dThevalues in parentheses are the percentage differences between |R ChB − R sum,1 | and R sum,1 .e The values in square brackets are the percentage differences between |R ChB − R sum,2 | and R sum,2 . B , kJ/mol) and geometrical parameters associated with the ChBs for the studied complexes.a

Table 2 .
Topological properties of the BCPs related to the chalcogen•••chalcogen interactions in all twelve complexes.All the values are reported in a.u.

Table 2 .
Topological properties of the BCPs related to the chalcogen•••chalcogen interactions in all twelve complexes.All the values are reported in a.u.

Table 3 .
The donor-acceptor orbital interactions and the corresponding E All the energetical values are given in kJ/mol.b The parenthesized values indicate the proportion of each attractive component contributing to the total attractive interactions. a