Noncovalent interactions between benzochalcogenadiazoles and nitrogen bases

A theoretical study has been carried out on the intermolecular interactions between tetrafluoro-benzochalcogenadiazoles (chalcogen = S, Se, Te) and a series of nitrogen bases (FCN, ClCN, NP, trans-N2H2, pyridine, pyrazole, imidazole) at the B97-D3/def2-TZVP level, to obtain a better insight into the nature and strength of Ch···N chalcogen bond and secondary interaction in the binary and 1:2 ternary complexes. The dispersion force plays a prominent role on the stability of the sulfur complexes, and the electrostatic effect enhanced for the heavier chalcogen complexes. Most of intermolecular bonds display the characters of closed-shell and noncovalent interaction. For the complexes involving pyridine and imidazole, chalcogen bond is stronger than hydrogen bond, while the strength of chalcogen bond is equivalent to the secondary interaction for other complexes. With the addition of nitrogen base in the 1:2 complexes, chalcogen bond is weakened, while the secondary interaction remains unchanged. In the 1:2 complexes formed by pyridine and imidazole, stronger chalcogen bond results in larger negative cooperativity than that of other complexes.


Introduction
Noncovalent interaction exists in many chemical, biological, and functional systems and plays an important role in supramolecular chemistry, crystal engineering, biology, and catalysis [1,2]. Noncovalent interactions cover all main groups of the Periodic Table, including hydrogen bond (HB), tetrel bond, chalcogen bond, halogen bond, and so on [3][4][5][6]. The chalcogen bond (ChB) was defined [7] as an attractive interaction between an electrophilic region associated with a chalcogen atom in a molecular entity and a nucleophilic region in another, or the same, molecular entity. The chalcogen atom, such as S, Se, and Te, is characterized by the region of positive electrostatic potential, which is designated as σ-hole or π-hole [8][9][10][11][12]. Chalcogen bond shares more similarities with hydrogen and halogen bonds, while there are several specific features, such as directionality, tunability, hydrophobicity, donor atom size, and multiplicity [13]. It can be used as a driving force toward desired selectivity in the design of materials, molecular recognition, and self-assembly and play a crucial role in organic synthesis and noncovalent organocatalysis [14][15][16][17][18].
In the present work, we focused on the detailed theoretical studies on the intermolecular interactions between tetrafluoro-benzochalcogenadiazoles (chalcogen = S, Se, Te) and a series of nitrogen bases, including the sphybridized bases (FCN, ClCN, NP) and sp 2 -hybridized bases (trans-N 2 H 2 , pyridine, pyrazole, imidazole). The purposes are the following: First, determine the strength of intermolecular interactions and nature of intermolecular bonding. Second, insight into the main factor that controls the intermolecular interaction; and figure out the difference between sulfur atom and heavier chalcogen atoms. It has been demonstrated that no evidence was obtained for the formation of 1:2 complexes with Cl − or other anions in solution [28]. What about the 1:2 complexes with neutral N-bases in gas? So, the third

Computational methods
The geometries of the monomers and the complexes were optimized and characterized in the light of frequency computations with the Gaussian09 program [37]. Geometries were fully optimized with the dispersion-corrected B97-D3 functional and the def2-TZVP basis set. This method has been proved to give good agreement with the experimental free energies of ChB interactions involving benzotelluradiazoles [28,29]. The binding energies were evaluated as the difference in energy between the complex and the sum of the isolated optimized monomers, which include the zero point vibrational energy (ZPVE) and basis set superposition error (BSSE) [38] corrections. The energy decomposition analysis was performed by the GAMESS program [39] with the localized molecular orbital energy decomposition analysis (LMOEDA) method [40] at the B97-D3/def2-TZVP level. The molecular electrostatic potentials (MEPs) of monomers and complexes were calculated on the 0.001 a.u. contour of density surface with the WFA-SAS program [41]. The topological properties of electron density at the bond critical points (BCPs) were obtained using the AIMAll program [42]. The Multiwfn program [43] and VMD program [44] were used to calculate and plot the map of noncovalent interaction (NCI) index, and molecule formation density difference (MFDD).

Geometries and binding energies of the binary complexes
As a preliminary gauge of intermolecular interaction, MEPs analyses of monomers were performed. From Fig. 1, tetrafluoro-benzotelluradiazole exhibits two "σ-holes" [9,10] regions of electron deficiency centered at the tellurium atom, situated roughly at the terminus of a Te−N bond. The most positive MEP values (V s,max ) of benzochalcogenadiazoles  Figure 2 shows the optimized geometries of the tellurium complexes; the sulfur and selenium ones are analogous. In this paper, symbols 1, 2, and 3 were used for representing tetrafluoro-benzochalcogenadiazoles, which correspond to Ch = S, Se, and Te. The difference of type-a and type-b in the complexes is different interacting H atom of imidazole and pyrazole. Table 1 gives the binding energies, main geometrical parameters, and their variations in the binary complexes, in which Δd(Ch···N3) and Δd(H···N2) indicate the difference between binding distances Ch···N3, H···N2 and the sum of the corresponding van der Waals radii [46] (r vdW (S)=1.80Å, r vdW (Se)=1.90Å, r vdW (Te)=2.06Å, r vdW (N)=1.55Å, r vdW (H)=1.20Å,). For the same nitrogen base, the values of Δd(Ch···N3) and Δd(H···N2) become more negative from Ch = S to Se and Te, indicating more strong interaction occurs. For the same benzochalcogenadiazole, sp 2 hybrid nitrogen bases have much larger variations than those for sp hybrid nitrogen bases.
From Table 1, the binding energies are in the range from −12.1 kJ/mol for 1···NCF to −56.9 kJ/mol for 3···o-C 3 N 2 H 4a. For the same nitrogen base, the binding energy becomes more negative in the sequence Ch = S < Se < Te. For the same benzochalcogenadiazole, the strength of intermolecular interaction increases with the order of FCN < ClCN < NP < N 2 H 2 < C 5 NH 5 < m-C 3 N 2 H 4 -a < o-C 3 N 2 H 4 -a. For the complexes with C 3 N 2 H 4 , the binding energy of type-a is more negative than that of type-b.

NCI analyses
Noncovalent interaction (NCI) analysis [47,48] provides an index, based on the electron density (ρ) and its reduced gradient (s), and the information for van der Waals interactions, Fig. 3 Plots of the RDG versus sign(λ 2 )ρ and the gradient isosurfaces (s = 0.05 a.u.) for the complexes hydrogen bonds, and steric repulsion. This index visualizes the extent to which NCIs stabilize a supramolecular assembly qualitatively and reveals which molecular regions interact. The scatter diagram of reduced density gradient (RDG) versus the electron density multiplied by the sign of the second Hessian eigenvalue (sign(λ 2 )ρ) and plots of gradient isosurfaces were generated and shown in Fig. 3. A large irregular area with different colors is found between both molecules, indicative of the coexistence of more than one interaction. For example, there are two near spikes in the low-density, low-gradient trough (sign(λ 2 )ρ b < −0.013 a.u.) in the 3···NCCl complex, corresponding green regions shown in the gradient isosurfaces, which is indicative of the weak attractive interaction between them. In the complexes of 3···C 3 N 2 H 4 ; the intermolecular region is marked by one bluish and one green isosurface, which corresponding to the moderate Te···N chalcogen bond and the weak H···N hydrogen bond, respectively.

QTAIM analyses
According to the Bader's QTAIM [49,50], the topological properties at the critical points are vital criteria to be considered when discussing the strength and nature of a chemical bond. The molecular graphs of representative complexes 3···N-bases are displayed in Fig. 4, the properties at the intermolecular bond critical points (BCPs) are calculated and listed in Table 2. There are two BCPs and one ring critical point (RCP) in the complexes; chalcogen bond is evidenced by the presence of Te···N3 BCP and a pair of bond path between Te and N3 atoms. In the complexes containing sp-hybridized nitrogen bases, bond paths connecting N2-atom to the C or P-atom of nitrogen base correspond to a π-hole or pnicogen bond. In the complexes containing sp 2 -hybridized nitrogen bases, hydrogen bond is evidenced by the presence of N2···H BCP and corresponding bond paths. The result is in agreement with the conclusion which is drawn from NCI analyses.
The strength of the bond between two nuclei could be predicted from the electron density (ρ b ) [49] and potential energy density (V b ) [51,52] at the BCP that characterize the interaction. From Table 2, for the complexes formed by C 5 NH 5 and m-C 3 N 2 H 4 , the values of ρ b and V b at the BCP of Ch···N3 contact are larger than those of N2···H contact, indicating the strength of ChB is stronger than that of HB. For other complexes, the ρ b and V b values at the

MFDD analyses
According to Politzer et al. [54][55][56], polarization is a real physical phenomenon, corresponding to the electron density shifts from one molecule to the electric field of another. Dispersion is a part of the polarization that occurs when two species approach each other. In order to achieve a visual description of the electron density shift upon complexation, the maps of molecular formation density difference (MFDD) were calculated and plotted, as shown in Fig. 5. The red regions represent gains of electron density due to intermolecular interactions and losses are shown in blue. The lone pair outside the N atom of nitrogen base causes a decrease (Δn e1 ) in the electric field adjacent to chalcogen atom and an increase (Δn e2 ) of electron density in region between Ch and N atoms. Meanwhile, the lone pair outside the N atom of benzochalcogenadiazole causes an increase (Δn e3 ) of electron density in region between N atom and C/P/H atom of nitrogen base, indicating that polarization plays a role in the formation of the complexes. Table 3 lists the integral values (Δn e ) of the negative and positive charges of the density difference in the corresponding regions. For the complexes  involving sp-hybridized base, the chalcogen bond is so weak that there is no basin between Ch and N atoms. From Ch = S to Se and Te, more and more electron shift (Δn e1 ) between the Ch···N region means increasingly strong ChB interactions. Compare Δn e2 and Δn e3 , polarization of secondary interaction is larger than that of ChB interaction.

Energy decomposition analysis
A partitioning of the total interaction energy of each complex into its individual contributing factors can provide useful insights into its origins. In order to gain further understanding of the nature of the complexes, we performed an energy decomposition analysis within the GAMESS package. The total interaction energy is composed of five parts: electrostatic energy (ΔE ele ), exchange energy (ΔE exch ), repulsion energy (ΔE rep ), polarization energy (ΔE pol ) and dispersion energy (ΔE disp ), which are listed in Table 4. From Table 4, ΔE exch were determined to be positive values for most complexes except for 3···N-bases with sp 2 hybrid, i.e., a repulsive energy. For the sulfur complexes, the dispersion interaction was found to play a prominent role with its contribution (%ΔE disp ) ranging from 47 to 70% of the total attractive force, the contribution of electrostatic force (%ΔE ele ) is in the range of 26~39%, and polarization contributes little. From Ch = S to Se and Te, the contribution of dispersion decreases, while that of electrostatic force and polarization increases gradually. For the weak selenium and tellurium complexes involving sp-hybridized N-bases, dispersion still plays a major role. The contribution of electrostatic is equivalent to that of dispersion for the selenium complexes involving sp 2 -hybridized N-bases. The electrostatic force makes the biggest contribution, and polarization is comparable to dispersion for the tellurium complexes containing sp 2 -hybridized N-bases.

Cooperativity in the 1:2 complexes
The optimized geometries of the representative 1:2 complexes are shown in Fig. 6. It can be seen that N-bases are symmetrically distributed on both sides of the benzochalcogenadiazoles and have the same topological properties at the intermolecular BCPs. The energetic and topological parameters are collected in Table 5. The total binding energy (ΔE total ) is calculated as the energy of ternary complex minus the sum of the optimized monomers, the cooperative energy (E coop ) is defined as the difference of the total binding energy in the ternary complex with the sum of the binding energy in the respective binary complex. The total binding energy varies from −22.7 kJ/mol 1 in NCCl···1···NCCl to −107.2 kJ/mol in a-o-C 3 N 2 H 4 ···3···o-C 3 N 2 H 4 -a. The binding energies (ΔE A···B,T ) between benzochalcogenadiazole and N-base in the ternary complexes are less negative than those in the binary complexes, indicating that the addition of N-base weakens the intermolecular Table 5 Total binding energy (ΔE total ), binding energy in the ternary complexes (ΔE AB,T ), their change (ΔΔE AB ) and the increased percentage (%ΔE AB ) relative to the binary complexes, and the cooperative energy (E coop ) (energies are in kJ/mol 1 )  The cooperativity in the 1:2 complex is also estimated with the electron density at the intermolecular BCP. From Tables 5, it can be seen that the electron density (ρ b ) at the ChB BCP in the ternary complex is smaller than the corresponding density in the binary complex, while ρ b at the BCP of secondary interaction pretty much constant. For example, ρ b at the Te···N3 and N2···H BCPs is 0.032 a.u. and 0.011 a.u. in 3···m-C 3 N 2 H 4 -a, it becomes 0.023 a.u. and 0.011a.u. in a-m-C 3 N 2 H 4 ···3···m-C 3 N 2 H 4 -a. These results indicate that bifurcated ChB in the 1:2 complex is weaker than ChB in the binary complex, π-hole bond, pnicogen bond, or hydrogen bond is unchanged.

Conclusion
The Ch···N chalcogen bonds and the secondary interactions between tetrafluoro-benzochalcogenadiazoles (chalcogen = S, Se, Te) and a series of nitrogen bases (FCN, ClCN, NP, trans-N 2 H 2 , pyridine, pyrazole, imidazole) were investigated at the B97-D3/def2-TZVP level of theory. The binding energies become more negative in the sequence Ch = S < Se < Te and N-base = FCN < ClCN < NP < N 2 H 2 < C 5 NH 5 < m-C 3 N 2 H 4 -a < o-C 3 N 2 H 4 -a, with the values in the range of −12.1 to approximately −56.9 kJ/mol. From Ch = S to Se and Te, the contribution of dispersion decreases, while that of electrostatic force and polarization increases gradually. For the tellurium complexes with sp 2 -hybridized N-bases, the electrostatic force makes the biggest contribution, and polarization is comparable to dispersion. Most of intermolecular bonds display the characters of closed-shell and noncovalent interactions, and Te···N3 chalcogen bonds in the complexes involving sp 2 -hybridized N-bases have the nature of partially covalent interactions. With the addition of nitrogen base, chalcogen bond becomes weaker, while the strength of secondary interaction is unchanged. In the complexes formed by C 5 NH 5 and m-C 3 N 2 H 4 , stronger chalcogen bond results in larger negative cooperativity in the 1:2 complexes. Author contribution The manuscript was written through the contributions of all authors. ZL: data curation and writing-original draft. ZY: formal analysis and supervision. LX: methodology and visualization. ZX: conceptualization and writing-review and editing. All authors have read and approved the manuscript.
Funding This work was supported by the National Natural Science Foundation of China (Contract No. 21973027 of Prof. Li X) and Natural Science Foundation of Hebei Province (Contract Nos. B2020205002 of Prof. Li X, B2022205022 of Prof. Zeng Y) Data availability The manuscript has full control of all primary data, and the authors agree to allow the journal to review their data if requested.
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