Tuning σ‑Hole Chalcogen···Nitrogen Bonding Between C₂F₄Ch₂ and Nitrogen Bases: Dual Modulation by Chalcogen Atomic Size and Nitrogen Hybridization (Ch = S, Se, Te, Po)

Abstract

Chalcogen bonds (ChBs), a prominent subclass of σ-hole interactions in which Group 16 elements serve as electrophilic sites, have attracted considerable attention in recent years because of their pivotal roles in diverse chemical and biological systems. However, the combined influence of the chalcogen atomic size and the nitrogen atomic hybridization state on the nature and strength of chalcogen···nitrogen (Ch···N) interactions remains underexplored. Herein, σ-hole-type Ch···N ChBs formed between 2,2,4,4-tetrafluoro-1,3-dichalcogenetanes (C₂F₄Ch₂, Ch = S, Se, Te, Po) and nitrogen bases with distinct hybridization patterns (sp-NCH, sp²-NHCH₂, sp²-pyridine, sp³-NH₃) are systematically investigated using quantum chemical calculations. The computed interaction energies vary from −16.8 to −62.5 kJ/mol. The two moieties are held together primarily through the Ch···N ChBs. These ChBs show substantial bond contraction, with Ch···N distances approximately 12–29% shorter than the sum of the respective van der Waals radii. Topological analysis indicates that although most Ch···N ChBs exhibit noncovalent closed-shell characteristics, Te/Po···N ChBs in complexes with NH₃, NHCH₂, or pyridine display a partially covalent nature. Notably, the Ch···N ChB strength typically increases in the order Ch = S < Se < Po < Te and follows the nitrogen base sequence: NCH (sp) < NH₃ (sp³) < NHCH₂ (sp²) < pyridine (sp²). Natural bond orbital (NBO) analysis suggests that the predominant orbital interaction associated with the Ch···N ChB involves charge transfer from the nitrogen lone pair into the σ*­(C–Ch) antibonding orbitals. Energy decomposition analysis reveals that electrostatic interactions provide the largest attractive contribution to the stabilization of these chalcogen-bonded complexes. These findings provide critical insights into the tunability of chalcogen bonding interactions by modulating the atomic and electronic structures of the interacting partners.

Introduction

σ-Hole interactions − represent an emerging class of noncovalent interactions (NCIs), characterized as the attractive forces between the electron-poor regions (the σ-holes − ) situated on the extension of the covalently bonded atoms from Groups 14–18 and various electron-rich nucleophiles (lone pair donors, π-systems, and anions). Consequently, these interactions can be termed as tetrel bond (TtB, Group 14), pnictogen bond (PnB, Group 15), chalcogen bond (ChB, Group 16), , halogen bond (HaB, Group 17), , and aerogen or noble gas bond (NgB, Group 18), respectively, a categorization which is determined by the specific position of the p-block element within the periodic table. σ-Hole interactions have aroused a notable surge of interest from the scientific community in recent years because of their critical roles in a variety of chemical and biological systems. −

Among various σ-hole interactions, halogen bond has been extensively investigated and is now well established in its applications across crystal engineering, , supramolecular chemistry, and molecular recognition. In parallel, increasing evidence has indicated that chalcogen bonds play pivotal roles in a variety of disciplines such as coordination chemistry, , materials science, , organocatalysis, , organic synthesis, , drug design, anion recognition, , and biological systems. − This growing body of evidence has prompted a shift in focus toward the exploration of such interactions. A chalcogen bond is generally defined as an attractive interaction between an electrophilic region associated with Group 16 elements (S to Te to Po) and a Lewis base. Analogous to halogen bonds, chalcogen bonds exhibit pronounced directionality, typically favoring the approach of the electron donor along the extension of an R–Ch covalent bond to the chalcogen center (Ch). Additionally, chalcogen bonds have also been found to demonstrate greater hydrophobicity and pH stability in comparison to hydrogen bonds (HBs). It is evidenced that the physical nature of such interactions is widely understood to originate from a combination of electrostatic attraction, orbital interactions (particularly charge transfer), and dispersion forces, ,,− with their relative contributions being system-dependent.

Energetically, chalcogen bonding interactions are on par with halogen and hydrogen bonds in magnitude, with certain instances exhibiting a greater strength than hydrogen bonds. , It was found that the strength and characteristics of chalcogen bonds can be modulated by several key factors. First, the identification of Group 16 elements is of crucial importance, as descending the group (S → Po) leads to an increase in atomic size and polarizability, which typically enhances the σ-hole potency and can strengthen chalcogen bonding interactions. − Second, the electronic nature of the substituents covalently attached to the chalcogen center is a major determinant. Specifically, the electron-withdrawing groups typically deepen the σ-hole’s positive electrostatic potential and strengthen Lewis acid behavior, whereas the electron-donating groups can attenuate electrophilicity and weaken the interaction. ,, Moreover, the introduction of electron-donating substituents into Lewis bases has also been demonstrated to enhance such interactions, which is attributable to an augmentation of the nucleophilicity of the electron-rich subunits. Finally, the electronic structure of electron-rich donor atoms (notably O and N) exerts a significant influence on not only the interaction strength but also directionality and charge-transfer propensity. In particular, the hybridization state (e.g., sp, sp², sp³) of electron-rich donor lone pair, which controls spatial orientation, energy, and s/p character, can markedly modulate the donor → acceptor interactions and the balance between electrostatics and induction components, thereby impacting the interaction energy. −

Currently, numerous experimental and computational investigations have concentrated on chalcogen bonding interactions between the chalcogen centers, where chalcogen atoms act as both electrophilic (ChB donor) and nucleophilic (ChB acceptor) sites, − as evidenced by the significance of these chalcogen···chalcogen interactions in the above-mentioned chemical and biological realms. ,,,,,, Nevertheless, chalcogen···nitrogen (Ch···N) interactions are equally important because Ch···N contacts play a critical role in crystal engineering and materials science, ,, given the ubiquity of nitrogen atom in functional molecules (e.g., heteroaromatics, nitriles, amines). In recent years, many theoretical and crystallographic studies have been dedicated to exploring Ch···N interactions, ,,,− thereby demonstrating their importance in the relevant fields. For instance, Scheiner’s group computationally investigated the complexes between SF₄ and various sp²- and sp³-hybridized amines and revealed that the hybridization state of the electrophilic nitrogen atoms exerts a significant influence on the strength of S···N ChBs. Li et al. examined the binary complexes formed between F₂CSe and various nitrogen bases (N₂, NCH, NH₃, NHCH₂, NCLi, and NMe₃) and indicated that the strength of Se···N ChBs increases with the order of NCH (sp) < NH₃ (sp³) < NHCH₂ (sp²), which contradicts the expected trend based on the electronegativity of the hybridized N atom. Furthermore, the introduction of the Li and methyl substituents can further strengthen such interactions. Lu and coworkers systematically studied the 2Ch–2N square and hexagon interactions in the homodimers of 2,1,3-benzochalcogenadiazole, 2,1,3-pyridochalcogenadiazole, chalcogenazole-pyridine and triazolo-chalcogenadiazole using crystallographic data analysis and theoretical calculations. The results indicated that these 2Ch–2N interactions become stronger in the sequence of S < Se < Te, and the presence of the electron-withdrawing groups can significantly enhance their strength. Concomitantly, analogous findings have also been observed in the 2,1,3-pyrazinochalcogenadiazole homodimers reported by Wang and coworkers.

It is important to note that most previous studies on the Ch···N ChBs have focused exclusively on a single factor: either the chalcogen atomic identity was varied while the nitrogen hybridization state was held constant, , or the nitrogen hybridization state was varied while the chalcogen atomic identity was fixed. , To the best of our knowledge, the synergistic effects of both chalcogen atomic size (S, Se, Te, Po) and nitrogen hybridization state (sp, sp², sp³) on the strength and nature of the Ch···N ChBs have not yet been systematically examined within a unified framework. Moreover, studies on chalcogen bonds involving the Po atom remain comparatively limited. , To address this knowledge gap, this work presents an ab initio computational study on σ-hole-type Ch···N ChBs in a series of model complexes formed between 2,2,4,4-tetrafluoro-1,3-dichalcogenetanes (C₂F₄Ch₂, Ch = S, Se, Te, Po) and four representative nitrogen-bearing Lewis bases (NCH, NH₃, NHCH₂, and pyridine, denoted as NC₅H₅) at the MP2/aug-cc-pVDZ­(PP) level. The C₂F₄Ch₂ molecules are well-established ChB donors ,,− because the presence of the two strongly electron-withdrawing −CF₂ groups can significantly polarize the chalcogen atoms. As a result, four equivalent regions of positive electrostatic potential, known as σ-holes, are generated on the two chalcogen atoms (see Figure ). These symmetric and localized electron-deficient sites are ideally suited for a systematic and interference-free investigation of the directionality and strength of the Ch···N ChBs. Furthermore, the rigid four-membered ring can lock the chalcogen atoms into a well-defined geometry, thereby eliminating any uncertainties caused by conformational flexibility. Notably, the −CF₂ groups may also act as secondary noncovalent interaction sites such as in C–F···H hydrogen bonds. Regarding the ChB acceptors, four nitrogen bases covering the principal hybridization states of nitrogensp (NCH), sp² (NHCH₂), aromatic sp² (NC₅H₅), and sp³ (NH₃)were deliberately selected to examine how the electronic structure of the nitrogen center influences the ChB strength. Accordingly, the combination of chalcogen-based (C₂F₄Ch₂) donors with the selected nitrogen-bearing acceptors constitutes an ideal set of model systems for the systematic investigation of the Ch···N ChBs. A diverse array of theoretical methodologies, encompassing molecular electrostatic potential (MEP) surfaces, quantum theory of atoms in molecules (QTAIM), noncovalent interaction plot (NCIplot), natural bond orbital (NBO), and symmetry-adapted perturbation theory (SAPT), has also been employed to thoroughly characterize the Ch···N ChBs in terms of their strength and nature.

1.

MEP diagrams of nitrogen-containing Lewis bases and C₂F₄Ch₂ (Ch = S, Se, Te, Po) molecules depicted at the 0.001 a.u. isodensity surfaces. The electrostatic potential ranges from −0.03 (blue) to +0.03 (red) a.u. The V _S,max and V _S,min values are provided in kJ/mol.

Computational Methods

The Gaussian16 program was employed for the execution of all calculations. The geometries of both monomers and binary complexes were optimized through the implementation of the MP2 approach, paired with the aug-cc-pVDZ basis set. The optimized structures have been confirmed as real energy minima with no imaginary frequencies by conducting harmonic vibrational frequency analysis at the same level. Based on the MP2/aug-cc-pVDZ level predicted geometries, the MP2/aug-cc-pVTZ, MP2/aug-cc-pVQZ, and CCSD­(T)/aug-cc-pVDZ levels were also employed to implement single-point energy calculations. For the heavier Te and Po atoms, the effective core potentials (ECPs) were utilized to account for relativistic effects through the usage of the corresponding pseudopotentials obtained from the EMSL library. The interaction energy (E _int) and binding energy (E _b) of each complex were calculated using the following equations:

$$E_{int}=E_{AB}-E_{\mathrm{A}}-E_B+E_{BSSE}$$ 1

$$E_b=E_{AB}-E_{A\prime }-E_{B\prime }+E_{BSSE}$$ 2

where E _AB indicates the energy of the complex, E _A and E _B denote the energies of the monomers that were frozen within the geometry of the complex, and E _A′ and E _B′ represent the energies of the optimized monomers. Both E _int and E _b have been corrected by considering the basis set superposition error (BSSE) using the counterpoise method. The energy difference between these two quantities represents the deformation energy (E _def), which is required to distort each monomer from its optimized state to the geometry frozen within the complex. Additionally, the interaction energies and binding energies for all the studied complexes were also benchmarked at the CCSD­(T)/CBS level using the following equations:

$$E_{\mathrm{C}\mathrm{C}\mathrm{S}\mathrm{D}(\mathrm{T})/\mathrm{C}\mathrm{B}\mathrm{S}}=\mathrm{\Delta }{E}_{\mathrm{M}\mathrm{P}2/\mathrm{C}\mathrm{B}\mathrm{S}}+\mathrm{\Delta }{E}_{\mathrm{C}\mathrm{C}\mathrm{S}\mathrm{D}(\mathrm{T})}$$ 3

where

$$\mathrm{\Delta }{E}_{\mathrm{M}\mathrm{P}2/\mathrm{C}\mathrm{B}\mathrm{S}}=(64E_{\mathrm{M}\mathrm{P}2/\mathrm{a}\mathrm{u}\mathrm{g}-\mathrm{c}\mathrm{c}-\mathrm{p}\mathrm{V}\mathrm{Q}\mathrm{Z}(\mathrm{P}\mathrm{P})}-27E_{\mathrm{M}\mathrm{P}2/\mathrm{a}\mathrm{u}\mathrm{g}-\mathrm{c}\mathrm{c}-\mathrm{p}\mathrm{V}\mathrm{T}Z(\mathrm{P}\mathrm{P})})/37$$ 4

$$\mathrm{\Delta }{E}_{\mathrm{C}\mathrm{C}\mathrm{S}\mathrm{D}(\mathrm{T})}=E_{\mathrm{C}\mathrm{C}\mathrm{S}\mathrm{D}(\mathrm{T})/\mathrm{a}\mathrm{u}\mathrm{g}-\mathrm{c}\mathrm{c}-\mathrm{p}\mathrm{V}\mathrm{D}\mathrm{Z}(\mathrm{P}\mathrm{P})}-E_{MP2/\mathrm{a}\mathrm{u}\mathrm{g}-\mathrm{c}\mathrm{c}-\mathrm{p}\mathrm{V}\mathrm{D}\mathrm{Z}(\mathrm{P}\mathrm{P})}$$ 5

The molecular electrostatic potential (MEP) analysis was performed to identify the nucleophilic and electrophilic sites within all the isolated monomers and generate their MEP maps using the Multiwfn 3.6 program. The 0.001 electron/Bohr³ isosurface value was utilized for MEP analysis, as it effectively represents the electron density distribution of the chemical systems involving noncovalent interactions. , The QTAIM analysis was implemented at the same level for identifying the bond critical points (BCPs) and evaluate the topological properties at each BCP within the studied complexes employing the Multiwfn program. The strength of the identified noncovalent interactions was also estimated using the following equation:

$$E_{\mathrm{N}\mathrm{C}\mathrm{I}}=0.5V$$ 6

where V denotes the potential energy density at the BCP.

The NCIplot analysis was carried out to characterize and visualize the noncovalent interactions within the examined complexes by means of the Multiwfn program. For the purpose of obtaining the information on the charge transfer and second-order perturbation energy (E ⁽²⁾) related to orbital interactions between C₂F₄Ch₂ and Lewis bases, the NBO analysis was conducted employing the NBO 7.0 software package. The magnitude of charge transfer from a donor orbital to an acceptor orbital has been evaluated utilizing the following approximation:

$$\mathrm{\Delta }q=q_{\mathrm{i}}{(\frac{F_{ij}}{{\epsilon }_j-{\epsilon }_i})}^2$$ 7

where q _i indicates the orbital occupancy, ε _i and ε _j denote diagonal elements, and F _ij represents the off-diagonal NBO Fock matrix element. The MEP, QTAIM, NCIplot, and NBO maps were then generated with the help of Visual Molecular Dynamics (VMD) program.

For the purpose of estimating the electronic parameters and chemical reactivities of the interacting species, the frontier molecular orbital (FMO) theory was employed for all the monomers and complexes. According to the evaluated energies of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the Fermi-level energy (E _FL) and energy gap (ΔE) have been computed in eqs –, and some global reactivity descriptors such as ionization potential (I), electron affinity (A), chemical potential (μ), chemical hardness (η), chemical softness (S), electronegativity (χ), and electrophilicity index (ω) were also estimated using the eqs –:

$$E_{FL}=E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}+0.5(E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}})$$ 8

$$\mathrm{\Delta }E=E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}$$ 9

$$I=-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}$$ 10

$$A=-E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}$$ 11

$$\mu =0.5(E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}+E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}})$$ 12

$$\eta =0.5(E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}})$$ 13

$$S=2/(E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}})$$ 14

$$\chi =-0.5(E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}+E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}})$$ 15

$$\omega =0.25/{(E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}})}^2/(E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}})$$ 16

In order to further understand the physical nature of the chalcogen···nitrogen interactions from a quantitative perspective, energy decomposition analysis (EDA) based on the symmetry-adapted perturbation theory (SAPT) method was executed at the SAPT2+/aug-cc-pVDZ­(PP) level employing the PSI4 software. In the framework of SAPT-EDA, the total SAPT2+ energy of (E _SAPT2+) of the complex can be decomposed into four physically meaningful components: electrostatic (E _elst), induction (E _ind), dispersion (E _disp), and exchange-repulsion (E _ex‑re), as delineated in eq . Furthermore, the percentage contribution $(E_{\mathrm{attractive}}^{\%})$ of each attractive energy has also been calculated to estimate the extent to which individual attractive component contributes to the total attractive interaction energy, as described by eq .

$$E_{\mathrm{S}\mathrm{A}\mathrm{P}\mathrm{T}2+}=E_{\mathrm{e}\mathrm{l}\mathrm{s}\mathrm{t}}+E_{\mathrm{i}\mathrm{n}\mathrm{d}}+E_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{p}}+E_{\mathrm{e}\mathrm{x}-\mathrm{r}\mathrm{e}}$$ 17

$$E_{\mathrm{attractive}}^{\%}=(E_{\mathrm{attractive\; component}}/E_{\mathrm{total\; attractive\; interaction\; energy}})\times 100$$ 18

Results and Discussion

MEP Analysis of the Monomers

In order to identify the electrophilic and nucleophilic sites within the C₂F₄Ch₂ (Ch = S, Se, Te, Po) and four nitrogen-based Lewis bases, MEP analysis was executed. The MEP diagrams of all the optimized monomers were displayed in Figure , where the blue areas represent the negative electrostatic potentials and the red areas indicate the positive electrostatic potentials. It was observed that there exist the positive electrostatic potential regions surrounding two chalcogen atoms within the C₂F₄Ch₂ (Ch = S, Se, Te, Po) molecules. These positively charged regions are referred to as σ-holes, which are positioned in the direction of the C–Ch bond axis. Interestingly, each C₂F₄Ch₂ molecule exhibits four equivalent σ-hole regions because it has a D _2h symmetry. The regions of negative electrostatic potential are located surrounding the fluorine atoms, as depicted by the blue areas. The calculated maximum positive electrostatic potential (V _S,max) values on the chalcogen atoms for the C₂F₄S₂, C₂F₄Se₂, C₂F₄Te₂, and C₂F₄Po₂ molecules are 166.2, 166.9, 180.7, and 188.0 kJ/mol, respectively. It is evident that the V _S,max value becomes greater as the chalcogen atomic size increases. This phenomenon is in agreement with the well-established understanding that the electronegativity of the chalcogen atoms reduces while their polarizability increases as the chalcogen atomic size grows. For four nitrogen-bearing Lewis bases, the regions of negative electrostatic potential are positioned around the nitrogen atoms, as represented by the blue areas. Conversely, the regions of positive electrostatic potential (depicted in red) are distributed around the hydrogen atoms. The minimum negative electrostatic potential (V _S,min) values related to the nitrogen atoms vary between −138.1 and −168.0 kJ/mol. It can be seen that the V _S,min value becomes less negative in the following sequence: NH₃ (sp³) < NHCH₂ (sp²) < NC₅H₅ (sp²) < NCH (sp). This change does not align with the known gas-phase basicity in terms of their proton affinities (PA). It is therefore to be expected that the chalcogen atoms of the C₂F₄Ch₂ monomers are capable of interacting with the nucleophilic regions (situated at the N atoms) of four Lewis bases to form the Ch···N ChBs.

Geometries of the Studied Complexes

Based on the MEP analysis results, we constructed four groups of binary complexes, including C₂F₄Ch₂···NCH, C₂F₄Ch₂···NH₃, C₂F₄Ch₂···NHCH₂, and C₂F₄Ch₂···NC₅H₅ (Ch = S, Se, Te, Po). It should be pointed out that C₂F₄Ch₂ can form not only chalcogen-bonded complexes but also hydrogen-bonded complexes with these nitrogen bases, leading to multiple potential conformational isomers. However, this study focuses exclusively on the most stable conformer of each Ch···N chalcogen-bonded complex, characterized by the most negative binding energy and identified as the global minimum without any imaginary frequencies. Given the lack of significant structural differences among the configurations of the chalcogen-bonded complexes within each group, their optimized stable structures are representatively illustrated in Figure to display the relevant geometric characteristics. The corresponding Cartesian coordinates are provided in Table S1. Notably, the configurations of all 16 studied complexes exhibit C _s symmetry. One can clearly observe that the N atoms of all the Lewis bases are positioned toward the chalcogen atoms in the direction of one of the C–Ch covalent bonds within the C₂F₄Ch₂ moieties for all the examined complexes. The important geometrical parameters of these complexes are provided in Table . One can find that the R _S···N binding distance ranges from 2.951 to 2.677 Å, the R _Se···N binding distance varies between 2.935 and 2.600 Å, the R _Te···N binding distance is the range of 2.923–2.570 Å, and the R _Po···N binding distance spans from 2.911 to 2.630 Å. All the R _Ch···N binding distances are significantly shorter than the sum (R _sum) of the van der Waals radii of N and Ch atoms (3.35, 3.45, 3.61, and 3.52 Å when Ch = S, Se, Te, and Po, respectively). The degree of shortening has been found to reach 11.9 ∼ 28.8%, thereby indicating the presence of a strong Ch···N ChB in each complex. Noticeably, the ∠C¹–Ch¹···N angle ranges from 148.7° to 159.6°, which significantly deviates from 180°. This could be due to a combination of steric effects, the specific location of the σ-hole in a strongly electron-withdrawing environment, and the attractive interactions between the F atoms of C₂F₄Ch₂ and the H atoms of Lewis bases. Moreover, for a fixed Lewis base, the degree to which the ∠C¹–Ch¹···N angle deviates from collinearity increases as the size of the chalcogen atom grows. The weaker directionality of strong chalcogen bonds involving heavier Ch (Ch = Te, Po) atoms may be attributed to the Pauli repulsion (steric interactions), which has already been observed in relevant chalcogen-bonded systems.

2.

Optimized geometries for the C₂F₄Ch₂···NCH, C₂F₄Ch₂···NH₃, C₂F₄Ch₂···NHCH₂, and C₂F₄Ch₂···NC₅H₅ complexes (Ch = S, Se, Te, Po).

1. Ch···N Distances (R _Ch···N, Å) and C–Ch···N Angles (α, °) in the Complexes as Well as the Sum (R _sum, Å) of the van der Waals Radii of the Two Interacting Atoms in the Complexes.

Complexes	ChBs	R Ch···N	α	R sum	λ
C2F4S2···NCH	S···N	2.951	157.8	3.35(11.9%)	0.88
C2F4S2···NH3	S···N	2.845	157.9	3.35(15.1%)	0.85
C2F4S2···NHCH2	S···N	2.829	159.6	3.35(15.6%)	0.84
C2F4S2···NC5H5	S···N	2.677	158.9	3.35(20.1%)	0.80
C2F4Se2···NCH	Se···N	2.935	155.1	3.45(14.9%)	0.85
C2F4Se2···NH3	Se···N	2.790	155.4	3.45(19.1%)	0.81
C2F4Se2···NHCH2	Se···N	2.781	157.9	3.45(19.4%)	0.81
C2F4Se2···NC5H5	Se···N	2.600	156.9	3.45(24.6%)	0.75
C2F4Te2···NCH	Te···N	2.923	150.9	3.61(19.0%)	0.81
C2F4Te2···NH3	Te···N	2.727	151.0	3.61(24.5%)	0.76
C2F4Te2···NHCH2	Te···N	2.726	155.2	3.61(24.5%)	0.76
C2F4Te2···NC5H5	Te···N	2.570	152.6	3.61(28.8%)	0.71
C2F4Po2···NCH	Po···N	2.911	149.5	3.52(17.3%)	0.83
C2F4Po2···NH3	Po···N	2.776	148.7	3.52(21.1%)	0.79
C2F4PO2···NHCH2	Po···N	2.768	154.0	3.52(21.4%)	0.79
C2F4Po2···NC5H5	Po···N	2.630	150.2	3.52(25.3%)	0.75

^aThe van der Waals radii of the N, S, Se, and Te atoms determined by Bondi are 1.55, 1.80, 1.90, and 2.06, respectively, and the van der Waals radius of the Po atom determined by Truhlar is 1.97 Å.

^bλ represents the reduction ratio of R_Ch···N/R_sum.

^cThe parenthesized values refer to the percentage differences, which corresponds to (|R_Ch···N – R_sum|/R_sum)*100.

In order to estimate the strength of each Ch···N ChB qualitatively, a reduction ratio of λ = R _Ch···N/R _sum was also computed and is listed in Table . It is generally accepted that the smaller value of λ is associated with a stronger chalcogen bond. These λ values vary between 0.71 and 0.88 for all the Ch···N ChBs, which further demonstrates the formation of the strong chalcogen···nitrogen interactions within the studied complexes. The NC₅H₅-containing complex in each group involving C₂F₄Ch₂ (Ch = S, Se, Te, or Po) possesses the shortest R _Ch···N binding distance and the corresponding smallest λ, suggesting that the sp²-hybridized N atom of NC₅H₅ forms the strongest Ch···N ChB. This phenomenon can be attributed to the intrinsic electron delocalization, dispersion-driven density reorganization within the aromatic ring upon complex formation, as well as the fact that the gas-phase basicity of NC₅H₅ is the strongest among these four nitrogen bases. Additionally, it is noteworthy that the Ch···N ChB involving a sp²-hybridized N atom is stronger than those involving sp- or sp³-hybridized N atoms.

For the fixed Lewis acid, the interatomic distance between chalcogen and nitrogen atoms becomes shorter with the sequence of NCH (sp) > NH₃ (sp³) > NHCH₂ (sp²) > NC₅H₅ (sp²), which is inconsistent with the established gas-phase basicity order of these nitrogen bases. For the same HCN, the R _Ch···N binding distances decrease as the mass of chalcogen atom increases. Conversely, the variation in the R _Ch···N binding distance does not exbibit a consistent trend when the Lewis base is fixed at NH₃, NHCH₂, or NC₅H₅. Concretely, the R _Ch···N binding distance diminishes in the order of S > Se > Po > Te within complexes involving NH₃, NHCH₂, or NC₅H₅ as the base. This phenomenon may be the result of a subtle interplay between electrostatic interactions, charge transfer, relativistic effects, and dispersion-induced density polarization. A similar trend was observed in the YF₄···(NH₃)₂ complexes (Y = S, Se, Te, Po). In addition, it should be pointed out that microwave spectroscopic investigation of the C₂F₄S₂···NH₃ heterodimer in the supersonic expansion revealed the experimentally determined R _S···N binding distance to be 2.811(5) Å and the corresponding ∠C–S···N angle to be 158.6(2)°. These two quantities are in good agreement with the calculated values of 2.845 Å and 158.9°, respectively, further indicating the reliability of the computational method employed in the present study.

Energies of the Studied Complexes

Based on the optimized geometries at the MP2/aug-cc-pVDZ­(PP) level, we calculated the interaction energies (E _int) and binding energies (E _b) of all the examined complexes using different levels of theory (Table ). For the MP2 method, the E _int values exhibit a systematic increase as the basis set expands from double-ζ to triple-ζ and then quadruple-ζ. Notably, the interaction energies estimated at the CCSD­(T)/aug-cc-pVDZ­(PP) level are slightly smaller than those from all the MP2 calculations. However, the variation trend of the E _int remains consistent across both the CCSD­(T) and MP2 methods. Additionally, the CCSD­(T)/CBS results also follow a comparable trend to those observed in the above-discussed methods. The binding energies display an analogous trend to the interaction energies, although the binding energies are consistently smaller than the corresponding interaction energies at each considered level of theory. Remarkably, both the E _int and E _b values computed at the MP2/aug-cc-pVQZ­(PP) level are in excellent agreement with the CCSD­(T)/CBS benchmark values. Focusing on the MP2/aug-cc-pVDZ­(PP) data, the deformation energy, defined as the difference between the E _b and E _int, is generally small across the studied complexes. The maximum deformation energy has been observed to be 2.7 kJ/mol for both the C₂F₄Te₂···NC₅H₅ and C₂F₄Po₂···NC₅H₅ complexes. Overall, these findings suggest that both C₂F₄Ch₂ species and nitrogen bases only undergo slight geometric distortion upon complexation.

2. Interaction Energy (E _int) and Binding (E _int) Energy (kJ/mol) for the Studied Complexes Calculated at the MP2/aug-cc-pVDZ­(PP) (MD), MP2/aug-cc-pVTZ­(PP) (MT), MP2/aug-cc-pVQZ­(PP) (MQ), CCSD­(T)/aug-cc-pVDZ­(PP) (CD), and CCSD­(T)/CBS (CC) Levels.

	MD		MT		MQ		CD		CC
Complexes	E int	E b	E int	E b	E int	E b	E int	E B	E int	E b
C2F4S2···NCH	–14.2	–13.9	–15.9	–15.4	–16.7	–16.2	–13.7	–13.4	–16.8	–16.3
C2F4S2···NH3	–21.2	–20.7	–24.3	–22.6	–25.7	–23.9	–20.7	–20.2	–26.3	–24.4
C2F4S2···NH CH2	–22.4	–21.9	–25.5	–24.2	–27.0	–25.6	–21.8	–21.3	–27.4	–26.0
C2F4S2···NC5H5	–28.4	–27.5	–32.6	–30.6	–34.5	–32.4	–27.4	–26.5	–35.0	–32.8
C2F4Se2···NCH	–16.6	–16.4	–18.5	–17.9	–19.4	–18.7	–16.1	–15.8	–19.5	–18.8
C2F4Se2···NH3	–27.0	–26.3	–30.2	–27.7	–31.8	–29.0	–26.3	–25.6	–32.3	–29.3
C2F4Se2···NHCH2	–27.2	–26.6	–30.6	–28.7	–32.1	–30.1	–26.5	–25.8	–32.5	–30.4
C2F4Se2···NC5H5	–35.6	–34.2	–40.4	–37.1	–42.5	–38.9	–33.5	–33.0	–41.9	–39.0
C2F4Te2···NCH	–20.8	–20.6	–23.5	–22.7	–24.8	–24.0	–20.1	–19.8	–25.1	–24.2
C2F4Te2···NH3	–38.3	–36.9	–43.1	–38.9	–45.5	–40.6	–37.3	–35.9	–46.2	–40.8
C2F4Te2···NHCH2	–36.7	–35.5	–41.6	–38.4	–43.8	–40.2	–35.7	–34.5	–44.4	–40.5
C2F4Te2···NC5H5	–50.2	–47.5	–57.1	–51.5	–60.2	–53.6	–48.5	–45.8	–60.7	–53.4
C2F4Po2···NCH	–22.8	–22.4	–26.0	–24.8	–27.6	–26.1	–22.2	–21.8	–28.1	–26.4
C2F4Po2···NH3	–40.4	–38.9	–45.2	–40.3	–47.7	–41.7	–39.6	–38.0	–48.6	–41.9
C2F4Po2···NHCH2	–38.7	–37.3	–43.6	–39.7	–46.0	–41.2	–37.7	–36.4	–46.8	–41.5
C2F4Po2···NC5H5	–51.1	–48.4	–58.2	–51.9	–61.5	–53.7	–49.6	–46.9	–62.5	–53.5

As shown in Table , the interaction energies (E _int) range from −16.8 kJ/mol for the C₂F₄S₂···NCH complex to −62.5 kJ/mol for the C₂F₄Po₂···NC₅H₅ complex. For the fixed Lewis base, the magnitude of the E _int in absolute value undergoes a progressive increase as the chalcogen atomic size grows, suggesting that the heavier Ch atoms facilitate the formation of more stable complexes. The trend is in accordance with the variations in the V _S,max value of Lewis acids. Interestingly, the E _int value becomes more negative in the order of NCH (sp) < NH₃ (sp³) < NHCH₂ (sp²) < NC₅H₅ (sp²) when Lewis acids are fixed at C₂F₄S₂ or C₂F₄Se₂, while for C₂F₄Te₂ and C₂F₄Po₂ as Lewis acids, an abnormal order of NCH (sp) < NHCH₂ (sp²) < NH₃ (sp³) < NC₅H₅ (sp²) is observed, a sequence that consistently aligns with their gas-phase Lewis basicity trend. A similar trend is also observed in the Se···N chalcogen-bonded complexes with F₂CSe as the ChB donor. Generally, the more negative the interaction or binding energy, the shorter the corresponding binding distance. Indeed, it was found that there exists a good linear relationship between the interaction energy and binding energy and the Ch···N binding distance within subsets defined by a fixed Lewis acid (C₂F₄Ch₂), as displayed in Figure with the linear correlation coefficients greater than 0.96.

3.

Correlation plots of the Ch···N distance versus the interaction energy (E _int, (a)) and the binding energy (E _b, (b)) within subsets defined by a fixed Lewis acid (C₂F₄Ch₂).

Quantum Theory of Atoms in Molecules (QTAIM) Analysis

According to the MP2/aug-cc-pVDZ (PP) theoretical level predicted structures, we conducted the QTAIM analysis for characterizing the strength and nature of the Ch···N ChBs within the studied complexes in terms of their topological properties at the bond critical points (BCPs). The QTAIM analysis diagrams of the 16 studied complexes are presented in Figure . The QTAIM analysis findings reveal that there exists a BCP and a bond path (BP) between chalcogen and nitrogen atoms in all the complexes, thus corroborating the existence of the Ch···N ChBs. Furthermore, two C–H···F hydrogen bonds have also been found, each characterized by one BCP and one BP, within the complexes involving NHCH₂. Interestingly, two additional BCPs and BPs are also observed between the fluorine atoms and the nitrogen atoms in the C₂F₄S₂···NCH and C₂F₄Po₂···NH₃ complexes.

4.

QTAIM graphs of the 16 chalcogen-bonded complexes. BCPs are marked with orange dots, and BPs are illustrated with brown lines.

Table collects the estimated electron density (ρ), Laplacian of electron density (∇²ρ), kinetic energy density (G), potential energy density (V), and total energy density (H) at the identified BCPs. Furthermore, the |G/V| ratio was also calculated and is presented in the second-to-last column of Table . At the Ch···N BCPs, the ρ values vary from 0.0133 a.u. to 0.0427 a.u., and the corresponding ∇²ρ values increase from 0.0458 a.u. to 0.1043 a.u. It is noteworthy that the ρ and ∇²ρ values for the Ch···N ChBs involving NC₅H₅ are markedly larger than those observed in the chalcogenadiazole (C₂N₂H₂Ch) homodimers and 2,1,3-benzochalcogendiazole (C₆N₂H₄Ch) and its fluoro-substituted C₆N₂H₃FCh homodimers (Ch = S, Se, Te), where these systems contain the sp²-hybridized nitrogen atoms. For the same Lewis acid (C₂F₄Ch₂), the ρ value increases in the order NCH (sp) < NHCH₂ (sp²) < NH₃ (sp³) < NC₅H₅ (sp²), which aligns with the gas-phase basicity of four nitrogen bases. When the identical NCH molecule is employed, the ρ values become more positive in the sequence of Ch = S < Se < Te < Po, while an irregular order of Ch = S < Se < Po < Te is observed for the fixed NH₃, NHCH₂, or NC₅H₅ bases. Moreover, both ρ and ∇²ρ values exhibit a good linear correlation with the Ch···N binding distances and binding energies, respectively (Figure S1). This suggests that an increased electron density is indicative of a stronger ChB.

3. Topological Parameters at the Identified BCPs for the Studied Complexes.

Complexes	BCP	ρ (a.u.)	∇2ρ (a.u.)	G (a.u.)	V (a.u.)	H (a.u)	|G/V|	E NCI (kJ/mol)
C2F4S2···NCH	S···N	0.0133	0.0458	0.0099	–0.0084	0.0015	1.1832	–11.0
	F···N	0.0073	0.0318	0.0068	–0.0056	0.0012	1.2058	–7.4
C2F4S2···NH3	S···N	0.0193	0.0558	0.0129	–0.0119	0.0010	1.0872	–15.6
C2F4S2···NHCH2	S···N	0.0191	0.0579	0.0132	–0.0110	0.0013	1.1063	–15.7
	F···H a	0.0057	0.0300	0.0059	–0.0044	0.0016	1.3561	–5.7
C2F4S2···NC5H5	S···N	0.0269	0.0755	0.0185	–0.0181	0.0004	1.0216	–23.8
C2F4Se2···NCH	Se···N	0.0155	0.0502	0.0112	–0.0099	0.0013	1.1310	–13.1
C2F4Se2···NH3	Se···N	0.0239	0.0628	0.0155	–0.0154	0.0001	1.0096	–20.2
C2F4Se2···NHCH2	Se···N	0.0234	0.0645	0.0157	–0.0153	0.0004	1.0276	–20.1
	F···H a	0.0065	0.0322	0.0066	–0.0051	0.0015	1.2863	–6.7
C2F4Se2···NC5H5	Se···N	0.0348	0.0847	0.0232	–0.0252	–0.0020	0.9206	–33.0
C2F4Te2···NCH	Te···N	0.0192	0.0546	0.0133	–0.0129	0.0004	1.0282	–17.0
C2F4Te2···NH3	Te···N	0.0318	0.0705	0.0201	–0.0225	–0.0025	0.8914	–29.6
C2F4Te2···NHCH2	Te···N	0.0308	0.0720	0.0200	–0.0220	–0.0020	0.9096	–28.9
	F···H a	0.0082	0.0367	0.0079	–0.0066	0.0013	1.1915	–8.7
C2F4Te2···NC5H5	Te···N	0.0427	0.0913	0.0286	–0.0345	–0.0058	0.8311	–45.3
C2F4Po2···NCH	Po···N	0.0207	0.0630	0.0153	–0.0148	0.0005	1.0304	–19.5
C2F4Po2···NH3	Po···N	0.0306	0.0777	0.0211	–0.0227	–0.0016	0.9277	–29.8
	F···N a	0.0097	0.0431	0.0095	–0.0082	0.0013	1.1535	–10.8
C2F4Po2···NHCH2	Po···N	0.0302	0.0802	0.0214	–0.0227	–0.0013	0.9422	–29.8
	F···H a	0.0086	0.0372	0.0081	–0.0070	0.0012	1.1643	–9.2
C2F4Po2···NC5H5	Po···N	0.0404	0.1043	0.0300	–0.0339	–0.0039	0.8849	–44.5

^aSince each complex has C _s symmetry, the topological parameters and E _NCI values of the two F···N/H contacts are identical.

In addition, it is also noteworthy that the sign of ∇²ρ and H at the BCP can provide additional information on the nature of the interaction. , Specifically, the conditions ∇²ρ > 0 and H > 0 are characteristic of a closed-shell interaction, whereas ∇²ρ < 0 and H < 0 suggest the presence of a covalent bond. Furthermore, the interaction exhibits partial covalent character when ∇²ρ > 0, H < 0, and 0.5 < |G/V| < 1. One can see from Table , the positive ρ and ∇²ρ values illustrate closed-shell intermolecular interactions for the Ch···N ChBs present in all the investigated complexes. The Ch···N ChBs in the C₂F₄Se₂···NC₅H₅, C₂F₄Te₂···NH₃/NHCH₂/NC₅H₅, and C₂F₄Po₂···NH₃/NH CH₂/NC₅H₅ complexes exhibit a partially covalent nature, indicated by H < 0 and 0.8 < |G/V| < 1, while the Ch···N ChBs in the other complexes have a noncovalent character in nature because of the existence of H > 0 and |G/V| > 1.

It is evident from Table that the ρ and ∇²ρ values associated with N···F contacts in the C₂F₄S₂···NCH and C₂F₄Po₂···NH₃ complexes, as well as those related to H···F hydrogen bonds in the complexes containing NHCH₂, vary from 0.0057 to 0.0097 a.u. and from 0.0030 to 0.0431 a.u., respectively. These values are markedly lower than those observed for the corresponding Ch···N ChBs, suggesting that these H/N···F contacts are comparatively weaker compared to the Ch···N ChBs. Furthermore, all of these H/N···F interactions are characterized as purely closed-shell noncovalent interactions, as evidenced by the positive values of both ∇²ρ and H, along with the |G/V| values exceeding 1.

In addition to confirming the existence of Ch···N ChBs and characterizing their topological parameters, the QTAIM analysis also allows for a convenient semiquantitative estimate of the strength of each identified interaction based on the potential energy density at the corresponding BCP, as described by eq . Accordingly, we calculated the energy (denoted as E _NCI) of each identified intermolecular interaction, and these quantities are summarized in the last column of Table . It is found that the E _NCI values for the Ch···N ChBs range from −11.0 kJ/mol for the C₂F₂S₂···NCH complex to −45.3 kJ/mol for the C₂F₄Te₂···NC₅H₅ complex. Regarding the F···N contacts in the C₂F₂S₂···NCH and C₂F₄Po₂···NH₃ complexes, the E _NCI values vary between −7.4 and −10.8 kJ/mol, while those for the F···H interactions in the C₂F₄Ch₂···NHCH₂ (Ch = S, Se, Te, Po) complexes range from −5.7 to −9.2 kJ/mol. Interestingly, the F···H hydrogen bonds strengthen progressively with increasing chalcogen atomic size. Notably, although these F···N and F···H contacts are weaker than the Ch···N ChBs, they still make appreciable contributions to the stability of the corresponding complexes. Finally, it should be noted that the E _NCI values derived from V tend to be overestimated, while their relative magnitudes still provide a reliable indication of the comparative strengths of these intermolecular interactions.

Non-Covalent Interaction Plot (NCIplot) Analysis

The chalcogen···nitrogen interactions occurring within the studied complexes have been visually analyzed with the help of the NCIplot approach, which is based on the electron density and its reduced density gradient (RDG). The NCI isosurfaces of the C₂F₄Se₂···NCH, C₂F₄Se₂···NH₃, C₂F₄Se₂···NHCH₂, and C₂F₄Se₂···NC₅H₅ complexes as representative examples are presented in Figure , while Figure S2 displays the NCI isosurfaces for the other complexes. It should be noted that strong and weak attractive interactions are indicated by blue and green RDG isosurfaces, respectively, while red RDG isosurfaces indicate repulsive interactions. Noticeably, there exists a green or blue circular RDG isosurface between the Ch atom of C₂F₄Ch₂ and the N atom of Lewis base for all the investigated complexes, further demonstrating the existence of the attractive Ch···N ChBs as the primary interactions. Interestingly, the bifurcated C–F···N contacts, illustrated by the green RDG isosurfaces between the two F atoms of C₂F₄Ch₂ and the N atom of Lewis base, were also found in all the examined complexes except for the C₂F₄Te₂···NHCH₂ and C₂F₄Po₂···NHCH₂ complexes. However, these C–F···N contacts were not identified in the QTAIM analysis for most of the examined complexes. The observed discrepancy between QTAIM and NCIplot findings regarding the C–F···N secondary interactions most likely reflects the dispersion-dominated nature of these weak contacts, which are more appropriately characterized by the NCIplot approach. Additionally, the bifurcated C–H···F hydrogen bonds within the complexes involving NHCH₂ have been characterized by the presence of small green RDG isosurfaces between two F atoms of C₂F₄Ch₂ and one H atom of NHCH₂.

5.

NCI isosurfaces and scatter plots of RDG versus sign­(λ₂)­ρ for four selected complexes. The isosurfaces are depicted with an RDG value of 0.55 a.u. and the color scale varies from blue to red based on the sign­(λ₂)­ρ that varies between −0.035 to 0.020 a.u. The green and blue regions represent the weak and strong attractive interactions, respectively, and the red regions denote the repulsive interactions.

In addition, Figure and Figure S2 also illustrates the scatter plots of RDG versus sign­(λ₂)­ρ, which represents the product of the electron density (ρ) and the sign of the second eigenvalue (λ₂) of the Hessian matrix. It is important to note that the sign­(λ₂)­ρ value can be employed to predict the type and strength of the interactions. Specifically, negative sign­(λ₂)­ρ values indicate attractive interactions, whereas positive sign­(λ₂)­ρ values represent repulsive interactions. In general, the sign­(λ₂)­ρ value becomes more negative, the strength of the corresponding interaction becomes stronger. It is found that the first spikes at more negative sign­(λ₂)­ρ values are related to the Ch···N ChBs, which confirm the formation of attractive chalcogen···nitrogen interactions. Remarkably, for the fixed Lewis acid, the sign­(λ₂)­ρ value reduces in the sequence of NCH (sp) < NHCH₂ (sp²) < NH₃ (sp³) < NC₅H₅ (sp²). When Lewis base is fixed at NCH, the sign­(λ₂)­ρ value becomes increasingly negative with an increase in the Ch atomic radius. Conversely, the sign­(λ₂)­ρ value undergoes a progressive decrease in an irregular sequence of Ch = S > Se > Po > Te for a given Lewis base corresponding to NH₃, NHCH₂, or NC₅H₅. This observation is consistent with the results obtained from the QTAIM analysis previously discussed.

Natural Bond Orbital (NBO) Analysis

For the objective of achieving a more profound understanding of the nature of intermolecular interactions between C₂F₄Ch₂ and Lewis bases from the perspective of orbital interactions, we also executed the NBO analysis, which can identify donor–acceptor interactions and obtain their second-order perturbation energy (E ⁽²⁾). Table summarizes the findings of the NBO analysis. The results suggest that the charge transfer occurs primarily from the lone pair (LP) of the N atom in the Lewis base to the σ*­(C–Ch) antibonding orbitals of C₂F₄Ch₂ (Ch = S, Se, Te, Po). Concretely, the corresponding donor–acceptor interactions involve the LP­(N)→σ*­(C¹–Ch¹) and LP­(N)→σ*­(C²–Ch¹) orbital interactions, where the former plays a predominant role in stabilizing each complex. It has been estimated that the second-order perturbation energy (E ⁽²⁾) of the LP­(N)→σ*­(C¹–Ch¹) orbital interaction varies from a minimum of 9.3 kJ/mol for the C₂F₄S₂···NCH complex to a maximum of 84.9 kJ/mol for the C₂F₄Po₂···NC₅H₅ complex, which is significantly larger than that of the corresponding LP­(N)→σ*­(C²–Ch¹) orbital interaction in each complex (1.2 ∼ 23.7 kJ/mol). Simultaneously, the former exhibits a noticeably higher charge transfer compared to the latter. The NBO diagrams related to these two orbital interactions for the four representative heterodimers are illustrated in Figure . The overlap of the two lobes of the LP­(N)→σ*­(C¹–Ch¹) orbital interaction is greater than that of the LP­(N)→σ*­(C²–Ch¹) orbital interaction. This observation suggests that the larger the E ⁽²⁾ value of the orbital interaction correlates with a greater degree of overlap between the two lobes of the respective orbital interaction. Moreover, the LP­(F)→σ*­(C–H) charge transfer has also been found in the heterodimers involving NHCH₂, the corresponding E ⁽²⁾ values are less than 2 kJ/mol. It is interesting to note that the back-transfer of charge from the C₂F₄Ch₂ (Ch = S, Se, Te, or Po) moiety into the Lewis base has been observed for all the investigated heterodimers. Concretely, the charge transfer takes place from the LP­(Ch¹) of the C₂F₄Ch₂ into the π*­(CN), σ*­(N–H), or π*­(CN) antibonding orbitals of Lewis bases. The E ⁽²⁾ values of these donor–acceptor interactions range from 0.3 to 4.1 kJ/mol, which are markedly smaller than those of the LP­(N)→σ*­(C¹–Ch¹) orbital interactions. It should be pointed out that because the E ⁽²⁾ values for these orbital interactions are too small, the amounts of the corresponding charge transfer are not reported.

4. Findings of NBO Analysis on the Studied Heterodimers.

Complexes	LP(N) →σ*(C1–Ch1)	Δq	LP(N) → σ*(C2–Ch1)	Δq	LP(Ch1) → π*(CN)	LP(Ch1) → σ*(N–H)	LP(Ch1) →π*(CN)
C2F4S2···NCH	9.3	0.0060	1.2	0.0008	2.1
C2F4Se2···NCH	16.2	0.0116	2.4	0.0017	2.8
C2F4Te2···NCH	25.9	0.0194	6.9	0.0051	4.1
C2F4Po2···NCH	33.9	0.0264	7.7	0.0059	4.1
C2F4S2···NH3	20.5	0.0177	2.0	0.0018		0.3
C2F4Se2···NH3	36.4	0.0337	4.9	0.0046		0.5
C2F4Te2···NH3	56.7	0.0522	17.6	0.0169		0.9
C2F4Po2···NH3	60.3	0.0581	16.3	0.0158		0.9
C2F4S2···NHCH2	19.0	0.0147	2.1	0.0017		0.5	2.0
C2F4Se2···NHCH2	33.8	0.0274	4.9	0.0039		0.8	2.7
C2F4Te2···NHCH2	56.0	0.0445	15.4	0.0129		1.4	4.1
C2F4Po2···NHCH2	62.4	0.0519	14.3	0.0127		1.8	3.1
C2F4S2···NC5H5	28.7	0.0233	3.1	0.0026			1.0
C2F4Se2···NC5H5	54.8	0.0464	8.3	0.0076			1.5
C2F4Te2···NC5H5	82.7	0.0706	23.7	0.0221			2.2
C2F4Po2···NC5H5	84.9	0.0809	21.3	0.0203			1.8

^aThe atomic numbering is indicated in Figure and all the E⁽²⁾ values are reported in kJ/mol.

^bThe Δq values are given in e.

^cThe bold values are related to the LP­(F)→σ*­(C–H) orbital interactions.

6.

NBO schematic diagrams of the LP­(N)→σ*­(C^1/2–Se¹) orbital interactions for four selected heterodimers. Blue and green lobes represent opposite sign of each wave function, with an orbital isosurface value of ±0.05 a.u. The atomic numbering is given in Figure .

For the fixed Lewis base, the E ⁽²⁾ value related to the LP­(N)→σ*­(C¹–Ch¹) orbital interaction progressively increases as the size of chalcogen atom grows in the sequence of S < Se < Te < Po. For the same C₂F₄Ch₂ subunit, except for ChPo, the corresponding E ⁽²⁾ value exhibits an increasing trend in the order of NCH (sp) < NHCH₂(sp²) < NH₃(sp³) < NC₅H₅(sp²), which corresponds to the sequence of the gas-phase basicity order of these nitrogen bases. The NBO analysis results align closely with the earlier QTAIM and NCIplot outcomes. Furthermore, Figure S3 illustrates a significant correlation between the interaction energies, binding energies, and the second-order perturbation energies associated with the LP­(N)→σ*­(C¹–Ch¹) orbital interactions, as the corresponding linear correlation coefficients are higher than 0.96.

Frontier Molecular Orbital (HOMO–LUMO) Analysis

Frontier Molecular Orbital (FMO) theory provides a powerful tool for examining the electronic and chemical properties of chemical systems. Within this theory, the energy of the higher occupied molecular orbitals (HOMO) represents the electron-donating capacity while that of the lowest unoccupied molecular orbitals (LUMO) reflects the electron-accepting tendency. Consequently, the HOMO energy (E _HOMO), LUMO energy (E _LUMO), Fermi level energy (E _FL), and HOMO–LUMO gap (ΔE) were computed for both the monomers and complexes, and the results were collected in Table . As shown in Table , complexation induces pronounced shifts in these values. Taking the C₂F₄Te₂ monomer as an example, its E _HOMO, E _LUMO, E _FL, and ΔE values are −9.208, −0.397, −4.803, and 8.811 eV, respectively, whereas the corresponding values have changed to −8.579, 0.646, −3.967, and 9.225 eV for the C₂F₄Te₂···NC₅H₅ complex. These marked variations indicate that C₂F₄Ch₂ molecules have a propensity to participate in σ-hole-type chalcogen bonding interactions with nitrogen-containing Lewis bases.

5. The E _HOMO, E _LUMO, E _FL, and ΔE of All the Monomers and Complexes Estimated at the MP2/aug-cc-pVDZ­(PP) Level.

Systems		HOMO (eV)	LUMO (eV)	E FL (eV)	ΔE (eV)
	C2F4S2	–11.326	0.916	–5.205	12.241
	C2F4Se2	–10.392	0.349	–5.021	10.741
	C2F4Te2	–9.208	–0.397	–4.803	8.811
Monomers	C2F4Po2	–8.668	–0.439	–4.554	8.230
	NCH	–13.280	0.779	–6.250	14.059
	NH3	–11.693	0.971	–5.361	12.665
	NHCH2	–11.848	0.934	–5.457	12.782
	NC5H5	–9.402	0.871	–4.265	10.273
	C2F4S2···NCH	–10.843	0.681	–5.081	11.524
	C2F4S2···NH3	–10.873	0.871	–5.001	11.744
	C2F4S2···NHCH2	–10.805	0.807	–4.999	11.612
	C2F4S2···NC5H5	–9.704	0.771	–4.467	10.475
	C2F4Se2···NCH	–9.911	0.660	–4.625	10.571
	C2F4Se2···NH3	–9.933	0.800	–4.567	10.733
	C2F4Se2···NHCH2	–9.859	0.768	–4.545	10.627
Complexes	C2F4Se2···NC5H5	–9.762	0.732	–4.515	10.494
	C2F4Te2···NCH	–8.739	0.321	–4.209	9.059
	C2F4Te2···NH3	–8.746	0.421	–4.162	9.167
	C2F4Te2···NHCH2	–8.661	0.508	–4.077	9.169
	C2F4Te2···NC5H5	–8.579	0.646	–3.967	9.225
	C2F4Po2···NCH	–8.217	0.275	–3.971	8.492
	C2F4Po2···NH3	–8.246	0.345	–3.951	8.591
	C2F4Se2···NHCH2	–8.159	0.428	–3.865	8.587
	C2F4Po2···NC5H5	–8.084	0.592	–3.746	8.676

Additionally, we also estimated a set of global reactivity descriptors, including ionization energy (IE), electron affinity (EA), chemical potential (μ), chemical hardness (η), chemical softness (S), electrophilicity index (ω), and electronegativity (χ), using the HOMO and LUMO energies for unraveling the chemical reactivity features of the interacting species. The computed global reactivity parameters were summarized in Table S2. Complex formation consistently leads to noticeable changes in these global reactivity parameters across the entire series of the C₂F₄Ch₂···LB complexes (Ch = S, Se, Te, Po; LB = NCH, NH₃, NHCH₂, NC₅H₅). For illustration, the IE, EA, μ, η, S, ω, and χ values of the C₂F₄Te₂ monomer have been determined to be 9.208 eV, 0.397 eV, −4.803 eV, 4.405 eV, 0.227 eV^–1, 2.618 eV, and 4.803 eV, respectively. Upon complexation with NC₅H₅, these quantities changed to 8.579 eV, −0.646 eV, −3.967 eV, 4.613 eV, 0.217 eV^–1, 1.706 eV, and 3.967 eV, respectively. The substantial reorganization of the electronic structure, reflected in both the FMO energies and the global reactivity indices, corroborates the formation of σ-hole-type chalcogen bonding interactions between the C₂F₄Ch₂ donors and nitrogen-based acceptors, in full agreement with the previous analyses.

SAPT-EDA Calculation

In order to elucidate the intrinsic nature of the Ch···N interactions from a quantitative perspective, we also utilized the SAPT method to implement the energy decomposition analysis for the studied complexes. This method has the capacity to divide the total interaction energy (E _SAPT2+) of each complex into four physically meaningful components, including the electrostatics (E _elec), induction (E _ind), dispersion (E _disp), and exchange-repulsion (E _ex‑re) terms. Table collects the SAPT-EDA analysis findings obtained at the SAPT2+/aug-cc-pVDZ­(PP) level, which has been estimated and proposed as the silver standard of SAPT by Parker and colleagues due to its computational efficiency and accuracy in calculating the interaction energies. It is found that electrostatic component plays a crucial role in stabilizing the studied complexes, which accounts for 50–58% of the total attractive interaction energies for all the complexes. This provides additional evidence that electrostatic component is the most significant contributor to the chalcogen···nitrogen interactions within 1,2,5-chalcogenadiazole homodimers. Similarly, electrostatic interactions also provide the largest contribution to the S···N/O/S/P chalcogen-bonded complexes of C₂F₄S₂ with isopropylamine (IPA), H₂O, HCHO, CH₃OCH₃, CH₃SCH₃, and P­(CH₃)₃, where the corresponding SAPT analysis results estimated at the SAPT2+/aug-cc-pVDZ level of theory are collected Table S3. The dispersion contribution is greater than the induction contribution for the C₂F₄S₂/C₂F₄Se₂-containing complexes, except for the C₂F₄Se₂···NH₃ complex, where the contributions from dispersion and induction energies are equivalent. Conversely, the induction contribution surpasses the dispersion contribution for the complexes containing C₂F₄Te₂ and C₂F₄Po₂, with the exception of the C₂F₄Te₂/C₂F₄Te₂···NCH complexes, in which the latter mainly prevail over the former. However, it is important to note that both dispersion and induction contributions are also significant (42–50%), making them unneglectable. Moreover, for a given Lewis base, it appears that there has been no significant alteration in the electrostatic contribution. For the fixed C₂F₄Ch₂ molecule, the electrostatic component’s contribution progressively grows with the sequence of NCH (sp) < NHCH₂ (sp²) ≈ NC₅H₅ (sp²) < NH₃ (sp³).

6. SAPT-EDA Findings (kJ/mol) for the 16 Chalcogen-Bonded Complexes Calculated by Means of SAPT Method at the SAPT2+/aug-cc-pVDZ­(PP) Theoretical Level.

Complexes	E elec	E ind	E disp	E ex–re	E SAPT2+	ΔΔE
C2F4S2···NCH	–25.6(50%)	–7.7(15%)	–17.6(35%)	34.4	–16.6	–0.2
C2F4S2···NH3	–56.5(58%)	–18.0(18%)	–23.5(24%)	72.2	–25.9	–0.4
C2F4S2···NHCH2	–50.4(54%)	–17.2(18%)	–26.6(28%)	67.3	–27.0	–0.4
C2F4S2···NC5H5	–78.5(54%)	–27.1(19%)	–39.3(27%)	110.6	–34.4	–0.6
C2F4Se2···NCH	–32.4(51%)	–11.0(17%)	–20.3(32%)	44.0	–19.7	0.2
C2F4Se2···NH3	–77.9(58%)	–27.8(21%)	–28.2(21%)	100.6	–33.2	0.9
C2F4Se2···NHCH2	–67.9(54%)	–26.2(21%)	–31.3(25%)	92.0	–33.4	0.9
C2F4Se2···NC5H5	–115.3(55%)	–45.9(22%)	–48.7(23%)	164.3	–45.5	3.6
C2F4Te2···NCH	–44.5(51%)	–18.0(20%)	–25.1(29%)	62.5	–25.2	0.1
C2F4Te2···NH3	–110.1(56%)	–50.6(26%)	–36.9(18%)	148.8	–48.9	2.7
C2F4Te2···NHCH2	–94.8(52%)	–47.1(26%)	–39.8(22%)	135.3	–46.5	2.1
C2F4Te2···NC5H5	–149.2(52%)	–75.0(26%)	–61.6(22%)	221.4	–64.4	3.7
C2F4Po2···NCH	–50.5(51%)	–20.8(21%)	–26.9(27%)	69.8	–28.4	0.3
C2F4Po2···NH3	–108.9(57%)	–46.7(24%)	–36.2(19%)	140.3	–51.5	2.9
C2F4Po2···NHCH2	–95.8(53%)	–45.8(25%)	–39.5(22%)	131.3	–49.8	3.0
C2F4Po2···NC5H5	–145.1(53%)	–67.5(25%)	–60.8(22%)	207.3	–66.1	3.6

^aThe values in parentheses represent the percentage contribution of a single attractive component to the total attractive interaction energy.

^b E _SAPT2+ = E _elst + E _ind + E _disp + E _ex‑re.

^cΔΔE = E _CCSD(T)/CBS – E _SAPT2+.

As reported in Table , the E _SAPT2+ values of the studied complexes range from −16.6 to −66.1 kJ/mol. The observed change in the E _SAPT2+ values is qualitatively consistent with the Ch···N binding distance (R _Ch···N), interaction energies (E _int), and second-order perturbation energy (E ⁽²⁾). Indeed, a good linear relationship was noted between these variables (Figure S4). For instance, the E _SAPT2+ values are −19.7, −33.2, −33.4, and −45.5 kJ/mol for the C₂F₄Se₂···NCH, C₂F₄Se₂···NH₃, C₂F₄Se₂···NHCH₂, and C₂F₄Se₂···NC₅H₅ complexes that have R _Ch···N values of 2.935, 2.790, 2.781, and 2.600 Å, accompanied by the E ⁽²⁾ values of −16.2, −36.4, −33.8, and −54.8 kJ/mol, as well as the E _int values of −19.5, −32.3, −32.5, and −41.9 kJ/mol, respectively. Additionally, the energy difference (ΔΔE) between the interaction energies (E _CCSD(T)/CBS) computed at the CCSD­(T)/CBS level and the total E _SAPT2+ energies is tiny, corroborating the reliability of the employed SATP level.

Comparison with the Ch···C/N/O/P/S/F ChBs in Other Related Systems

As the first systematic examination of how chalcogen atomic size and nitrogen hybridization states synergistically influence the Ch···N ChBs, the comparison of our results with existing related systems can provide valuable insights. For complexes employing C₂F₄S₂ molecule as the ChB donor, the calculated S···N distances in the C₂F₄S₂···NCH, C₂F₄S₂···NH₃, and C₂F₄S₂···NHCH₂ complexes are slightly longer than the experimental values for the C₂F₄S₂···NH₃ (2.811(5) Å) and C₂F₄S₂···isopropylamine (2.731­(3) Å) complexes, but shorter than the experimental S···O distances in the C₂F₄S₂···H₂O (2.912­(5) Å) and C₂F₄S₂···HCHO (2.9260(1) Å) complexes, as well as the S···F distance in the C₂F₄S₂···CH₂F₂ (2.9759(6) Å) complex. Moreover, they are also significantly shorter than the S···S and S···P distances in the C₂F₄S₂···CH₃SCH₃ (3.19 Å) and C₂F₄S₂···P­(CH₃)₃ (3.36 Å) complexes. Across all the C₂F₄S₂-containing complexes, the ∠C–S···N angles are comparable to the corresponding ∠C–S···O/F/S/P angles, suggesting that the identity of the acceptor atom has little influence on the directionality of the interaction.

Comparisons with the complexes of other ChB donors are likewise instructive. The S···N distances reported here are markedly longer than those in the complexes of SF₄ with a series of amines (2.158 ∼ 2.571 Å), whereas the ∠C–S···N angles in the SF₄-containing complexes are significantly larger. This difference presumably reflects the distinct hypervalent bonding environment of the sulfur center in SF₄. Conversely, the Ch···N distances (Ch = S, Se, Te) reported here are clearly shorter than those in the complexes of tetrafluorobenzochalcogenadiazoles with various nitrogen bases. The ∠C–S···N angles in the former are also smaller than those in the latter. With regard to the heaviest congener, only two reports have documented the Po atom as a ChB donor. For the ChF₄···(NH₃)₂ (Ch = S, Se, Te, Po) complexes, both cis and trans configurations have been identified. The MP2/aug-cc-pVDZ­(PP) level predicted Ch···N distances for the σ-hole bonds in the cis forms and π-hole bonds in the trans forms are all shorter than those in the C₂F₄Ch₂···NH₃ complexes. However, the σ-hole Ch···N distances in the trans configurations are notably longer than those in the complexes of C₂F₄Ch₂ with NCH, NH₃, NHCH₂, and NC₅H₅, with the exception of the C₂F₄Po₂···NCH complex. Additionally, all the Ch···N distances obtained here are notably shorter than the Ch···C distances (calculated at the MP2/aug-cc-pVDZ­(PP) level) in the complexes of various chalcogenadiazoles (Ch = S, Se, Te, Po) with dimethyl beryllium and dimethyl magnesium, thus suggesting that the Ch···N ChBs are considerably stronger than their Ch···C counterparts.

Finally, it is noteworthy that organochalcogen-nitrogen heterocycles, such as various chalcogenadiazoles and benzochalcogenadiazoles, have a notable propensity to establish the [Ch-N]₂ supramolecular synthon through double Ch···N ChBs (Ch = S, Se, Te), − ,,,− in which the nitrogen atoms are typically sp²-hybridized state. For most diazoles, the Ch···N distances within these synthons are longer than those in the C₂F₄Ch₂···NH₃, C₂F₄Ch₂···NHCH₂, and C₂F₄Ch₂···NC₅H₅ complexes (Ch = S, Se, Te), the only exceptions being the C₂F₄Te₂···NH₃ and C₂F₄Te₂···NHCH₂ complexes. In all cases, however, the Ch···N distances decrease as the chalcogen atomic size increases from S to Te, which is in line with the trend established in the present work. It is also worth noting that the chalcogen bonding interactions in most of the above-discussed systems are predominantly electrostatic in nature.

Conclusions

In summary, the σ-hole-type chalcogen···nitrogen interactions between C₂F₄Ch₂ (Ch = S, Se, Te, Po) molecules and nitrogen-bearing Lewis bases (NCH, NH₃, NHCH₂, and NC₅H₅) have been systematically investigated using theoretical calculations. The comprehensive characterization of the strength and nature of the Ch···N ChBs has been achieved through the MEP, QTAIM, NCIplot, NBO, FMO, and EDA-SAPT methodologies. The CCSD­(T)/CBS level estimated interaction energies vary between −16.8 and −62.5 kJ/mol for the studied complexes, and the Ch···N distances (2.570–2.951 Å) are all markedly shorter than the sum of their respective van der Waals radii. QTAIM analysis confirms that all the Ch···N ChBs have closed-shell interaction characteristics, whereas the heavier Te···N and Po···N ChBs formed with NH₃, NHCH₂, and NC₅H₅ are sufficiently strong to exhibit a partially covalent character. The complexes involving NHCH₂ have two additional C–H···F hydrogen bonds, which are weaker than the corresponding Ch···N ChBs but provide additional stabilization. NBO analysis identifies the LP­(N)→σ*­(C–Ch) charge transfer as the dominant orbital contribution to the formation of the examined complexes. FMO analysis reveals that complexation induces pronounced changes in the frontier-orbital-related electronic parameters. SAPT-EDA results demonstrate that although electrostatic interactions are the dominant factor in stabilizing the chalcogen-bonded complexes, both induction and dispersion contributions play indispensable supporting roles.

Unlike previous studies that have typically focused on either the chalcogen atomic size or the nitrogen hybridization state in isolation, this work represents the first systematic investigation into the synergistic modulation of the strength and nature of Ch···N ChBs by simultaneously considering the heavy Group 16 elements (S, Se, Te, Po) across three distinct nitrogen hybridization patterns (sp, sp², sp³). Two clear trends emerge from the data: (i) the Ch···N ChB strength generally increases in the order of Ch = S < Se < Po < Te and NCH (sp) < NH₃ (sp³) < NHCH₂ (sp²) < NC₅H₅ (sp²), a sequence that does not simply follow the intrinsic basicity of these nitrogen bases; and (ii) the Te···N and Po···N ChBs with NH₃, NHCH₂, and NC₅H₅ exhibit partial covalent character, whereas their S···N and Se···N counterparts remain purely noncovalent closed-shell interactions, which deviates from conventional expectations. It is also worth noting that the Ch···N ChBs involving NHCH₂ and NC₅H₅ are generally stronger than those reported for most homodimers of chalcogenadiazoles and benzochalcogenadiazoles (Ch = S, Se, Te), all of which have nitrogen in a sp²-hybridized state. These findings provide a rational framework for fine-tuning the strength and nature of chalcogen bonds through the coupled selection of the chalcogen donor and the nitrogen hybridization state. Future investigations could extend this dual-variable strategy to other σ-hole interactions and to condensed-phase studies that account for solvent effects, thereby further bridging the gap between gas-phase models and practical applications in crystal engineering, catalysis, and material design.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.6c07591.

• Cartesian coordinates of the most stable isomers of all heterodimers; global reactivity parameters of all the monomers and complexes; SAPT-EDA analysis findings for the six C₂F₄S₂-containing complexes; correlation plots between the Ch···N distance and ρ and ∇²ρ, as well as between the binding energies (E _b) and ρ and ∇²ρ; 2D and 3D NCI diagrams for the C₂F₄Ch₂···NCH, C₂F₄Ch₂···NH₃, C₂F₄Ch₂···NHCH₂, and C₂F₄Ch₂···NC₅H₅ complexes (Ch = S, Te, Po); correlation plots of E _total with the Ch···N distance, E _int, and E ⁽²⁾; correlation plots between the E ⁽²⁾ value of the LP­(N) → σ*­(C¹–Ch¹) orbital interactions and E _int and E _b (PDF)

#.

K.P. and F.L. contributed equally. The manuscript was written through the contributions of all authors. All authors have approved the final version of the manuscript.

The authors declare no competing financial interest.