Cooperative halogen bonds in V-shaped H₃N·X1X2·X3Y (X1, X2, X3 = Cl and Br; Y = F, Cl and Br) complexes

Abstract

A series of V-shaped molecular complexes formed by NH₃, X1X2 and X3Y (X1, X2, X3 = Cl, Br; Y = F, Cl, Br) molecules via two halogen bonds (i.e., N⋯X1 and X2⋯X3 interactions) have been investigated at the MP2/aug-cc-pVTZ level of theory to obtain their optimized geometries, stretching modes and interaction energies. Molecular electrostatic potential was used to illustrate how X1 and X2 act as the halogen bond donor and acceptor in N⋯X1 and X2⋯X3 interactions, respectively. The evaluation of the binding distances, interaction energies and the electron density at the bond critical points of the halogen bonds reveals the existence of cooperativity between the two halogen bonds. Subsequently, the concepts of pair interaction and pairwise non-additive contributions to the total interaction energy, and the cooperativity factor were further employed to assess the cooperativity. The formation mechanisms of these complexes were analyzed based on the contour maps of the Laplacian (∇²ρ) of electron density. Energy decomposition analysis suggests that electrostatic force is the main net contribution to the stability of these complexes. The work would provide valuable insights into the design of related halogen-bonded complexes.

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1. Introduction

The halogen bond (XB) has attracted great interest in recent decades because of its wide applications in crystal engineering, nanotechnology, drug design, chemical separation, and biology.^1–13 A XB, usually represented as Y–X⋯D, occurs between a halogen atom (e.g., X = Cl, Br or I) and an electron donor (D) which can be an electronegative atom like O or N or a group with a negative electrostatic potential region,^14–16 while the Y atom (e.g., C, N or X atom) is covalently bonded to the X atom.^17–20 Actually, F atom can also act as halogen donor in a XB.^19,21–29 Geometrically, the Y–X⋯D angle tends to be nearly linear, and the X⋯D binding distance is shorter than the sum of their van der Waals radii.^17,18,30 The X⋯D interaction strengths with the same electron donor (D) usually follow the order of Cl < Br < I.¹⁹ The halogen atom X possesses unique features, that is, it has positive electrostatic potential around the X atom-end (i.e., the so-called σ-hole^19,31) and negative electrostatic potential around the outer region of the X atom perpendicular to the bond axis (i.e., the so-called ‘lump’³²), giving it amphoteric features (i.e., electrophilic along the direction of covalent bond axis and nucleophilic along the vector perpendicular to the bond). Consequently, many experimental^1,33–47 and theoretical studies^{4,20,33,41,43,48–55} have been devoted to such interesting field.

In recent years, X⋯D halogen bonds have been widely investigated, including X⋯O, X⋯S and X⋯N halogen bonds.^{33,51,54–59} For instance, Glaser et al. studied the O⋯I halogen bonded complexes formed between DMSO and a series of iodoarenes experimentally and theoretically.³³ Sutradhar et al. investigated the O⋯Cl halogen bond in the complexes of fluorinated dimethyl ethers and FCl, and they suggested that the strength of the O⋯Cl halogen bond is weaker than that of the corresponding O⋯H hydrogen bond.⁵⁵ Joseph and McDowell suggested that the FKrCl molecule can form weak complex with H₂O via Cl⋯O halogen bond.⁵⁶ Similarly, the N atom can also serve as the electron donor of halogen bond. Li et al. reported the interplay between the X⋯N halogen bond and H⋯Li lithium bond in MCH–LiCN–XCCH (M = H, Li and Na; X = Cl, Br and I) complex, in which the X⋯N halogen bond is enhanced by the lithium bond.⁵¹ Also, they studied the cooperativity between the X⋯N halogen bond and the Y⋯H hydrogen bond in H₃N⋯XY⋯HF complexes (X, Y = F, Cl, Br).⁵⁷ Solimannejad and coworkers have studied the X⋯N halogen-bonded interactions in 4-Z–Py⋯XCN⋯XCN triads (Z = H, F, OH, OCH₃, CH₃, NH₂, NO₂, and CN; Py = pyridine; and X = Cl and Br), in which the substituent effects on the cooperativity of halogen bonds were elaborated.⁵⁴ The investigations of the complexes of XCN (X = F, Cl, Br and I) and NH₃ molecules showed that the N atom of NH₃ can interact with both X and C atoms of XCN via X⋯N halogen bond and X⋯C tetrel bond.⁵⁸ Besides the halogen bonds between O or N atom and X atom, the halogen–halogen interactions were also widely studied.^60–63 In the previous work,⁶⁴ the ring-shaped complexes via NH₃, X(Y) and HF (X = Cl, Br and Y = F, Cl, Br) were studied, which displayed that dihalogen molecules can simultaneously act as halogen-bonding donor and hydrogen-bonding acceptor. Hence, in the present continued work, a series of complexes formed by NH₃ and two dihalogen molecules with the V-shaped structures were further designed and investigated. Based on the amphoteric features of the halogen atom as shown in Scheme 1a, two dihalogen molecules can interact with each other to form halogen-bonded dimer, as shown in Scheme 1b. By adding an NH₃ molecule to one dihalogen molecule or the halogen-bonded dimer between two dihalogen molecules, the corresponding complexes can form, as displayed in Scheme 1c and d. In the designed model systems H₃N·X1X2·X3Y (X1, X2, X3 = Cl, Br and Y = F, Cl, Br), the N atom of NH₃ molecule and the halogen atom X2 in the dihalogen molecule X1X2 act as the halogen-bonding acceptors, while the halogen atom X1 in X1X2 and the halogen atom X3 in X3Y act as the halogen-bonding donors. Their geometry, spectroscopy and bonding properties were studied to examine the nature of XB, meanwhile, the cooperativity between two distinctive halogen bonds was also investigated.

Scheme 1 (a) Polar flattening effect, showing opposite polarized regions along bond axis and perpendicular to bond axis direction; (b) halogen⋯halogen interaction between two dihalogen molecules; (c) nitrogen⋯halogen interaction between a dihalogen molecule and NH₃; (d) the trimer formed by two dihalogen molecules and NH₃ via two halogen bonds. Herein, X1, X2 and X3 represent Cl and Br atoms while Y represents F, Cl and Br atoms.

2. Computational methods and details

The geometries of the isolated NH₃, dihalogen molecules and their corresponding halogen-bonded complexes have been optimized using the second-order Møller–Plesset perturbation theory (MP2) with the aug-cc-pVTZ basis set, which were implemented by GAUSSIAN 09 suite of programs.⁶⁵ The MP2 was chosen due to the reliable results provided by this density functional.⁶⁶ Harmonic vibrational frequency analyses were carried out at the same level of theory to demonstrate that the structures are local minima with no imaginary vibrational frequencies. The interaction energy (ΔE_int) is calculated as the energy difference between the total energy of the complex and those of the corresponding monomers. The basis set superposition error (BSSE) method is employed to correct the interaction energy according to the counterpoise (CP) method proposed by Boys and Bernardi.⁶⁷ The CP interaction energy (ΔE_int,CP) is calculated as the sum of the interaction energy (ΔE_int) and the BSSE content of the interaction energy (δ_BSSE).

To understand the topological properties of the complexes, quantum theory of atoms in molecules (QTAIM)⁶⁸ analysis was carried out at the MP2/aug-cc-pVTZ level using AIMAll (Version 09.11.29) program.⁶⁹ To investigate the formation mechanism of halogen-bonded trimers, the contour maps of the Laplacian (∇²ρ) of electron density for all the trimers were plotted using Multiwfn 3.3.8(dev) program.⁷⁰ Meanwhile, the molecular electrostatic potential (MEP) as a powerful tool in exploring the natures of intermolecular interactions^71–76 was also employed.

The cooperativity between weak intermolecular interactions have been well established.^{51,56,57,59,72,77–81} In this work, the concepts of pair interaction and pairwise non-additive contributions to ΔE_int proposed by McDowell and Joseph^56,77 were adopted to examine the cooperative effects. The pair interaction is the two interacted molecules in the optimized trimer, and the pairwise non-additive contribution (E_non-add) to ΔE_int is the energy difference between the total interaction energy of the trimer and the sum of total interaction energies of the corresponding dimers (∑E_ij). The energy decomposition analysis (EDA) which can tell us the nature of intermolecular interactions at the energy level⁸² was used. The localized molecular orbital-energy decomposition analysis (LMO-EDA) method of Su and Li⁸³ based on the methods developed by Kitaura and Morokuma, Ziegler and Rauk, and Hayes and Stone^84–86 was performed at the MP2/aug-cc-pVTZ level using the GAMESS program⁸⁷ because LMO-EDA method is basis-set insensitive. The total interaction energy (ΔE_int,EDA) can be decomposed into electrostatic energy (E_elst), exchange energy (E_exch), polarization energy (E_pol), dispersion energy (E_disp) and repulsion energy (E_rep) terms, that is, ΔE_int,EDA = E_elst + E_exch + E_pol + E_disp + E_rep.

3. Results and discussion

3.1 Molecular electrostatic potential (MEP) analysis

Molecular electrostatic potential (MEP) is an effective tool in investigating the formation mechanism of weak intermolecular interactions because it can reflect the electronic feature of a molecule through the positive and negative MEP regions participated in the formation of these noncovalent interactions.^{21,64,73–76,88} Fig. S1† displays the calculated MEPs for the six monomers (NH₃, FCl, FBr, Cl₂, ClBr, Br₂), which have been studied in the previous study (see ESI† for details).⁶⁴ For NH₃, the outer regions of the H atoms are positive, serving as the interacting sites with nucleophile, whereas the MEP of N atom is negative, serving as the site to interact with electrophile. In the five dihalogen molecules (FCl, FBr, Cl₂, ClBr, Br₂), the MEPs at the end of Cl or Br atom along the bond axis are positive, while the MEPs around their central portion perpendicular to the bond axis are negative. Thus, the positive MEP region of a monomer can interact with the negative MEP region of another monomer to form stable complexes. According to these results, the binding model systems for the dimers and trimers were constructed and their optimized structures were displayed in Fig. S2–S4 in ESI,† respectively. They are true minima because no imaginary frequencies were found. A dihalogen molecule can interact with another dihalogen molecule to form a series of halogen-bonded dimers (D1–24, Fig. S2†). In our previous work, the interactions between NH₃ and these dihalogen molecules have been investigated,⁶⁴ so they aren't displayed here (see D25–28 in Fig. S3† for details). Because of the negative MEP on the outer region of F atom, it cannot serve as the donor of halogen bond. The N atom of NH₃ can serve as nucleophile to interact with the halogen atoms of these dimers, leading to 24 trimers (T1–24, Fig. S4†) with V-shaped structures.

3.2 Geometries, stretching vibrational frequencies and interaction energies

The geometrical parameters and stretching vibrational frequencies for six monomers (NH₃, FCl, FBr, Cl₂, ClBr, Br₂) at the MP2/aug-cc-pVTZ level are listed in Table S1,† as same as the previous results.⁶⁴ The respective geometrical parameters, stretching vibrational frequencies and interaction energies obtained without (non-CP) and with CP methods at the same level of theory for dimers D1–24, D25–28 and trimers T1–24 are summarized in Tables 1, 2 and S2–S4.†

Table 1 Structural parameters (R, d, in Å), stretching vibrational frequencies (ν, in cm⁻¹) and interaction energies (ΔE_int,CP, in kcal mol⁻¹) of dimers D1–24 obtained at the MP2/aug-cc-pVTZ level with CP optimization

Complex	Bond	R	v	d	ΔEint,CP (δBSSE)
D1	Cl1–Cl2	1.9985	572.6	3.0371	−2.20 (0.44)
	Cl3–F4	1.6451	779.3
D2	Cl1–Cl2	1.9987	572.8	3.2726	−1.64 (0.39)
	Cl3–Cl4	2.0023	566.4
D3	Cl1–Cl2	1.9987	572.9	3.3227	−1.56 (0.49)
	Cl3–Br4	2.1412	456.5
D4	Cl1–Cl2	1.9986	571.6	3.0183	−3.07 (0.95)
	Br3–F4	1.7675	672.0
D5	Cl1–Cl2	1.9990	572.1	3.2507	−2.19 (0.81)
	Cl3–Br4	2.1441	453.1
D6	Cl1–Cl2	1.9989	572.3	3.3135	−2.03 (0.88)
	Br3–Br4	2.2834	336.6
D7	Cl1–Br2	2.1365	461.1	3.1029	−2.46 (0.89)
	Cl3–F4	1.6480	768.6
D8	Cl1–Br2	2.1375	460.8	3.3619	−1.77 (0.71)
	Cl3–Cl4	2.0035	563.3
D9	Cl1–Br2	2.1376	460.8	3.4115	−1.69 (0.81)
	Cl3–Br4	2.1422	454.2
D10	Cl1–Br2	2.1357	460.8	3.0684	−3.56 (1.51)
	Br3–F4	1.7720	660.9
D11	Cl1–Br2	2.1372	460.7	3.3208	−2.44 (1.22)
	Cl3–Br4	2.1466	449.0
D12	Cl1–Br2	2.1373	460.7	3.3853	−2.25 (1.28)
	Br3–Br4	2.2855	334.0
D13	Cl1–Br2	2.1394	459.2	3.0138	−2.50 (0.60)
	Cl3–F4	1.6462	776.3
D14	Cl1–Br2	2.1390	459.6	3.2507	−1.85 (0.57)
	Cl3–Cl4	2.0028	565.4
D15	Cl1–Br2	2.1388	459.8	3.3007	−1.75 (0.67)
	Cl3–Br4	2.1417	455.7
D16	Cl1–Br2	2.1400	458.3	2.9970	−3.47 (1.16)
	Br3–F4	1.7688	669.6
D17	Cl1–Br2	2.1397	458.9	3.2247	−2.50 (1.01)
	Cl3–Br4	2.1451	451.6
D18	Cl1–Br2	2.1394	459.1	3.2889	−2.31 (1.10)
	Br3–Br4	2.2842	335.8
D19	Br1–Br2	2.2781	341.0	3.0853	−2.73 (1.05)
	Cl3–F4	1.6492	765.3
D20	Br1–Br2	2.2785	340.9	3.3431	−1.98 (0.86)
	Cl3–Cl4	2.0042	562.0
D21	Br1–Br2	2.2785	341.0	3.3938	−1.88 (0.97)
	Cl3–Br4	2.1428	453.3
D22	Br1–Br2	2.2780	340.5	3.0554	−3.93 (1.70)
	Br3–F4	1.7733	658.2
D23	Br1–Br2	2.2786	340.7	3.2999	−2.73 (1.42)
	Cl3–Br4	2.1477	447.6
D24	Br1–Br2	2.2786	340.6	3.3636	−2.52 (1.49)
	Br3–Br4	2.2865	332.9

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Table 2 Structural parameters (R, d₁, d₂, in Å), stretching vibrational frequencies (ν, in cm⁻¹) and interaction energies (ΔE_int,CP, in kcal mol⁻¹) of trimers T1–24 obtained at the MP2/aug-cc-pVTZ level with CP optimization

Complex	Bond	R	v	d1	d2	ΔEint,CP (δBSSE)
T1	N1–H2	1.0125	3496.6	2.5146	2.9194	−8.51 (1.17)
	Cl1–Cl2	2.0457	481.3
	Cl3–F4	1.6527	760.4
T2	N1–H2	1.0125	3496.4	2.5714	3.1906	−7.26 (1.04)
	Cl1–Cl2	2.0371	497.7
	Cl3–Cl4	2.0054	560.9
T3	N1–H2	1.0125	3497.5	2.5840	3.2514	−7.00 (1.13)
	Cl1–Cl2	2.0356	500.8
	Cl3–Br4	2.1430	453.4
T4	N1–H2	1.0125	3495.7	2.4518	2.8864	−10.11 (1.89)
	Cl1–Cl2	2.0575	460.9
	Br3–F4	1.7785	652.1
T5	N1–H2	1.0125	3496.6	2.5243	3.1348	−8.36 (1.61)
	Cl1–Cl2	2.0447	483.8
	Cl3–Br4	2.1502	445.7
T6	N1–H2	1.0125	3497.0	2.5430	3.2059	−7.96 (1.68)
	Cl1–Cl2	2.0418	489.1
	Br3–Br4	2.2880	332.3
T7	N1–H2	1.0126	3496.0	2.6213	3.0139	−7.49 (1.79)
	Cl1–Br2	2.1686	403.1
	Cl3–F4	1.6554	749.2
T8	N1–H2	1.0125	3497.1	2.6761	3.3001	−6.22 (1.49)
	Cl1–Br2	2.1651	412.3
	Cl3–Cl4	2.0063	558.0
T9	N1–H2	1.0124	3497.7	2.6851	3.3519	−5.98 (1.58)
	Cl1–Br2	2.1642	414.1
	Cl3–Br4	2.1440	450.9
T10	N1–H2	1.0126	3496.2	2.5666	2.9734	−9.21 (2.56)
	Cl1–Br2	2.1764	388.9
	Br3–F4	1.7825	641.1
T11	N1–H2	1.0125	3496.6	2.6315	3.2299	−7.36 (2.15)
	Cl1–Br2	2.1693	403.6
	Cl3–Br4	2.1528	441.4
T12	N1–H2	1.0125	3497.0	2.6469	3.3008	−6.97 (2.20)
	Cl1–Br2	2.1680	406.7
	Br3–Br4	2.2901	329.3
T13	N1–H2	1.0129	3491.3	2.4317	2.8525	−13.08 (2.58)
	Cl1–Br2	2.2171	381.0
	Cl3–F4	1.6581	746.0
T14	N1–H2	1.0127	3493.0	2.4741	3.1250	−11.39 (2.38)
	Cl1–Br2	2.2066	388.7
	Cl3–Cl4	2.0079	555.7
T15	N1–H2	1.0127	3493.5	2.4848	3.1883	−11.02 (2.47)
	Cl1–Br2	2.2034	391.3
	Cl3–Br4	2.1451	449.7
T16	N1–H2	1.0130	3489.4	2.3889	2.8279	−15.12 (3.40)
	Cl1–Br2	2.2301	372.6
	Br3–F4	1.7856	639.1
T17	N1–H2	1.0128	3492.0	2.4390	3.0592	−12.87 (3.08)
	Cl1–Br2	2.2158	381.5
	Cl3–Br4	2.1558	439.1
T18	N1–H2	1.0128	3492.2	2.4504	3.1286	−12.33 (3.15)
	Cl1–Br2	2.2123	384.2
	Br3–Br4	2.2924	327.9
T19	N1–H2	1.0128	3492.4	2.5067	2.9496	−11.45 (3.20)
	Br1–Br2	2.3416	286.3
	Cl3–F4	1.6620	731.0
T20	N1–H2	1.0127	3493.6	2.5536	3.2398	−9.78 (2.81)
	Br1–Br2	2.3330	292.3
	Cl3–Cl4	2.0092	551.8
T21	N1–H2	1.0127	3494.0	2.5646	3.2973	−9.46 (2.88)
	Br1–Br2	2.3309	293.8
	Cl3–Br4	2.1464	446.5
T22	N1–H2	1.0129	3490.9	2.4627	2.9256	−13.59 (4.06)
	Br1–Br2	2.3520	280.3
	Br3–F4	1.7900	627.1
T23	N1–H2	1.0128	3492.5	2.5122	3.1616	−11.28 (3.61)
	Br1–Br2	2.3413	286.5
	Cl3–Br4	2.1587	433.7
T24	N1–H2	1.0127	3493.0	2.5267	3.2313	−10.77 (3.65)
	Br1–Br2	2.3383	288.4
	Br3–Br4	2.2949	324.3

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Compared to the monomers in Table S1,† with the non-CP and CP optimizations, the bond lengths for the electron donors X1X2 in dimers D1–12 and D19–24 are contracted while those in dimers D13–18 are elongated (Tables 1 and S2†), their stretching vibrational frequencies decrease or increase a few. Obviously, the Cl or Br atom in ClBr acting as the electron donor brings different effect on the X1–X2 bond length. The bond lengths for the electron acceptors X3Y in all the dimers are elongated which are accompanied by the decreased vibrational frequencies, indicating that the X3–Y bonds in these complexes are weakened and red-shifted. In both cases of non-CP and CP optimizations, the X2⋯X3 binding distances (d) are shorter than the sums of the van der Waals radii of the atoms involved in the halogen bonds. Here, the van der Waals radii values of 1.80 and 1.95 Å for Cl and Br atoms are used, respectively.⁸⁹ Compared to non-CP optimizations, CP optimizations have a little effect on the bond lengths (R) and the vibrational stretching frequencies (v), but they strongly affect the binding distances (d) and interaction energies ΔE_int. The ΔE_int,CP for dimers D1–24 with CP optimizations are weaker than the ΔE_int with non-CP method (<1.70 kcal mol⁻¹), and the BSSE correction energies range from 0.39 to 1.70 kcal mol⁻¹. The results reveal that it is indispensable to consider the BSSE correction for the dimers. Thus, the geometries obtained with CP method will be used for all discussion in the following sections.

For dimers D1–3, D4–6, D7–9, D10–12, D13–15, D16–18, D19–21 and D22–24, their interaction energies have the orders: D1 > D2 > D3, D4 > D5 > D6, D7 > D8 > D9, D10 > D11 > D12, D13 > D14 > D15, D16 > D17 > D18, D19 > D20 > D21 and D22 > D23 > D24, opposite to the orders of the corresponding binding distances (d) shown in Fig. 1 but consistent with the electronegativity order of Y atom: F > Cl > Br. It is in agreement with the fact that the strength of halogen bond can be measured via the binding distance, that is, the shorter the binding distance, the stronger the halogen bond.^90–93 In the previous studies, it demonstrates that the strength of halogen bond has close relationship with the electronegativity of the halogen atoms, because the electronegativity of halogen atom can affect the electron-accepting or electron-donating abilities of dihalogen molecules.^74,88 The stronger electronegativity of Y atom in X3Y molecule leads to the stronger electron-accepting ability of the σ-hole of X3 atom, enabling X3 atom to form stronger halogen bond.

Fig. 1 The relationships between the interaction energy ΔE_int,CP and the binding distance (d); and between the electron density (ρ) on the X2⋯X3 halogen bond and the binding distance (d) in dimers D1–24.

With respect to trimers T1–24, in both cases of the non-CP and CP optimizations, all the X1–X2 and X3–Y bond lengths are elongated accompanied by the decreased vibrational frequencies (Tables 2 and S4†), so they are weakened and red-shifted. The changes of X1–X2 bonds in trimers T1–24 are different from those in dimers D1–24. The reason should be ascribed to the fact that X1X2 simultaneously acts as an electron donor to X3Y and as an electron acceptor to NH₃ in the trimer while it acts only as an electron donor to X3Y in the dimer. The elongation of X3–Y bond length in the trimer is larger than that in the dimer, implying that there exists the cooperativity in the trimer. Addition of NH₃ molecule to the dimer leads to the interaction of N atom of NH₃ with X1 atom of the halogen-bonded dimer, forming a V-shaped structure connected by N⋯X1 and X2⋯X3 halogen-boned interactions. The BSSE correction energies are in the range from 1.04 to 4.06 kcal mol⁻¹ (Table 2), so it is important to take the BSSE correction into account. All discussion was based on the calculation results obtained with CP method.

The interaction energies of T1–3, T4–6, T7–9, T10–12, T13–15, T16–18, T19–21 and T22–24 have the orders: T1 > T2 > T3, T4 > T5 > T6, T7 > T8 > T9, T10 > T11 > T12, T13 > T14 > T15, T16 > T17 > T18, T19 > T20 > T21 and T22 > T23 > T24, which are contrary to the orders of the binding distances (d₁, d₂) shown in Fig. 2 but agree with the electronegativity order of Y atom: F > Cl > Br. It can be seen that the shorter N⋯X1 and X2⋯X3 binding distances lead to the stronger interactions. In each trimer, there are two halogen bonds, and it can be seen from Table 2 that the N⋯X1 binding distance is shorter than X2⋯X3 binding distance. It is in accord with the fact that the N⋯X1 interaction is stronger than the X2⋯X3 interaction, which can be derived from the comparison of the interaction energies of H₃N⋯X1X2 and X1X2⋯X3Y (Tables 1, S2 and S3†). The formation of N⋯X1 halogen bond by adding NH₃ molecule to the X1X2⋯X3Y dimer causes shorter N⋯X1 and X2⋯X3 binding distances in the trimer, meaning both the N⋯X1 and X2⋯X3 interactions are strengthened by the cooperativity of the two halogen bonds.

Fig. 2 The relationships between the interaction energy ΔE_int,CP and the binding distances (d₁, d₂); and between the electron densities on the N⋯X1 (ρ₁) and X2⋯X3 (ρ₂) halogen bonds and the binding distances (d₁, d₂) in trimers T1–24.

To assess the cooperativity between H₃N⋯X1X2 and X1X2⋯X3Y halogen-boned interactions in trimers T1–24, the pair interactions and pairwise non-additive contributions to ΔE_int,CP were employed. Meanwhile, a cooperativity factor B_d defined by B_d = Δd_T/Δd_D was introduced, where Δd_D is the difference between the sum of the atomic van der Waals radii involved in the N⋯X1 (or X2⋯X3) interaction in the dimer and the corresponding binding distance d (Table S5†), and Δd_T is the difference between the sum of the atomic van der Waals radii involved in the N⋯X1 (or X2⋯X3) interaction in the trimer and the corresponding binding distance d₁ or d₂ (Table S6†). As outlined in Table 3, all the pair interaction energies (ΔE_ab, ΔE_ac, E_bc) for trimers T1–24 are negative, suggesting that all the H₃N⋯X1X2 and X1X2⋯X3Y complexes are attractive in contributing to the stability of the trimers. The negative E_non-add suggests that ∑E_ij is weaker than ΔE_int,CP, so it can be concluded that the cooperativity between the pair interactions exists and results in a stronger trimer. These results further confirm that the H₃N, X1X2, X3Y (X1, X2, X3 = Cl, Br and Y = F, Cl, Br) molecules form trimeric complexes via two cooperative XBs. Both the cooperativity factors (B_d1 and B_d2) are larger than 1.000, indicating that the N⋯X1 (or X2⋯X3) halogen bonds in dimers D25–28 (or D1–24) are enhanced due to the addition of X3Y (or NH₃) molecule. Thereby, the combination of H₃N⋯X1X2 and X1X2⋯X3Y interactions will lead to a stronger trimeric complexes because of their cooperativity. Indeed, the trimer with a stronger interaction energy than the sum of the interaction energies (ΔE_sum) of H₃N⋯X1X2 and X1X2⋯X3Y dimers further proves the existence of cooperativity.

Table 3 Pair interactions (ΔE_ab, ΔE_ac, E_bc) and pairwise non-additive contributions (E_non-add) to ΔE_int,CP, and cooperativity factors (B_d1, B_d2) for trimers T1–24, the sum of total interaction energies (ΔE_sum) for H₃N⋯X1X2 and X1X2⋯X3Y halogen-bonded complexes in the trimer^a

Complex	ΔEab	ΔEbc	ΔEac	∑Eij	ΔEint,CP	Enon-add	ΔEsum	Bd1	Bd2
a Enon-add = ΔEint,CP − ∑Eij, ∑Eij = ΔEab + ΔEbc + ΔEac, and ΔEab, ΔEbc, and ΔEac are calculated at the geometry of each pair in the corresponding optimized trimer, ∑Eij is the sum of their interaction energy values. The subscripts (a, b and c) represent NH3, X1X2 and X3Y (X1, X2, X3 = Cl, Br and Y = F, Cl, Br) molecules, respectively. ΔEsum is the sum of the interaction energies of H3N⋯X1X2 and X1X2⋯X3Y dimers with CP method taken from Tables S3 and 1.
T1	−5.30	−2.15	−0.28	−7.73	−8.51	−0.78	−7.13	1.178	1.209
T2	−5.25	−1.62	−0.15	−7.02	−7.26	−0.24	−6.57	1.093	1.251
T3	−5.23	−1.54	−0.10	−6.87	−7.00	−0.13	−6.49	1.074	1.257
T4	−5.34	−2.98	−0.40	−8.72	−10.11	−1.39	−8.00	1.272	1.180
T5	−5.30	−2.13	−0.26	−7.69	−8.36	−0.67	−7.12	1.164	1.232
T6	−5.29	−1.98	−0.21	−7.48	−7.96	−0.48	−6.96	1.135	1.246
T7	−3.96	−2.46	−0.24	−6.66	−7.49	−0.83	−6.33	1.197	1.138
T8	−4.00	−1.75	−0.13	−5.88	−6.22	−0.34	−5.64	1.101	1.159
T9	−4.00	−1.68	−0.07	−5.75	−5.98	−0.23	−5.56	1.085	1.176
T10	−3.92	−3.57	−0.35	−7.84	−9.21	−1.37	−7.43	1.294	1.114
T11	−3.99	−2.41	−0.23	−6.63	−7.36	−0.73	−6.31	1.179	1.157
T12	−4.00	−2.22	−0.18	−6.40	−6.97	−0.57	−6.12	1.152	1.164
T13	−9.55	−2.43	−0.27	−12.25	−13.08	−0.83	−10.96	1.105	1.275
T14	−9.39	−1.81	−0.14	−11.34	−11.39	−0.05	−10.31	1.059	1.360
T15	−9.33	−1.72	−0.08	−11.13	−11.02	0.11	−10.21	1.048	1.376
T16	−9.72	−3.38	−0.38	−13.48	−15.12	−1.64	−11.93	1.152	1.224
T17	−9.54	−2.40	−0.25	−12.19	−12.87	−0.68	−10.96	1.098	1.315
T18	−9.80	−2.07	−0.19	−12.06	−12.33	−0.27	−10.77	1.085	1.348
T19	−7.49	−2.71	−0.24	−10.44	−11.45	−1.01	−9.62	1.123	1.204
T20	−7.43	−1.94	−0.12	−9.49	−9.78	−0.29	−8.87	1.068	1.254
T21	−7.41	−1.85	−0.07	−9.33	−9.46	−0.13	−8.77	1.054	1.271
T22	−7.53	−3.94	−0.34	−11.81	−13.59	−1.78	−10.82	1.176	1.154
T23	−7.50	−2.66	−0.22	−10.38	−11.28	−0.90	−9.62	1.117	1.231
T24	−7.48	−2.44	−0.17	−10.09	−10.77	−0.68	−9.41	1.100	1.247

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3.3 Quantum theory of atoms in molecules (QTAIM) analysis

Bader's quantum theory of atoms in molecules (QTAIM) has been widely applied to analyze the topological properties of halogen bonds.^82,94,95 To understand the nature of intermolecular interactions in dimers D1–28 and trimers T1–24, QTAIM analysis was conducted based on the optimized geometries at the MP2/aug-cc-pVTZ level. As shown in Fig. 3, the contour graphs of the Laplacian (∇²ρ) for trimers T1–24 were plotted to reflect the formation mechanisms of these halogen-bonded trimers. The existence of bond critical point (BCP) between the interacting molecules indicates the formation of halogen-bonded intermolecular interaction. For the H₃N⋯X1X2⋯X3Y trimer, the N atom of NH₃ possesses an electron-rich (e_r) region, while X1 atom possesses an electron-deficient (e_d) region along the X1–X2 bond axis. Thus, they can interact with each other to form N⋯X1 halogen bond. The X2 atom possesses an e_r region in the direction perpendicular to the X1–X2 bond axis, while X3 possesses an e_d region along the X3–Y bond axis, so they can interact with each other to form X2⋯X3 halogen bond. As a result, trimers T1–24 form through two halogen bonds, agreeing with the aforementioned MEP analysis.

Fig. 3 Contour graphs of the Laplacian (∇²ρ) of the electron density for trimers T1–24. Blue points are the BCPs. Brown lines correspond to the bond paths. e_r and e_d denote the electron-rich and electron-deficient regions, respectively.

The electron density (ρ) and its Laplacian (∇²ρ) at the BCPs of dimers D1–28 and trimers T1–24 are listed in Tables S7† and 4, respectively. It can be seen that the ρ and ∇²ρ values are in the ranges of 0.0080–0.0540 a.u. and 0.0331–0.1183 a.u., respectively. These values are comparable to the corresponding intervals for the hydrogen bond (i.e., 0.002–0.035 a.u. for ρ and 0.024–0.139 a.u. for ∇²ρ (ref. 64 and 96)). The ρ value can be used to estimate the XB strength, the larger the ρ value at the BCP of XB, the stronger the interaction energy.^21,68 It can be clearly seen from Fig. 1 and 2 that the larger ρ value corresponds to the stronger interaction energy for dimers D1–24 and trimers T1–24 with a smaller binding distance. The ρ(N⋯X1) values for dimers D25–28 are larger than the ρ(X2⋯X3) values for dimers D1–24, so dimers D25–28 are stronger than dimers D1–24 in interaction energy (Tables 1, S2 and S3†). For the H₃N⋯X1X2⋯X3Y trimer, the ρ(N⋯X1) and ρ(X2⋯X3) values become larger than the corresponding ρ values for dimers D1–28, which also confirm the cooperativity between the N⋯X1 and X2⋯X3 halogen bonds. The electronic energy density (H) at the BCP is the sum of the kinetic electron energy density (G) and the potential electron energy density (V), which can be used to characterize the intermolecular interaction. The sign of the electronic energy density (H) is indicative of the electrostatic dominant (H > 0) or covalent dominant (H < 0) interaction.^97,98 Thereby, we observed that the N1⋯Cl1 halogen bonds for T1, T4–6, the Br2⋯Br3 halogen bond for T10, the N1⋯Br2 halogen bonds for T13–18, the N1⋯Br1 halogen bonds for T19–24, the Cl1⋯Br3 halogen bond for T16 and the Br2⋯Br3 halogen bond for T22 are part covalent features due to their negative H values at these BCPs, while other N1⋯X1 and X2⋯X3 halogen bonds are of primarily electrostatic character due to the positive H values.

Table 4 Topological parameters at the BCPs for trimers T1–24 (all units are in a.u.)

Complex	Binding	ρ	∇^2ρ	V	G	H
T1	N1⋯Cl1	0.0362	0.1012	−0.0266	0.0260	−0.0007
	Cl2⋯Cl3	0.0201	0.0647	−0.0134	0.0148	0.0014
T2	N1⋯Cl1	0.0319	0.0937	−0.0227	0.0231	0.0004
	Cl2⋯Cl3	0.0114	0.0414	−0.0065	0.0084	0.0019
T3	N1⋯Cl1	0.0310	0.0921	−0.0219	0.0225	0.0006
	Cl2⋯Cl3	0.0102	0.0372	−0.0056	0.0074	0.0019
T4	N1⋯Cl1	0.0415	0.1095	−0.0318	0.0296	−0.0022
	Cl2⋯Br3	0.0255	0.0704	−0.0175	0.0175	0.0001
T5	N1⋯Cl1	0.0354	0.1000	−0.0259	0.0255	−0.0005
	Cl2⋯Br4	0.0156	0.0482	−0.0093	0.0107	0.0014
T6	N1⋯Cl1	0.0340	0.0975	−0.0246	0.0245	−0.0001
	Cl2⋯Br3	0.0136	0.0430	−0.0078	0.0093	0.0015
T7	N1⋯Cl1	0.0290	0.0867	−0.0199	0.0208	0.0009
	Br2⋯Cl3	0.0207	0.0567	−0.0129	0.0136	0.0006
T8	N1⋯Cl1	0.0258	0.0797	−0.0170	0.0185	0.0014
	Br2⋯Cl3	0.0115	0.0368	−0.0062	0.0077	0.0015
T9	N1⋯Cl1	0.0253	0.0786	−0.0166	0.0181	0.0015
	Br2⋯Cl3	0.0105	0.0339	−0.0055	0.0070	0.0015
T10	N1⋯Cl1	0.0327	0.0939	−0.0232	0.0233	0.0002
	Br2⋯Br3	0.0266	0.0613	−0.0171	0.0162	−0.0009
T11	N1⋯Cl1	0.0284	0.0854	−0.0193	0.0203	0.0010
	Br2⋯Br4	0.0162	0.0429	−0.0092	0.0099	0.0008
T12	N1⋯Cl1	0.0275	0.0834	−0.0185	0.0197	0.0012
	Br2⋯Br3	0.0142	0.0387	−0.0078	0.0087	0.0010
T13	N1⋯Br2	0.0493	0.1086	−0.0392	0.0332	−0.0060
	Cl1⋯Cl3	0.0235	0.0715	−0.0161	0.0170	0.0009
T14	N1⋯Br2	0.0450	0.1052	−0.0349	0.0306	−0.0043
	Cl1⋯Cl3	0.0133	0.0466	−0.0078	0.0097	0.0019
T15	N1⋯Br2	0.0440	0.1042	−0.0338	0.0299	−0.0039
	Cl1⋯Cl3	0.0118	0.0418	−0.0066	0.0085	0.0019
T16	N1⋯Br2	0.0540	0.1116	−0.0442	0.0361	−0.0081
	Cl1⋯Br3	0.0291	0.0758	−0.0203	0.0196	−0.0007
T17	N1⋯Br2	0.0485	0.1081	−0.0384	0.0327	−0.0057
	Cl1⋯Br4	0.0184	0.0543	−0.0113	0.0124	0.0012
T18	N1⋯Br2	0.0447	0.1183	−0.0401	0.0348	−0.0053
	Cl1⋯Br3	0.0150	0.0531	−0.0102	0.0117	0.0015
T19	N1⋯Br1	0.0425	0.1012	−0.0319	0.0286	−0.0033
	Br2⋯Cl3	0.0239	0.0618	−0.0152	0.0153	0.0001
T20	N1⋯Br1	0.0385	0.0965	−0.0281	0.0261	−0.0020
	Br2⋯Cl3	0.0133	0.0406	−0.0073	0.0087	0.0014
T21	N1⋯Br1	0.0376	0.0953	−0.0272	0.0255	−0.0017
	Br2⋯Cl3	0.0119	0.0372	−0.0064	0.0078	0.0015
T22	N1⋯Br1	0.0466	0.1055	−0.0361	0.0312	−0.0048
	Br2⋯Br3	0.0294	0.0645	−0.0191	0.0176	−0.0015
T23	N1⋯Br1	0.0420	0.1008	−0.0314	0.0283	−0.0031
	Br2⋯Br4	0.0187	0.0472	−0.0108	0.0113	0.0005
T24	N1⋯Br1	0.0407	0.0993	−0.0302	0.0275	−0.0027
	Br2⋯Br3	0.0165	0.0428	−0.0092	0.0099	0.0008

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3.4 Energy decomposition analysis (EDA)

Energy decomposition analysis (EDA) of the interaction energies for trimers T1–24 were carried out at the MP2/aug-cc-pVTZ level. The total interaction energy (ΔE_int,EDA) for these trimers are decomposed into five terms: electrostatic energy (E_elst), exchange energy (E_exch), polarization energy (E_pol), dispersion energy (E_disp) and repulsion energy (E_rep), and the data are summarized in Table 5. We found that the ΔE_int,EDA values are close to the ΔE_int,CP values, and there is a linear relationship between them with a correlation coefficient of 0.991, as shown in Fig. 4a. The E_elst, E_exch, E_pol and E_disp terms are attractive interactions contributing to the total EDA energies while the E_rep term is repulsive interaction. The relative contributions of the attractive interactions (E_elst, E_exch, E_pol and E_disp) to the total EDA energy are in the ranges of 22–28%, 46–50%, 12–19% and 8–15%, respectively. Evidently, the electrostatic and exchange energies are dominant driving forces in forming the halogen-bonded complexes. A linear relationship between E_elst and ΔE_int,EDA was found, which has a correlation coefficient of 0.994 (Fig. 4b), similar to the previous study.⁹⁹ Fig. 4c displays a linear relationship between E_rep and the sum of E_exch, E_pol and E_disp with a correlation coefficient of 0.999 and a slope of −1.269, which indicates that the three attractive terms (E_exch, E_pol and E_disp) and the repulsive E_rep balance each other in trimers T1–24. Therefore, we can see that the electrostatic term E_elst is the net contribution to the ΔE_int,EDA, so it is the dominant driving force to stabilize the halogen-bonded trimers.

Table 5 EDA analysis of the physical components of total interaction energy (ΔE_int,EDA, in kcal mol⁻¹) at the MP2/aug-cc-pVTZ//MP2/aug-cc-pVTZ level of theory for trimers T1–24 and the magnitudes of the attractive components^a

Complex	Eelst (%)	Eexch (%)	Epol (%)	Edisp (%)	Erep	ΔEint,EDA
a The total attractive components are the sum of Eelst + Eexch + Epol + Edisp, while the magnitude is the percentage of each component contributing to the total attractive components.
T1	−21.54 (24.7)	−42.14 (48.3)	−13.60 (15.6)	−9.99 (11.4)	77.89	−9.38
T2	−16.73 (25.1)	−32.27 (48.5)	−9.09 (13.6)	−8.51 (12.8)	58.78	−7.82
T3	−15.88 (25.1)	−30.75 (48.6)	−8.39 (13.3)	−8.28 (13.0)	55.83	−7.47
T4	−27.46 (24.3)	−54.29 (48.1)	−19.10 (16.9)	−11.95 (10.7)	101.54	−11.26
T5	−20.34 (24.7)	−39.95 (48.5)	−11.96 (14.5)	−10.09 (12.3)	73.28	−9.06
T6	−18.87 (24.7)	−37.12 (48.7)	−10.66 (14.0)	−9.64 (12.6)	67.76	−8.53
T7	−17.22 (22.9)	−37.07 (49.2)	−11.30 (15.0)	−9.70 (12.9)	67.51	−7.78
T8	−12.69 (23.1)	−27.21 (49.6)	−6.90 (12.6)	−8.10 (14.7)	48.56	−6.34
T9	−12.12 (23.1)	−26.16 (49.8)	−6.40 (12.2)	−7.90 (14.9)	46.53	−6.05
T10	−22.56 (22.8)	−48.37 (48.9)	−16.31 (16.5)	−11.62 (11.8)	89.31	−9.55
T11	−16.04 (22.9)	−34.74 (49.6)	−9.53 (13.6)	−9.74 (13.9)	62.57	−7.48
T12	−14.82 (22.9)	−32.26 (49.8)	−8.41 (13.0)	−9.31 (14.3)	57.79	−7.01
T13	−37.84 (27.1)	−65.61 (46.9)	−24.10 (17.2)	−12.23 (8.8)	125.03	−14.75
T14	−31.29 (27.7)	−53.31 (47.1)	−17.75 (15.7)	−10.76 (9.5)	100.57	−12.54
T15	−30.00 (27.7)	−51.19 (47.3)	−16.64 (15.4)	−10.50 (9.6)	96.33	−12.00
T16	−45.07 (26.7)	−78.93 (46.7)	−30.97 (18.3)	−13.88 (8.3)	151.63	−17.22
T17	−36.36 (27.1)	−63.15 (47.1)	−21.98 (16.4)	−12.47 (9.4)	119.64	−14.32
T18	−37.20 (27.0)	−65.18 (47.4)	−22.38 (16.3)	−12.81 (9.3)	123.57	−14.00
T19	−32.12 (25.6)	−60.26 (48.0)	−20.68 (16.5)	−12.36 (9.9)	113.10	−12.32
T20	−25.51 (26.3)	−46.96 (48.3)	−14.17 (14.6)	−10.51 (10.8)	86.90	−10.25
T21	−24.40 (26.3)	−45.03 (48.5)	−13.22 (14.2)	−10.25 (11.0)	83.08	−9.82
T22	−39.09 (25.4)	−73.53 (47.7)	−27.26 (17.7)	−14.15 (9.2)	139.39	−14.64
T23	−30.79 (25.8)	−57.69 (48.3)	−18.46 (15.5)	−12.48 (10.4)	107.50	−11.92
T24	−28.90 (25.8)	−54.23 (48.5)	−16.70 (14.9)	−12.00 (10.8)	100.60	−11.23

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Fig. 4 Correlations for (a) ΔE_int,CP versus ΔE_int,EDA; (b) ΔE_int,EDA versus E_elst; (c) E_rep versus (E_exch + E_pol + E_disp).

4. Conclusions

In the work, theoretical investigations of a series of V-shaped halogen-bonded trimers formed by NH₃, X1X2 and X3Y (X1, X2, X3 = Cl, Br; Y = F, Cl, Br) molecules have been carried out at the MP2/aug-cc-pVTZ level of theory without and with CP methods. Based on the MEP analysis, it is known that the N atom of NH₃ and the X2 atom of X1X2 in the direction perpendicular to the X1–X2 bond axis possess a negative electrostatic potential, while the X1 atom of X1X2 and the X3 atom of X3Y in the directions along their bond axes possess a positive electrostatic potential, so they can interact to form the V-shaped trimers connected by N⋯X1 and X2⋯X3 halogen bonds. The geometries of these trimers have some common features with the H₃N–XY–HF trimers (X, Y = F, Cl, Br) connected by N⋯X halogen bond and Y⋯H hydrogen bond which were investigated by Li and coworkers,⁵⁷ but the difference is that the cooperativity exists between two halogen bonds in our systems and between one halogen bond and one hydrogen bond in their systems. The strength of the halogen bond is closely associated with the binding distance as well as the electron density at the BCP of the halogen bond. The two N⋯X1 and X2⋯X3 halogen bonds cooperate with each other to form a stable trimer, and the N⋯X1 and X2⋯X3 halogen bond strengths are stronger than the corresponding N⋯X1 and X2⋯X3 halogen-bonded dimers. QTAIM analysis illustrates the nature of the halogen bonds at the BCPs. The electrostatic term is the main net contribution to the total interaction energy of each trimer in terms of EDA analysis. The halogen-bonded complexes studied in this work would provide valuable insights into the design of related systems.

Acknowledgements

The work was financially supported by the National Natural Science Foundation of China (Grant No. 21403097) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-45).

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Footnote

† Electronic supplementary information (ESI) available: The optimized geometries, structural parameters and stretching vibrational frequencies of the six monomers (NH₃, FCl, FBr, Cl₂, ClBr, Br₂), their MEPs; the optimized geometries of dimers D1–24 and D25–28 with CP methods, the geometrical parameters, stretching vibrational frequencies and interaction energies of dimers D1–24 and D25–28 obtained without CP (non-CP) and with CP methods; the optimized geometries of trimers T1–24 with CP methods, the geometrical parameters, stretching vibrational frequencies and interaction energies of trimers T1–24 obtained without CP (non-CP) method; topological properties for dimers D1–28. See DOI: 10.1039/c6ra21018j

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