Comparison of tetrel bonds and halogen bonds in complexes of DMSO with ZF₃X (Z = C and Si; X = halogen)

Abstract

A theoretical study of the complexes formed by dimethylsulfoxide (DMSO) with ZF₃X (Z = C and Si; X = halogen) has been performed at the MP2/aug-cc-pVTZ level. Three local minima were found on the potential surface of complex DMSO–ZF₃X, forming tetrel bonds and halogen bonds with O⋯Z and O⋯X contacts, respectively. The halogen-bonded complexes are more stable for CF₃X than for SiF₃X with an exception of CF₄, on the contrary, the tetrel-bonded complexes DMSO–SiF₃X are more stable than the analogues DMSO–CF₃X. The strength of the tetrel bonds in DMSO–CF₃X has a small dependence on the nature of the halogen atom, and DMSO–SiF₃X has an abnormal dependence on it. Surprisingly, the tetrel bond in DMSO–SiF₃X is stronger than that with an anion as the electron donor, exhibiting a partially covalent bond nature. A red shift was observed for the S=O stretch vibration in most complexes, particularly in the tetrel-bonded complexes of DMSO–SiF₃X. The Z–X stretch vibration exhibits a red shift in the tetrel bond but an irregular shift in the halogen bond.

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1. Introduction

The interaction between the atoms (Group 14) acting as Lewis acids and any entity with the ability to act as an electron donor has been found in the solid-state structure of Si(ONMe₂)₄ (ref. 1) and perhalocyclohexasilane compounds.² However, this interaction had not attracted much attention until Bauzá and coauthors named it tetrel bonding in 2013 and expected it might serve as a new possible molecular linker in the field of supramolecular chemistry.³ They pointed out that tetrel bonding is highly directional and it has comparable strength with hydrogen bonding.³ At the same time, Grabowski⁴ performed a systemic study on the complexes of ZH₄, ZFH₃ and ZF₄ (Z = C, Si, and Ge) molecules with HCN, LiCN, and Cl⁻, and thought that the formation of tetrel bonding is an incipient stage of the S_N2 reaction. Since then, the tetrel bonding interaction has been explored stepwisely.

The formation of tetrel bonding can be explained with the term “σ-hole” (a region with positive electrostatic potentials) on the covalent-bonded Group 14 atom proposed by Politzer and coauthors.⁵ The magnitude of the σ-hole on the Group 14 atom can be tuned through changing the atom of Group 14 or the remainder of the molecule, that is, it will be more positive in going from the light to the heavy (more polarizable) atoms in the Group 14 atom, and as the electron-withdrawing ability of the remainder of the molecule becomes larger.⁶ The interaction between the σ-hole on the Si atom and the lone pair on the N atom logically explains the Si–O–N angle contraction in XYZSi–O–N(CH₃)₂.⁷ The six cyclic silicon atoms in perhalocyclohexasilane Si₆X₁₂ (X = Cl or Br) form a planar hexagon with the two halide anions via the formation of the anion⋯Si tetrel bonding interactions,⁸ similarly the case for the complexes of Si₅Cl₁₀ with organocyanides due to the existence of N⋯Si interactions.⁹ The nature of both interactions in these complexes were then studied theoretically.^10,11 It was demonstrated that the Lewis acid⋯base interactions between Si₆H₁₂ and the carbonyl groups of amphiphilic invertible macromolecules is responsible for the stable composition of both molecules in solution.^12,13

The aqueous solutions of dimethylsulfoxide (DMSO) have been frequently studied both experimentally and theoretically^14–18 due to their unique biological and physicochemical properties. DMSO is an effective solvent not only for polar solutes but also for aromatic compounds due to the arrays of positive and negative sites in DMSO which give rise to a variety of simultaneous intermolecular electrostatic interactions.¹⁹ Recently, the interactions between DMSO and ionic liquids have also attracted much attention,^20–22 in which hydrogen bonding is a main driving force. In addition, DMSO can form halogen bonding, which can compete with hydrogen bonding,^23–25 with dihalogen molecules²⁶ and halobenzene²³ investigated with excess infrared spectroscopy and quantum chemical calculations. It has been demonstrated that some oxygen-containing molecules can act as an electron donor in tetrel bonds.^27–34 As a common solvent, little study is performed for tetrel bonding with DMSO as the electron donor. It is necessary to investigate the structures, properties, and nature of tetrel bonds involving DMSO.

In this paper, we study the complexes of DMSO and ZF₃X (Z = C and Si; X = halogen) with quantum chemical calculations. To the best of our knowledge, neither theoretical nor experimental data regarding the structural information of the interaction of DMSO with ZF₃X are available in the literature. This work presents a detailed examination of the stabilities, electronic structures, and vibrational frequencies of these complexes. Our aim is to predict and characterize the tetrel bond and to compare it with the halogen bond in the complexes consisted of molecules ZF₃X and DMSO.

2. Computational methods

The geometries of all complexes and monomers were optimized at the MP2/aug-cc-pVDZ level and the corresponding frequency calculations were also performed at the same level to confirm that all structures are minima with no imaginary frequency. To obtain reliable results, these structures were then re-optimized at the MP2/aug-cc-pVTZ level, which has usually been used to study the complexes with halogen bonds²⁴ and tetrel bonds.⁴ Interaction energy was computed as the difference between the energy of a complex and the energy sum of the isolated molecules. Basis-set superposition error (BSSE) was considered with the counterpoise method by Boys and Bernardi.³⁵ The absolute chemical shieldings have been evaluated within the GIAO approximation³⁶ at the WB97XD/aug-cc-pVTZ computational level. All calculations were carried out with the Gaussian 09 suite of programs.³⁷

Molecular electrostatic potentials (MEPs) on the 0.001 electrons Bohr⁻³ contour of electronic density were obtained at the MP2/aug-cc-pVTZ level with the wavefunction analysis-surface analysis suite (WFA-SAS) program.³⁸ Electron densities of complexes have been analyzed by employing the Atoms in Molecules (AIM) methodology³⁹ with the AIM2000 program.⁴⁰ Natural Bond Orbital (NBO) method⁴¹ has been used to obtain natural atomic charges and analyze charge–transfer interactions between occupied and virtual orbitals at the WB97XD/aug-cc-pVDZ level. In addition, energy decomposition analysis (EDA) was carried out to obtain a deep insight into the nature of the interactions using GAMESS program⁴² with the localized molecular orbital-energy decomposition analysis (LMOEDA) method⁴³ at the MP2/aug-cc-pVTZ level.

3. Results and discussion

3.1. MEP analyses

Fig. 1 shows the MEP maps of SiF₃Br, taken as an example of ZF₃X. As expected, four positive σ-holes are found on the extensions of Si–Br and Si–F bonds (shown in red), and the positive MEP is greater for the σ-hole on the extension of Si–Br bond than that of Si–F bond. Furthermore, a positive σ-hole is also found on the outer side of Br atom (shown in yellow, Fig. 1). Consequently, it is expected that a SiF₃Br molecule can simultaneously combine with five DMSO molecules. In this work, we focus on the study of tetrel and halogen bonds between DMSO and the σ-holes on the extension of Si–Br bond and the outer side of the Br atom, respectively.

Fig. 1 Molecular electrostatic potentials of SiF₃Br. Color ranges, in kJ mol⁻¹, are: red, greater than 105; yellow, between 105 and 52; green, between 52 and 0; and blue, less than 0.

The most positive MEPs (V_max) of the σ-holes on both the extension of Z–X bond and the outer side of the X atom in ZF₃X are collected in Table 1. No σ-hole is found on the F atom. For a given X, the V_max value of the σ-hole on the extension of Si–X is larger than that of C–X due to the lower electronegativity and greater polarizability of Si atom than that of C. Furthermore, the value of this V_max is also related to the X atom, exhibiting a growing tendency for the lighter X atom. In addition, the V_max on the X atom is also dependent on the Z atom, and it becomes more positive in CF₃X than in SiF₃X owing to the larger electronegativity of the C atom. The V_max on the X atom is more positive than that on the side of C atom in CF₃X but less positive than that on the side of Si atom in SiF₃X. These values obtained at the MP2/aug-cc-pVTZ level have a consistent variation with those reported at the M06-2X/6-311G(d) level,⁶ but the values in the latter case are greater than those in the former.

Table 1 The most positive MEPs (V_max, kJ mol⁻¹) of the σ-holes on both the extension of Z–X bond and the outer side of the X atom in ZF₃X

Molecules	Z=	X=	Vmax,Z	Vmax,X
CF3F	C	F	88.40	—
CF3Cl	C	Cl	71.29	88.86
CF3Br	C	Br	70.13	106.35
CF3I	C	I	60.47	129.95
SiF3F	Si	F	191.03	—
SiF3Cl	Si	Cl	168.85	57.02
SiF3Br	Si	Br	162.81	77.27
SiF3I	Si	I	151.36	101.97

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3.2. Structure and energy analyses

Fig. 2 shows the optimized structures of tetrel-bonded (ZX–TB) and halogen-bonded (ZX–XB) complexes. Two types of halogen-bonded structures are obtained, represented with ZX–XB-I and ZX–XB-II, respectively. The direction of X atom attacking to the O atom of DMSO is different in ZX–XB-I and ZX–XB-II. In addition, one X⋯H hydrogen bond is present in ZX–XB-I and two X⋯H hydrogen bonds are found in ZX–XB-II. The halogen-bonded complexes of CF₄ and SiF₄ are not obtained due to the absence of σ-hole on the F atom. The geometrical and energetic parameters are given in Table 2. In order to figure out the deformation of ZF₃X, we define the angle ∠F–Z–X as α. A comparison for three types of complexes indicates that a large deformation occurs for the SiF₃X subunit in tetrel-bonded complexes SiX–TB and a very small one for the ZF₃X molecule in other complexes. The ∠F–Si–X amounts to about 100° in SiX–TB and is equal to about 110° in other complexes. The angle in the former complex is smaller than that in the isolated molecule (110–111°), and the latter one is close to that in the monomer. Thus in order to compare the binding strength of three type interactions, we compute the interaction energy in the following section using the frozen geometries of the monomer ZF₃X in the complexes to take into account of the effect of structural deformation.

Fig. 2 Schemes of three types of complexes.

Table 2 Interaction energies (ΔE, kJ mol⁻¹), binding distances (R, Å), angels (α, deg), and changes of bond lengths (Δr, Å) in the complexes

Complexes	ΔEpVDZ	ΔEpVTZ	RTB/RXB	α1/α2	ΔrS=O	ΔrZ–X
CF–TB	−6.59	−8.10	3.259	109.4	0.001	0.006
CCl–TB	−5.98	−7.68	3.315	110.2	0.001	0.009
CBr–TB	−5.99	−7.79	3.302	110.2	0.001	0.009
CI–TB	−5.48	−7.31	3.326	110.5	0.001	0.008
SiF–TB	−159.77	−129.30	2.001	96.8	0.040	0.044
SiCl–TB	−160.53	−137.89	1.985	96.4	0.042	0.089
SiBr–TB	−164.95	−146.60	1.966	96.0	0.044	0.104
SiI–TB	−170.24	−157.11	1.946	95.3	0.046	0.122
CCl–XB-I	−13.69	−14.21	2.893	110.6	0.004	−0.006
CBr–XB-I	−19.70	−19.47	2.829	110.8	0.007	−0.004
CI–XB-I	−29.77	−28.53	2.808	111.2	0.013	0.002
SiBr–XB-I	−13.51	−12.88	3.088	110.6	0.004	−0.002
CCl–XB-II	−14.60	−15.14	2.861	110.9	0.004	−0.005
CBr–XB-II	−20.85	−20.72	2.796	111.0	0.007	−0.002
CI–XB-II	−30.83	−30.02	2.777	111.4	0.012	0.005
SiCl–XB-II	−7.92	−9.58	3.105	111.0	0.002	−0.003
SiBr–XB-II	−14.12	−13.14	3.045	111.0	0.004	−0.001
SiI–XB-II	−21.54	−19.58	2.989	111.5	0.007	0.004

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The interaction energies of tetrel and halogen bonds are obtained at both MP2/aug-cc-pVDZ and MP2/aug-cc-pVTZ levels. For the tetrel bond, the interaction energy at the MP2/aug-cc-pVTZ level is a little larger than that at the MP2/aug-cc-pVDZ level for the complexes CX–TB. On the contrary for SiX–TB, it is larger at the MP2/aug-cc-pVDZ level than at the MP2/aug-cc-pVTZ level. The possible reason is that a larger deformation of SiF₃X is found at the former level. For the halogen bond, the interaction energies at both levels are nearly the same. Therefore, the basis sets used on the interaction energy is slightly different for the tetrel bond interactions. The following discussion on the interaction energy is based on the MP2/aug-cc-pVTZ results.

It is obvious from Table 2 that the interaction energy of SiX–TB is far more negative than that of CX–TB, indicating that SiF₃X forms a very stronger tetrel bond with DMSO than CF₃X. This result is in a line with the variation of the positive MEP on the σ-hole of the Z atom, showing the role of electrostatic interaction in the formation of tetrel bond. However, a comparative analysis shows that the ratio of the interaction energy between SiX–TB and CX–TB is much larger than that of the positive MEP on the σ-hole of the related Z atom between SiF₃X and CF₃X. We attribute this to the structural deformation of SiF₃X. The stronger tetrel bond corresponds to the larger deformation of SiF₃X, characterized with a smaller angle ∠F–Si–X.

The positive MEP on the σ-hole of the C atom in CF₃X shows an obvious decrease as the electronegativity of X becomes smaller, but the interaction energy of the related tetrel bond does not exhibit a remarkable reduction. We attribute this to another interaction present in the complexes CX–TB. In view of the conformation of CX–TB, we anticipate it may be an organic fluorine hydrogen bond C–F⋯H–C interaction, which is shown with a green disk between the H atom of DMSO and the F atom of CF₃X (Fig. 3). The F⋯H distance is 2.840, 2.792, 2.771 and 2.729 Å for X = F, Cl, Br and I, respectively, showing an enhancing order of the F⋯H interaction. The C–F⋯H–C interaction and the tetrel bond complement each other, which results in a small change of the interaction energy in CX–TB as X is varied.

Fig. 3 Gradient isosurfaces (s = 0.1 au) in the complexes of CF₃X (X = F, Cl, Br, and I). Green and orange areas correspond to weak attractive and weak repulsion interactions, respectively.

The interaction energies of tetrel bonds are −129.30, −137.89, −146.60 and −157.11 kJ mol⁻¹ in SiX–TB (X = F, Cl, Br, and I, respectively). Clearly, with the increase of X atomic mass, the interaction energy of tetrel bond increases in SiX–TB, inconsistent with the positive MEP on the σ-hole of the Si atom in SiF₃X. This indicates that the structural deformation of the monomer and other contributions including a F⋯C interaction (see the AIM analysis) are also very important in the formation of the O⋯Si tetrel bond although the electrostatic interaction is a main driving force (see the section of energy decomposition). Such abnormal dependence on the nature of halogen atom was also found in pnicogen-bonded complexes of silylene and YH₂X (Y = P, As, and Sb; X = F, Cl, Br, and I).⁴⁴ Surprisingly, the interaction energy of tetrel bond in SiX–TB is more negative than that in SiF₄⋯Cl⁻ [4], where an anion usually acts as a strong electron donor. In contrast, the interaction energy in CX–TB is less negative than that in CF₄⋯Cl⁻.⁴ It is known that DMSO has a large dipole moment (>4 Debye). The electronic distribution of Si in SiF₃X is more dispersive than that of C in CF₃X. Consequently, DMSO causes a greater polarization on the Si atom than on the C analogue and the former forms a stronger tetrel bond with DMSO. In addition, we think that an S⋯Si tetrel bond may be possible between DMSO and SiF₃X (Fig. S1†). However, this S⋯Si interaction is weaker than the O⋯Si tetrel bond due to the small negative MEP on the S atom of DMSO.²⁶ Thus the S⋯Si tetrel-bonded complexes are not studied here.

From Table 2, the halogen bond becomes stronger in ZX–XB-I/-II as Z is smaller and X is larger, consistent with the positive MEP on the σ-hole of the X atom in ZF₃X. The structure of SiCl–XB-I is not obtained, and it is optimized to be the S⋯Si bonded structure (Fig. S1†). The structure of SiI–XB-I can be obtained at the MP2/aug-cc-pVDZ level, and it is changed to be SiI–XB-II at the MP2/aug-cc-pVTZ level. This shows that the complex ZX–XB-II is more stable than ZX–XB-I, evidenced with the larger interaction energy in the former. It is obvious from Table 2 that the interaction energy of halogen bond in the CF₃X system is larger than that of tetrel bond, while in the SiF₃X system the former interaction is much weaker than the latter. As a result, DMSO is favorable to bind with CF₃X via a halogen bond with an exception of CF₄, for which only a tetrel bond is formed, while it prefers forming a strong tetrel bond with SiF₃X. A similar conclusion was found in the HCN counterparts.⁶ However, HCN forms a much weaker tetrel bond with SiF₃X than DMSO, due to the greater polarization ability of DMSO than HCN.

From Table 1, the O⋯Z distance shows a consistent change with the interaction energy of tetrel bond, that is, the larger interaction energy corresponds to a shorter O⋯Z distance. Furthermore, the linear relationship is better for the O⋯Si distance than the O⋯C distance with the interaction energy (Fig. 4). One can see that the interaction energy is more susceptible to the O⋯Si distance. The O⋯Si distance is about 2.0 Å, which is much shorter than the sum of van der Waals radii of both atoms (∼3.6 Å) but is slightly longer than the length of Si–O bond (∼1.6 Å). Accordingly, the O⋯Si tetrel bond exhibits a nature of partially covalent interaction, like the bond in Lewis acid–base complexes HCN–BF₃ and HCN–SO₃.⁴⁵ Similarly, the stronger halogen bond is related with a shorter O⋯X distance.

Fig. 4 Interaction energy versus binding distance in the tetrel-bonded complexes of CF₃X (up) and SiF₃X (down).

The S=O bond is elongated in ZX–TB and ZX–XB as well as that in hydrogen-bonded complexes of DMSO–H₂O⁴⁶ and halogen-bonded complexes of DMSO–dihalogen.²⁶ The elongation of S=O bond is very small (0.001 Å) in CX–TB due to the weak tetrel bond, while this double bond suffers a large elongation in the strong tetrel-bonded complex of SiX–TB as well as in the strong halogen-bonded ones. Upon complexation of a tetrel bond, the Z–X bond is extended. The extension of Si–X bond is much larger in SiX–TB than that of C–X bond in CX–TB. The extension of C–X bond displays an irregular variation with the different X and the magnitude of the tetrel bond; in remarkable contrast, the extension of Si–X bond shows an increasing tendency with the enhancement of tetrel bond. The formation of halogen bond causes an elongation or a contraction of Z–X bond. In addition, the change of Z–X bond in the halogen-bonded complexes is smaller than that in the tetrel-bonded ones.

3.3. Stretching frequency and chemical shift analyses

Infrared spectroscopy (IR) and nuclear magnetic resonance (NMR) are two important methods for detecting hydrogen-bonded clusters, thus we performed an analysis for the S=O and Z–X stretch vibration frequency and the chemical shielding of the F and T atoms in the tetrel- and halogen-bonded complexes. Their variations in the complexes with regard to the isolated monomers are listed in Table 3. The S=O stretch vibration exhibits a red shift in most tetrel-bonded complexes, consistent with the elongation of the S=O bond due to the electrostatic attractive interaction between the O atom of DMSO and the Z atom of ZF₃X. However, the S=O stretch vibration displays a small blue shift in CBr–TB and CI–TB, inconsistent with the bond elongation. This inconsistence is probably caused by the coupling of the S=O stretch vibration with other vibration modes including the Z–X stretch vibration. The strong tetrel bond in SiX–TB results in a larger red shift (−132 to −136 cm⁻¹) of the S=O stretch vibration than does the weak tetrel bond in CX–TB. The red shift of S=O stretch vibration in SiX–TB is bigger than that in the hydrogen-bonded complex of DMSO and water⁴⁶ as well as that in the halogen-bonded complex of DMSO and dihalogen molecules.²⁶ The halogen bond in ZX–XB also gives rise to a red shift of the S=O stretch vibration, which is smaller than that in the halogen-bonded complex of DMSO and dihalogen molecules.²⁶ According to the magnitude of the red shift of the S=O stretch vibration, it is expected that the halogen-bonded complex could be detected with matrix isolation infrared spectroscopy, and the tetrel-bonded complex SiX–TB with conventional infrared spectroscopy, while the tetrel-bonded complex CX–TB may not be.

Table 3 Frequency shifts of S=O and Z–X stretch vibrations (Δv, cm⁻¹) and variations of chemical shieldings (δ, ppm) in the complexes^a

Complexes	ΔvS=O	ΔvZ–X	δZ/δX	δF
a Note: δZ/δX is δZ in the TB system and δX in the XB system.
CF–TB	−3	−33	−0.46	−1.97
CCl–TB	−5	−18	−0.84	−3.38
CBr–TB	7	−28	0.01	−4.02
CI–TB	2	−23	0.02	−4.96
SiF–TB	−132	−164	19.01	−26.08
SiCl–TB	−133	−321	30.06	−32.96
SiBr–TB	−134	−28	32.83	−34.96
SiI–TB	−136	−9	38.23	−37.35
CCl–XB-I	−14	10	−14.54	3.16
CBr–XB-I	−24	15	−23.06	6.74
CI–XB-I	−40	20	−9.10	12.41
SiBr–XB-I	−13	0	−27.86	0.27
CCl–XB-II	−12	−2	−13.79	3.20
CBr–XB-II	−21	−6	−16.13	7.15
CI–XB-II	−35	−9	−9.90	13.54
SiCl–XB-II	−4	−1	−19.47	0.05
SiBr–XB-II	−12	−1	−44.70	0.35
SiI–XB-II	−21	−1	−10.57	1.90

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The Z–X stretch vibration exhibits a red shift in the tetrel-bonded complexes, consistent with the stretching of the Z–X bond. The elongation of Z–X bond is large in SiX–TB, but the red shift of Z–X stretch vibration is much small in SiBr–TB and SiI–TB due to the heavier mass of Br and I atoms. In the halogen bond, the Z–X stretch vibration displays a small blue shift in CX–XB-I, no shift in SiBr–XB-I and a small red shift in ZX–XB-II. A blue-shifting halogen bond has been reported in the complexes of CF₃X with NH₃, H₂O, and anions, where the authors mentioned that the blue-shifting halogen bond is much more ubiquitous in the halogen-bonded complexes than the blue-shifting hydrogen bond in the hydrogen-bonded complexes.^47,48

The formation of CX–TB makes the chemical shielding of the C atom in CF₃X nearly no shift, while the strong tetrel bond in SiX–TB shifts the signal of the silicon atom involved to the higher field, such as up to 38.23 ppm in SiI–TB. This shift is reverse to that of the proton in hydrogen bonds.²⁴ However, the formation of a tetrel bond results in a shift of the F atom to the lower field in ZX–TB. This lower shift is small in CX–TB but large in SiX–TB. These lower shifts of the F atoms in the tetrel-bonded complexes can be observed experimentally. The signal of the F atom involved in the halogen bond shows a reverse shift to that in the tetrel bond. The different halogen atom exhibits a shift to the lower field in all halogen bonds.

3.4. Natural bond orbital analyses

The tetrel and halogen bonds have been analyzed with orbital interaction and charge transfer (Table 4). Two main orbital interactions and are present in the tetrel bond, and only orbital interaction is found in the halogen bond. The orbital interaction is estimated with second-order perturbation energy (E). The sum of E of three orbital interactions (denoted as E₂) is listed in Table 4. It is evident from Table 4 that the orbital interaction is stronger than the single in the tetrel bond. Both types of orbital interactions are weak in CX–TB but very strong in SiX–TB. In CX–TB, the energy sum of three orbital interactions is comparable with that of , but the former energy is much larger than the latter in SiX–TB. The orbital interaction is responsible for the elongation of Z–X bond and its red shift in the tetrel bond. In beryllium-bonded complexes of BeX₂ (X = H, F, Cl, and OH) with different Lewis bases, there is an orbital interaction from the lone pairs of the Lewis base toward the empty p orbital of Be, resulting in the deformation of the BeX₂ molecule.⁴⁹ However, a similar orbital interaction is not found in ZX–TB. The large deformation of the SiF₃X molecule in SiX–TB is attributed to the formation of a weak O–Si bond, which can be characterized with Wiberg bond index (WBI). For example, WBI of the O–Si bond is 0.299 in SiI–TB and is about a third of that of the Si–I bond (0.868). With the increase of the WBI between O and Si in SiX–TB, the deformation of the SiF₃X molecule thus becomes larger. On the other hand, in the case of the halogen-bonded complexes, the orbital interaction increases with the size of the halogen atom, again in agreement with the tendency observed for the total interaction energy.

Table 4 Charge transfer (CT, e), second-order perturbation energies (E, kJ mol⁻¹), and Wiberg bond index (WBI) between two monomers in the complexes at the WB97XD/aug-cc-pVDZ level^a

Complexes	CT	E1	E2	WBI
a Note: CT is the sum of charge on all atoms of DMSO in the complexes. E1 corresponds to the orbital interactions of in both tetrel bond and halogen bond. E2 is the sum of three orbital interactions in the tetrel bond.
CF–TB	0.001	1.29	0.75	0.003
CCl–TB	−0.001	1.00	0.79	0.003
CBr–TB	−0.001	1.00	0.96	0.003
CI–TB	−0.002	0.88	1.00	0.003
SiF–TB	0.133	42.13	64.54	0.253
SiCl–TB	0.151	41.51	70.22	0.277
SiBr–TB	0.158	145.13	366.79	0.288
SiI–TB	0.163	148.81	386.52	0.299
CCl–XB-I	0.009	10.57	—	0.014
CBr–XB-I	0.020	20.61	—	0.028
CI–XB-I	0.038	54.26	—	0.053
SiBr–XB-I	0.005	5.77	—	0.011
CCl–XB-II	0.009	7.44	—	0.016
CBr–XB-II	0.021	18.64	—	0.033
CI–XB-II	0.041	39.79	—	0.061
SiCl–XB-II	0.001	2.22	—	0.007
SiBr–XB-II	0.003	5.02	—	0.013
SiI–XB-II	0.012	11.54	—	0.026

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A charge transfer occurs from DMSO to ZF₃X upon the formation of tetrel- and halogen-bonded complexes. The charge transfer is very small in complexes CX–TB, and even becomes negative in CX–TB (X = Cl, Br, and I). We ascribe it to the coexistence of both a tetrel bond and an organic fluorine hydrogen bond C–F⋯H–C interaction in CX–TB, with a reverse direction of charge transfer in both interactions. The O⋯Si tetrel bond in SiX–TB displays a very large charge transfer (0.133–0.163e), confirming its nature of the partially covalent interaction. Moreover, the interaction energy in SiX–TB takes on a nonlinear relationship with the corresponding charge transfer (Fig. 5). The charge transfer in the halogen-bonded complexes is larger than that in CX–TB but is much smaller than that in SiX–TB. In addition, a good linear relationship is found between the charge transfer and the interaction energy of halogen bond (Fig. 5).

Fig. 5 Interaction energy versus charge transfer in the tetrel- (up) and halogen-bonded (down) complexes.

The strength of tetrel and halogen bonds can also be measured with WBI. This index is very small in CX–TB but very large in SiX–TB, corresponding to a weak tetrel bond for the former complexes and a strong one for the latter, respectively. Similar with the tendency of the charge transfer as discussed above, the O⋯X halogen bond has a larger WBI than the O⋯C tetrel bond and a smaller one than the O⋯Si tetrel bond. Especially, the WBI of O⋯X halogen bond has a good linear relationship with the interaction energy (Fig. S2†).

3.5. Electron density topological analyses

The modes and features of the bonds in the complexes can be characterized with the topological parameters including the electron density (ρ), Laplacian (∇²ρ) and energy density (H) at the bond critical points (BCPs). The complexes of ZF₃Br are selected as an example to describe the interactions between ZF₃Br and DMSO, as shown in Fig. 6. In CBr–TB, there are three O⋯F BCPs and two F⋯H BCPs. The F⋯H BCP confirms the presence of the organic fluorine hydrogen bond C–F⋯H–C interaction. The O⋯C tetrel bond is represented with three paths through two electronegative atoms O and F. A similar case was also reported for the tetrel-bonded complexes of SiF₄–NCH.⁴ This supports the conclusion that BCPs are sometimes inadequate as indicators of a stabilizing interaction.⁵⁰ Both O⋯F and F⋯H BCPs possesses a positive Laplacian and energy density, indicating both types of interactions are a weak pure closed-shell interaction⁵¹ with a small electron density.

Fig. 6 Molecular maps of three types of complexes ZF₃Br (Z = C and Si).

In SiBr–TB, there are an O⋯Si BCP and a F⋯C BCP, respectively corresponding to the O⋯Si and F⋯C tetrel bonds. Mani and Arunan pointed out that a methyl group adjoined with an electron-withdrawing group or atom may form a carbon bond with a Lewis base.³⁴ The O and C atoms in DMSO act as the electron donor and acceptor in the O⋯Si and F⋯C tetrel bonds, respectively, thus a positive cooperativity is present between them. The electron density at the O⋯Si BCP is much larger than that at the F⋯C BCP, showing the complex SiBr–TB is mainly stabilized by the O⋯Si tetrel bond. The O⋯Si BCP has a positive Laplacian and a negative energy density, providing a further evidence for the nature of a partially covalent bond.⁵¹

In CBr–XB-I and SiBr–XB-I, an O⋯Br BCP and a Br⋯H BCP are found, indicating the coexistence of a halogen bond and a hydrogen bond in both complexes. The Br atom plays a dual role of the Lewis acid and base in the O⋯Br halogen bond and Br⋯H hydrogen bond, respectively. This dual role can be demonstrated by the anisotropic distribution of MEP on the Br atom (Fig. 1). The fact that the hydrogen atom of the methyl group in DMSO can participate in hydrogen bond has been demonstrated in the complexes of DMSO and water.⁵² According to the value of electron density, it is concluded that the halogen bond in CBr–XB-II is stronger than that in SiBr–XB-II, while the strength of the hydrogen bond is nearly the same in both complexes. The former result is consistent with the positive MEP on the σ-hole of the Br atom in CF₃Br and SiF₃Br (Table 1).

In CBr–XB-II and SiBr–XB-II, an O⋯Br BCP and two Br⋯H BCPs are observed, confirming the presence of one O⋯Br halogen bond and two Br⋯H interactions. Furthermore, these interactions have an equivalent strength with those in CBr–XB-I and SiBr–XB-I, evidenced with the equivalent electron density at the O⋯Br and Br⋯H BCPs in both types of halogen-bonded complexes. This supports the conclusion that the ZX–XB-II complex is more stable than the ZX–XB-I with the energy difference of −0.93, −1.25, and −1.49 kJ mol⁻¹ for the Cl⋯H, Br⋯H, and I⋯H interactions, respectively.

3.6. Energy decomposition analyses

To unveil the origin of the tetrel and halogen bonds in the complexes, the corresponding interaction energies are decomposed into five physical terms: electrostatic energy, exchange energy, repulsion energy, polarization energy, and dispersion energy, and the related results are presented in Table 5. For the tetrel bond in CX–TB, the dispersion energy is comparable with the electrostatic energy, and the polarization energy is small. Thus the weak tetrel bond in CX–TB is jointly stabilized by the electrostatic and dispersion interactions. This conclusion was also obtained for the weak single-electron tetrel bonds.⁵³ The relatively large dispersion energy corresponds to the long binding distance in CX–TB. For the tetrel bond in SiX–TB, the interaction energy is dominated by the electrostatic term although there are substantial contributions from polarization. The relatively large polarization energy suggests that the molecular orbitals undergo a significant deformation in their shapes, which is typical in the formation of a covalent bond and is confirmed by the deformation of the SiF₃X molecule in the complexes. The dispersion energy in SiX–TB is positive, and this case was also reported for Li⁺F⁻ and Na⁺F⁻, where the authors ascribed it to the differences in the intra- and interionic correlation energy on going from noninteracting to interacting ions, being sensitive to basis set and distance.⁴³ It should be pointed out that the energy decomposition formulation appears to be breaking down due to the formation of the covalent bond to Si. For the tetrel bond in SiX–TB, the exchange and repulsion terms are very large, which indicates the large orbital interactions and the short binding distance between two monomers, respectively.

Table 5 Electrostatic energy (E^ele), exchange energy (E^ex), repulsion energy (E^rep), polarization energy (E^pol), and dispersion energy (E^disp) in the complexes. All are in kJ mol⁻¹

Complexes	E^ele	E^ex	E^rep	E^pol	E^disp
CF–TB	−11.50	−19.69	34.49	−2.22	−7.65
CCl–TB	−9.57	−19.65	34.28	−2.26	−9.15
CBr–TB	−9.86	−20.86	36.41	−2.38	−9.66
CI–TB	−8.99	−21.74	37.87	−2.51	−10.45
SiF–TB	−297.41	−325.62	656.76	−168.54	17.85
SiCl–TB	−309.36	−336.62	681.42	−178.70	18.31
SiBr–TB	−323.03	−348.61	708.59	−190.27	20.40
SiI–TB	−342.26	−362.70	740.99	−201.48	23.16
CCl–XB-I	−23.20	−35.28	61.57	−7.11	−8.74
CBr–XB-I	−38.25	−58.98	104.29	−13.00	−10.99
CI–XB-I	−62.41	−95.64	169.67	−25.29	−11.75
SiBr–XB-I	−20.65	−38.12	65.33	−6.10	−11.54
CCl–XB-II	−26.46	−41.13	72.06	−8.40	−9.61
CBr–XB-II	−43.97	−70.39	124.98	−15.51	−12.87
CI–XB-II	−70.31	−113.61	201.81	−29.97	−14.34
SiCl–XB-II	−13.88	−27.84	47.44	−4.35	−9.91
SiBr–XB-II	−24.45	−46.44	80.05	−7.65	−12.75
SiI–XB-II	−43.14	−76.45	132.59	−15.63	−14.55

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The interaction energy of halogen bond is essentially determined by the electrostatic energy and the contributions from the polarization and dispersion energies are also substantial. The ratio of the polarization energy to the dispersion energy is increased with the enhancement of halogen bonding interaction.

4. Conclusions

A theoretical study of the tetrel- and halogen-bonded complexes formed by DMSO with ZF₃X (Z = C and Si; X = halogen) has been carried out by means of ab initio MP2 computational methods. The results show that CF₃X is favorable to form the halogen-bonded complexes and SiF₃X prefers the formation of the tetrel-bonded complexes rather than the halogen-bonded analogues. Interestingly, the interaction energy of tetrel bond in the SiF₃X complex is very large (−129.30 to −157.11 kJ mol⁻¹), which indicates that DMSO is a stronger electron donor even than anions. Moreover, the interaction energy of tetrel bond in the SiF₃X complex displays an abnormal dependence on the halogen atom.

The S=O stretch vibration in the tetrel-bonded complexes of SiF₃X shows a large red shift of about 130 cm⁻¹ and the halogen bond presents a small red shift of S=O stretch vibration. The Z–X stretch vibration exhibits a red shift in the tetrel bond but an irregular shift in the halogen bond. In the tetrel-bonded complexes of SiF₃X, the chemical shielding of Si and F is large enough to be detected with NMR.

NBO and AIM analyses indicate that the tetrel bond in the complexes of CF₃X is a weak interaction. In remarkable contrast, the tetrel bond in the complexes of SiF₃X is very strong with the nature of partially covalent bond, confirmed by the large electrostatic and polarization energy, and the interaction energy has a quadratic relationship with charge transfer, and a linear relationship is found between them in the halogen bond involving SiF₃X.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (21573188 and 21403127), the Natural Science Foundation of Shandong Province, China (ZR2014BQ015). The author thanks the fund of Young Scholars Program of Shandong University (Weihai) and the supercomputing system in the Supercomputing Center, Shandong University, Weihai.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra18316f

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