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. 2021 Oct 22;6(43):29037–29044. doi: 10.1021/acsomega.1c04085

Comparison for Electron Donor Capability of Carbon-Bound Halogens in Tetrel Bonds

Qingqing Yang 1, Xiaolong Zhang 1,*, Qingzhong Li 1,*
PMCID: PMC8567400  PMID: 34746592

Abstract

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The tetrel bond formed by HC≡CX, H2C=CHX, and H3CCH2X (X=F, Cl, Br, I) as an electron donor and TH3F (T=C, Si, Ge) was explored by ab initio calculations. The tetrel bond formed by H3CCH2X is the strongest, as high as −3.45 kcal/mol for the H3CCH2F···GeH3F dimer, followed by H2C=CHX, and the weakest bond is from HC≡CX, where the tetrel bond can be as small as −0.8 kcal/mol. The strength of the tetrel bond increases in the order of C < Si < Ge. For the H3CCH2X and HC≡CX complexes, the tetrel bond strength shows a similar increasing tendency with the decrease of the electronegativity of the halogen atom. Electrostatic interaction plays the largest role in the stronger tetrel bonds, while dispersion interaction makes an important contribution to the H2C=CHX complexes.

1. Introduction

The tetrel bond is an attractive interaction between a group 14 element and an electron donor.1 Politzer and coauthors proposed a concept of σ-holes, referred to the electron-deficient outer lobe of a half-filled p orbital of a covalent bond, to explain the formation of a halogen bond.2 Then, this concept was extended to other groups including the group 14 element (tetrel).3 This σ-hole displays a region with positive molecular electrostatic potentials (MEPs) on the atomic surface along a covalent bond; thus, it can interact attractively with a negative site in another molecule. Subsequently, these authors named a π-hole to describe a region with positive MEPs that is vertical to a portion of a molecular framework.4 Such a π-hole is also found for the group 14 element in sp2-hybridized molecules. The presence of a σ-hole/π-hole indicates that the tetrel bond is electrostatically driven. Both the σ-hole and π-hole become larger going from the lighter to the heavier atoms in a given group of the periodic table; thus, it is expected that the tetrel bond becomes stronger. Other than electrostatic contributions, the stability of a tetrel-bonded complex is in part attributed to charge transfer from the electron donor to the acceptor.5

Like hydrogen and halogen bonds, the tetrel bond is of great importance in crystal materials,1,6,7 chemical reactions,5,8,9 molecular recognition,10−12 and biological systems.13−15 Therefore, there are lots of theoretical and experimental studies of tetrel bonds.16−32 These applications are related to the directionality and strength of tetrel bond. Owing to the anisotropic distribution of electrostatic potentials and steric hindrance of a tetravalent tetrel atom,23 the tetrel bond is sensitive to angular distortions, displaying directionality. Both the electron-donating substituents in the electron donor and the electron-withdrawing groups in the tetrel donor have an enhancing effect on the strength of the tetrel bond.16−22 Sometimes, some unexpected substitution effects are found for tetrel bonds. For example, adding a −CH3 group in formamidine could greatly increase the interaction energy of the SiH3F complex from 60 to 80 kJ/mol.21 Cooperativity can also strengthen or weaken tetrel bonds, and this effect plays an important role in constructing crystal materials.24−32 Experimental and theoretical studies show that a tetrel bond is concurrent with an agostic Pb···H–C interaction in N′-(phenyl(pyridin-2-yl)methylene) isonicotinohydrazide–PbX complexes (X=Cl, I, NCS, NO2).30

The electron donor in the tetrel bond is varied from neutral molecules with lone pairs and anions33 to molecules with π electrons,34 metal hydrides,35 radicals,36 and carbenes.37 Even so, the electron donors used in studying tetrel bonds are usually from neutral molecules with lone pairs and anions. These molecules are often nitrogen/oxygen-containing,38−51 partly because some of these complexes such as SiF4···NH3 and SiF4···N(CH3)3 were identified experimentally.38 The N hybridization in the nitrogen electron donor affects the tetrel bond, becoming stronger in the sp < sp2 < sp3 sequence.39,40 When the carbonyl oxygen atom of malondialdehyde engages in a π-hole tetrel bond with F2SiO, the intramolecular hydrogen bond is enhanced with proton transfer within this H bond.46 NH3 is inclined to form a H bond with the −CF3 group adjoined to pyridine; however, the protonation on the nitrogen atom of pyridine promotes the formation of a tetrel bond.49 Dong and coauthors compared σ–/π-hole tetrel bonds between TH3F/F2TO and H2CX (X=O, S, Se) and found an interesting dependence of their strengths on the chalcogen electron donor.51 The σ-hole interaction is weaker for the heavier chalcogen electron donor, while the π-hole interaction involving F2TO (T=Ge, Sn, and Pb) has an opposite dependence.51

Halogen anions have been used in studying tetrel bonds since they can be utilized in molecular recognition.52−54 Regardless of which receptors (hydrogen, halogen, chalcogen, pnicogen, and tetrel), F– is bound much more strongly than Cl– and Br–.53 More surprisingly, the tetrel receptor shows the greatest selectivity for F– over the other halides, as much as 1013, an enhancement of six orders of magnitude when compared to the H-bonding receptor.53 Likely, the halogen anion in LiX forms a stronger tetrel bond than neutral molecules and the tetrel bond becomes weaker for the heavier halogen ion.55 The ionic property of HArF makes the negatively charged F atom become a good electron donor in the tetrel bond.56 The tetrel bonding interaction energy between HArF and SiH3X (X = halogen) is in a range of 95–135 kJ/mol at the MP2/CBS level.56 Interestingly, the interaction energy becomes larger with the increase of X atomic mass in SiH3X although the heavier X atom shrinks the σ-hole on the Si atom.56 However, hydrogen halides are seldom used as the electron donors in tetrel bonds.57,58 In the ground-state geometry, CO2 forms a hydrogen bond with HCl but a tetrel bond with HBr in which the negatively charged Br atom approaches the carbon atom of CO2.57 SiH4, SiF4, and SiCl4 bind with NH3 through a tetrel bond, but they form a hydrogen bond with HF where the hydrogen atom interacts with the silicon substituents.58 It was demonstrated that organic fluorine molecules have been extensively utilized in crystal engineering and functional materials.59 However, the study of tetrel bonds involving organofluorine electron donors is sporadic.60,61 CH3F forms a weaker tetrel bond with SiH3X (X=F and Cl) than NH3.60 There is evidence for the C–F···C=O π-hole tetrel bond in protein–drug interaction although its interaction energy is less than 5 kJ/mol.61

In this manuscript, we focus on the tetrel bond between TH3F (T=C, Si, Ge) and organic fluorine electron donors. The organic fluorine molecules studied contain CH3CH2F (sp3), CH2CHF (sp2), and CHCHF (sp). Then, the F atom in the organic fluorine is replaced by Cl, Br, and I. We systematically study the tetrel bond involving organic halogen electron donors. Can these organic halogens form a stable tetrel-bonded complex? How does the strength of tetrel bond depend on the nature of tetrel and halogen? What is the dominant origin of the tetrel bond? These tetrel bonds are characterized by means of geometries, energetics, natural bond orbital (NBO), atoms in molecules (AIM), and energy decomposition (EDA) analyses.

2. Computational Methods

The geometries of monomers and binary complexes were optimized at the MP2/aug-cc-pVTZ level. In addition, in order to consider the relativistic effects, the aug-cc-pVTZ-PP basis set was used for the I atom. Harmonic frequency calculations were performed at the same level to verify that the structures are local minima on their respective potential energy surfaces. The full counterpoise procedure was employed to correct for the basis set superposition error (BSSE).62 All calculations were carried out using the Gaussian 09 package.63

The molecular electrostatic potentials (MEPs) of the monomers on the 0.001 a.u. isodensity surface were evaluated at the MP2/aug-cc-pVTZ level using the Wave Function Analysis-Surface Analysis Suite (WFA-SAS) program.64 Natural bond orbital (NBO)65 analysis was performed at the HF/aug-cc-pVTZ level to obtain orbital interaction and charge transfer (CT). The AIM2000 software66 was carried out to obtain the electron density (ρ), energy density (H), and Laplacian (∇2ρ) at the relevant bond critical points (BCPs). The LMOEDA67 (localization molecular orbital energy decomposition analysis) was performed at the MP2/aug-cc-pVTZ level using the GAMESS program.68 According to LMOEDA, the total interaction energy of a complex was decomposed into electrostatic energy (Eele), exchange energy (Eex), repulsion energy (Erep), polarization energy (Epol), and dispersion energy (Edisp).

3. Results

3.1. MEP Analysis

The MEP maps of TH3F (T=C, Si, Ge) monomers are shown in Figure 1. As indicated in Figure 1, all TH3F monomers possess a region with positive MEPs (σ-hole) along the extension of the T–F bond. The increase of MEP on the σ-hole follows the order of C < Si < Ge, and the maximum value of GeH3F is 0.0766 a.u. According to our previous studies, the MEP distribution of CHCF exhibits a negative region on the F end.69 Thus, the σ-hole of TH3F monomer can form a weak tetrel bond with the most negative MEP region of CHCX (X=F, Cl, Br, I). In addition, the π-electrons in CH2CHX and CHCHX also participate in a tetrel bond with TH3F.34

Figure 1.

Figure 1

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MEP maps of CH3F, SiH3F, and GeH3F on the ρ = 0.001 a.u. isodensity surface. Color ranges, in a.u., are: red, greater than 0.02; yellow, between 0.02 and 0; green, between 0 and −0.02; and blue, smaller than −0.02.

Table 1 lists the most negative MEP value Vmin of all Lewis bases. The minimum value is only −0.0046 a.u. When the halogen atom is fixed, due to the difference in the electron donating ability of different hybridization types C, the negative MEP value decreases according to Csp3-X > Csp2-X > Csp-X. When the hybrid type is the same, the most negative MEP in Cspn-X (n = 2, 3) molecules gradually decreases in the order of F > Cl > Br > I, which is in agreement with the electronegativity trend observed for halogens. However, this is abnormal for Csp-X. The most negative electrostatic potential law is F > I > Br > Cl, probably because of the hyperconjugation effect between the π orbital on the C≡C bond and the lone pair on the halogen atom.

Table 1. Most Negative MEP (Vmin, a.u.) on the X (X=F, Cl, Br, I) Atomic Surface in the Monomers.

  n = 1 n = 2 n = 3
Cspn-F –0.0064 –0.0318 –0.0456
Cspn-Cl –0.0046 –0.0208 –0.0287
Cspn-Br –0.0055 –0.0198 –0.0265
Cspn-I –0.0056 –0.0177 –0.0213
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3.2. Energetics and Geometries

Figure 2 shows the geometries of complexes between Cspn-X and TH3F (X=F, Cl, Br, I; T=C, Si, Ge). For simplicity, CH3CH2X (sp3), CH2CHX (sp2), and CHCHX (sp) are represented as Csp3-X, Csp2-X, and Csp-X, respectively, while TH3F is denoted as T. As shown in Figure 2, R is the distance between the X atom in Cspn-X and the T atom in TH3F, and the related geometrical parameters are summarized in Table 2. For the sp-hybridized CHCX structures, the C–X···T (α) angle varies between 69 and 104° and is largest in the Csp-F system. This may be partly due to the coulomb attraction between the C≡C π electrons in Csp-X and the positive MEP near the H atoms in TH3F, which is the weakest in the Csp-F system owing to the strongest electron-withdrawing ability of the F atom.

Figure 2.

Figure 2

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Schematic diagrams of three complexes.

Table 2. Binding Distance (R, Å), Angles of C–X···T (α, °) (X=F, Cl, Br, I; T=C, Si, Ge) and X···T–F (β, °) in Complexes.

  n = 1
 n = 2
 n = 3
complexes R α β R α β R α β
Cspn-F···C 3.163 92.6 177.3 3.019 106.6 176.0 2.963 106.3 175.6
Cspn-F···Si 3.120 103.8 176.4 2.925 110.1 178.7 2.793 113.9 179.6
Cspn-F···Ge 3.098 100.8 173.8 2.871 110.5 178.2 2.754 110.5 177.7
Cspn-Cl···C 3.547 78.3 172.4 3.434 87.9 170.3 3.401 84.8 168.4
Cspn-Cl···Si 3.440 85.4 176.5 3.325 88.8 176.7 3.262 91.9 177.3
Cspn-Cl···Ge 3.435 82.6 175.0 3.301 87.7 175.7 3.239 88.9 175.2
Cspn-Br···C 3.561 76.6 174.3 3.501 83.6 168.9 3.478 80.3 167.9
Cspn-Br···Si 3.496 82.2 176.4 3.407 84.1 176.1 3.358 87.2 176.6
Cspn-Br···Ge 3.567 76.1 176.7 3.404 82.6 174.9 3.355 84.3 174.6
Cspn-I···C 3.728 72.0 173.5 3.706 76.2 162.8 3.682 73.8 162.8
Cspn-I···Si 3.679 76.9 175.0 3.604 78.4 174.7 3.567 80.9 175.1
Cspn-I···Ge 3.702 73.8 173.6 3.613 76.9 173.3 3.572 78.1 173.4
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With the increasing X electronegativity, the α (C–X···T) angles for both sp2 and sp3 cases are increased in the same order of I < Br < Cl < F. Compared with the sp hybridization, the α (C–X···T) angle increases 1–40° for the sp2 hybridization and 5–40° for the sp3 hybridization, respectively. However, the β (X···T–F) angles for the three types of hybridizations are almost in the similar range from 163 to 180°, which is basically close to 180°.

When the TH3F monomer is combined with the sp2-hybridized H2C=CHF, the TH3F molecule is located above the plane of the olefin molecule. The corresponding intermolecular distance R (0.02–0.227 Å) is shorter than that in the sp hybridization. However, for the sp3 hybridization, the intermolecular distance R is 0.01–0.116 Å, shorter than that in the sp2 case. Clearly, the C hybridization has an obvious effect on the intermolecular distance. As one might expect, this bond contraction is accompanied by a very significant strengthening of the tetrel bond.

Table 3 lists the BSSE-corrected interaction energies of the binary complexes. As is evident from Table 3, for the sp hybridization, the interaction energies (absolute values) are increased in the order of C < Si < Ge, which are the same as those of the sp2 and sp3 cases. For a given R substitution, the order of the interaction energies (absolute values) is increased with sp < sp2 < sp3. When the C atom hybridization changes from sp to sp2 and to sp3, the negative MEP on the connected halogen atom gradually becomes larger (can be seen from the data in Table 1), so the tetrel bond formed by it becomes stronger. The shortest intermolecular distance R (2.755 Å) for the Csp3-F···Ge complex has the largest Eint (−3.45 kcal/mol). However, there are some different trends for Csp-I···C, Csp-I···Si, and Csp-I···Ge complexes, i.e., R increases in the order of Si < Ge < C, while the Eint is C < Si < Ge. These tetrel bonds are much weaker than the charge-assisted tetrel bonds with the interaction energy larger than −16 kcal/mol.54 Considering the small interaction energy, we think that these tetrel-bonded complexes are not stable at 298 K.

Table 3. Interaction Energy (Eint, kcal/mol) in Complexes.

complexes n = 1 n = 2 n = 3
Cspn-F···C –0.80 –1.40 –1.67
Cspn-F···Si –0.97 –2.27 –3.20
Cspn-F···Ge –1.02 –2.53 –3.45
Cspn-Cl···C –1.25 –1.61 –1.56
Cspn-Cl···Si –1.69 –2.61 –3.05
Cspn-Cl···Ge –1.86 –2.88 –3.24
Cspn-Br···C –1.35 –1.60 –1.56
Cspn-Br···Si –1.79 –2.26 –3.01
Cspn-Br···Ge –1.98 –2.90 –3.17
Cspn-I···C –1.38 –1.60 –1.53
Cspn-I···Si –1.86 –2.57 –2.87
Cspn-I···Ge –2.10 –2.87 –3.04
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Figure 3 presents the relationship between the interaction energy Eint and the halogen substituents in different hybridization modes. For T=C complexes, the interaction energy shows a similar increasing tendency with the decrease of the electronegativity of halogen substituents. This is also the same for T=Si complexes in both sp and sp3 hybridization except for sp2 hybridization. However, for T=Ge complexes, the interaction energy decreases in the order of F < Cl < Br < I for both sp and sp2 hybridization. On the other hand, for sp3 hybridization, some inconsistent variations are found, i.e., for the X=Cl substituent, which exhibits the largest interaction energy.

Figure 3.

Figure 3

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Dependence of interaction energy (Eint) on the nature of X and T atoms.

3.3. NBO Analysis

We have performed the NBO calculations to study the nature of interaction. The results of the charge transfer and the second-order stabilization energies E(2) are gathered in Table 4. CT refers to the total amount of charge transfer from Cspn-X to TH3F, while E(2) focuses on the specific orbital transfer from LpX to σ*T-F (LpX is the lone pair of electrons of halogen atoms and σ*T-F is the antibonding orbital of the T-F bond). The charge transfer leads to the better understanding of the energetics: the largest for Ge and smallest for C, and it decreases with the increase of electronegativity X. From Table 4, for different hybridization, the value of CT increases significantly from sp to sp2 to sp3. The charge transfer of sp2 hybridization varies from a low of 0.0026e to as much as 0.0218e. Those quantities represent an 18–77% enhancement relative to the sp complexes. However, the charge transfer of sp3 hybridization is even twice that of sp.

Table 4. Charge Transfer (CT, e) and NBO Perturbation Energy (E(2), kcal/mol) for Transfer from the X (X=F, Cl, Br, I) Lone Pair to the T–F (T=C, Si, Ge) Unfilled Antibonding Orbital.

  n = 1
 n = 2
 n = 3
complexes CT E(2) CT E(2) CT E(2)
Cspn-F···C 0.0006 0.19 0.0026 0.32 0.0003 0.57
Cspn-F···Si 0.0038 0.56 0.0080 1.18 0.0112 2.74
Cspn-F···Ge 0.0038 0.71 0.0094 1.67 0.0134 3.86
Cspn-Cl···C 0.0018 0.33 0.0030 0.54 0.0021 0.81
Cspn-Cl···Si 0.0084 1.60 0.0138 2.66 0.0181 4.05
Cspn-Cl···Ge 0.0087 1.84 0.0156 3.41 0.0202 5.12
Cspn-Br···C 0.0024 0.57 0.0036 0.72 0.0038 1.03
Cspn-Br···Si 0.0122 2.36 0.0186 3.54 0.0234 4.94
Cspn-Br···Ge 0.0127 2.72 0.0199 4.34 0.0259 5.97
Cspn-I···C 0.0027 0.68 0.0033 0.73 0.0039 1.02
Cspn-I···Si 0.0145 2.76 0.0208 3.84 0.0260 5.00
Cspn-I···Ge 0.0140 2.96 0.0218 4.54 0.0272 5.88
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In order to further analyze the nature of the orbital interaction, we have studied the second-order perturbation energy corresponding to the orbital interaction, and its value is estimated to in the range of 0.18–5.88 kcal/mol for all the complexes. When the X atom is the same, the E(2) of the Cspn-X···T complex increases in the order of C < Si < Ge. The E(2) of the Cspn-X···T complex increases in the order of F < Cl < Br < I for the same T atom, which is consistent with the change order of charge transfer CT. However, the largest amount of charge transfer does not necessarily correspond to the strongest bond. For example, Cspn-I···Ge has the largest charge transfer, but the interaction energy is not the largest.

3.4. AIM Analysis

The electron density (ρ), its Laplacian (∇2ρ), and energy density (H) at the bond critical point between X and T are listed in Table 5. All Cspn-X···T interactions are characterized by a positive ∇2ρ value and a positive H, which are indicative of a closed-shell interaction in these systems. The electron density exhibits the relationship with the X···T binding distance. One can see, the capacity of the complex to concentrate electrons increases as T=C < Si < Ge and X=F < Cl < Br < I, which is consistent with the tetrel bond distance as discussed above. In addition, for the different C hybridizations, the electron density is increased in the order of sp < sp2 < sp3. This has good agreement with the interaction energy discussed above. The electron density of the complexes is much less than 0.01 a.u., which means that the tetrel bond formed is a weak interaction. The Laplacian contour of CH2=CHCl···SiH3F is plotted in Figure 4, where the spatial display of Laplacian of electron densities is confined separately to both molecules, indicative of a weak closed-shell interaction.

Table 5. Electron Density (ρ), its Laplacian (∇2ρ), and Total Energy Density (H) at the X···T BCP in Complexes (All in a.u.).

  n = 1
 n = 2
 n = 3
complexes ρ ∇2ρ H ρ ∇2ρ H ρ ∇2ρ H
Cspn-F···C 0.0036 0.0219 0.0013 0.0052 0.0287 0.0015 0.0056 0.0331 0.0018
Cspn-F···Si 0.0054 0.0243 0.0011 0.0080 0.0332 0.0011 0.0103 0.0399 0.0010
Cspn-F···Ge 0.0061 0.0266 0.0011 0.0094 0.0399 0.0014 0.0121 0.0507 0.0016
Cspn-Cl···C 0.0042 0.0209 0.0013 0.0043 0.0210 0.0013 0.0055 0.0242 0.0013
Cspn-Cl···Si 0.0063 0.0231 0.0011 0.0080 0.0270 0.0010 0.0092 0.0289 0.0009
Cspn-Cl···Ge 0.0066 0.0242 0.0011 0.0088 0.0299 0.0011 0.0103 0.0317 0.0010
Cspn-Br···C 0.0049 0.0224 0.0013 0.0061 0.0242 0.0012 0.0063 0.0257 0.0013
Cspn-Br···Si 0.0071 0.0236 0.0009 0.0079 0.0246 0.0007 0.0098 0.0276 0.0007
Cspn-Br···Ge 0.0073 0.0241 0.0009 0.0092 0.0280 0.0008 0.0104 0.0290 0.0007
Cspn-I···C 0.0053 0.0210 0.0011 0.0063 0.0221 0.0010 0.0065 0.0224 0.0010
Cspn-I···Si 0.0074 0.0212 0.0006 0.0087 0.0233 0.0005 0.0096 0.0239 0.0004
Cspn-I···Ge 0.0073 0.0210 0.0007 0.0088 0.0234 0.0005 0.0100 0.0241 0.0004
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Figure 4.

Figure 4

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Laplacian contour of CH2=CHCl···SiH3F.

3.5. EDA Analysis

To deepen the understanding of the nature of the tetrel bond, we performed an energy decomposition analysis for these complexes. The interaction energies were decomposed into electrostatic energy (Eele), exchange energy (Eex), repulsion energy (Erep), polarization energy (Epol), and dispersion energy (Edisp), which are collected in Table 6. This energy decomposition was performed with the GAMESS program and its energy terms have some different physical meanings from other energy decomposition schemes. The physical meanings of five terms obtained with the GAMESS program have been elaborated in the previous study;67 thus, they are not described here. Eex and Erep are the largest attractive and repulsive terms, respectively, but both terms are dependent and partly cancel each other; thus, they are not discussed. As shown in Table 6, among three attractive terms (Eele, Epol, and Edisp), the contribution of Edisp to the stability of tetrel-bonded complexes is greater than the Eele for the sp hybridization, while the Epol has the smallest contribution. In addition, these five kinds of energies are increased in the order of sp < sp2 < sp3. This also shows good agreement with the interaction energy discussed above. For the sp2 hybridization, both Eele and Edisp have similar degrees of magnitude, except for the Csp2-F···Ge complex. This suggests that both terms make comparable contributions to the energetic stability of sp2 complexes. For the sp3 hybridization, the percentage for the Eele contribution is 41–56% (except for Csp3-X···C, X=Cl, Br, I), which means the Eele term plays a dominant role in the energetic stability of most sp3 complexes.

Table 6. Electrostatic (Eele), Exchange (Eex), Repulsion (Erep), Polarization (Epol), and Dispersion (Edisp) Energies in Complexes (All in kcal/mol).

complexes Eele Eex Erep Epol Edisp
Csp-F···C –0.47(22%) –2.02 3.34 –0.15(7%) –1.52(71%)
Csp-F···Si –0.74(25%) –2.92 4.91 –0.30(10%) –1.95(65%)
Csp-F···Ge –0.96(26%) –3.73 6.32 –0.43(12%) –2.24(62%)
Csp-Cl···C –0.95(28%) –3.26 5.32 –0.25(7%) –2.17(64%)
Csp-Cl···Si –1.45(27%) –5.76 9.40 –0.74(14%) –3.23(60%)
Csp-Cl···Ge –1.76(28%) –6.63 10.95 –0.91(15%) –3.56(57%)
Csp-Br···C –1.21(30%) –4.24 6.94 –0.33(8%) –2.52(62%)
Csp-Br···Si –1.99(29%) –7.69 12.62 –1.04(15%) –3.76(55%)
Csp-Br···Ge –2.29(30%) –8.34 13.84 –1.18(16%) –4.04(54%)
Csp-I···C –1.47(31%) –5.28 8.65 –0.43(9%) –2.85(60%)
Csp-I···Si –2.40(30%) –9.46 15.51 –1.33(17%) –4.21(53%)
Csp-I···Ge –2.63(31%) –9.73 16.14 –1.42(17%) –4.48(53%)
Csp2-F···C –1.44(45%) –2.76 4.58 –0.25(8%) –1.54(48%)
Csp2-F···Si –3.06(48%) –5.83 9.84 –0.81(13%) –2.46(39%)
Csp2-F···Ge –4.07(52%) –7.43 12.75 –1.13(14%) –2.67(34%)
Csp2-Cl···C –1.09(41%) –2.20 3.58 –0.21(8%) –1.35(51%)
Csp2-Cl···Si –3.29(39%) –8.93 14.66 –1.28(15%) –3.88(46%)
Csp2-Cl···Ge –4.11(42%) –10.44 17.41 –1.58(16%) –4.21(43%)
Csp2-Br···C –1.92(38%) –5.35 8.79 –0.47(9%) –2.66(53%)
Csp2-Br···Si –3.35(39%) –9.46 15.62 –1.39(16%) –3.76(44%)
Csp2-Br···Ge –4.60(41%) –12.31 20.59 –1.88(17%) –4.73(42%)
Csp2-I···C –2.13(37%) –6.50 10.68 –0.57(10%) –3.04(53%)
Csp2-I···Si –4.10(38%) –12.88 21.19 –1.90(17%) –4.92(45%)
Csp2-I···Ge –4.69(39%) –13.54 22.61 –2.07(17%) –5.19(43%)
Csp3-F···C –1.76(53%) –2.46 4.11 –0.30(9%) –1.26(38%)
Csp3-F···Si –5.04(54%) –8.50 14.58 –1.50(16%) –2.81(30%)
Csp3-F···Ge –6.52(56%) –11.03 19.18 –1.96(17%) –3.15(27%)
Csp3-Cl···C –1.46(35%) –4.13 6.76 –0.41(10%) –2.33(55%)
Csp3-Cl···Si –4.43(43%) –10.64 17.68 –1.68(16%) –4.09(40%)
Csp3-Cl···Ge –5.70(46%) –13.27 22.47 –2.14(17%) –4.65(37%)
Csp3-Br···C –1.75(34%) –5.53 9.08 –0.54(11%) –2.81(55%)
Csp3-Br···Si –4.99(43%) –12.86 21.41 –2.04(18%) –4.62(40%)
Csp3-Br···Ge –6.07(45%) –14.95 25.33 –2.40(18%) –5.10(38%)
Csp3-I···C –1.93(33%) –6.68 10.98 –0.65(11%) –3.19(55%)
Csp3-I···Si –5.17(41%) –14.58 24.22 –2.29(18%) –5.09(41%)
Csp3-I···Ge –6.01(43%) –16.03 27.10 –2.56(18%) –5.55(39%)
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4. Discussion

As discussed above for each type of C hybridization, the electrostatic and dispersion energies roughly reflect the behavior of the interaction energy. Figure 5a shows the linear relationship between Eint and Eele for all complexes, with a correlation coefficient R2 = 0.95. In addition, the slope in Figure 5a is 2.3, which indicates that the electrostatic energy increases faster than the interaction energy, while the slope is much closer to the dispersion energy in Figure 5c. Although dispersion energy plays an important role in the total interaction energy, its correlation with Eint is very poor, with R2 = 0.53. In contrast, the correlation between Eint and Epol is not very poor, with R2 = 0.84 as indicated in Figure 5b.

Figure 5.

Figure 5

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Relationship of interaction energy (Eint) with (a) electrostatic (Eele), (b) polarization (Epol), and (c) dispersion energies (Edisp).

The total amount of charge from the electron donor to the acceptor is less than 0.03e for the complexes. This quantity is much smaller than the charge transfer amount of the triel bond formed by Cspn-F.69 For three types of C hybridizations, AIM parameters suggest that the GeH3F species is the strongest, followed by the Si and C, which corresponds to their Lewis acid strength.

The F atom has been considered as the nucleophilic source of electron density in triel bonds in the recent study.69 However, the pertinent F was not bonded to C in the triel bond. Nonetheless, this previous study can provide enlightenment for the results shown here. For example, the Cspn-F and TrR3 (Tr=B, Al, Ga) complex is held together by a pair of triel bonds. The interaction energy of the complex varies from −0.94 to −29.74 kcal/mol at the MP2/aug-cc-pVTZ level.69 The sp3 hybridization has a stronger effect than sp2 and sp, and the interaction energy is decreased in the order of sp3 < sp2 < sp.69

5. Conclusions

The tetrel-bonded complexes between the organic halogen connected with differently hybridized C atoms and TH3F (T=C, Si, Ge) have been investigated by ab initio calculations. The strength of the tetrel bond is related to the C hybridization as well as the nature of both X and T. For any type of C hybridization, the GeH3F complexes are more strongly bound than the SiH3F analogues, which are stronger than the CH3F analogues. For T=C complexes, the interaction energy shows a similar increasing tendency with the decrease of the electronegativity of halogen substituents. This is also same for T=Si complexes in both sp and sp3 hybridization except for the sp2 hybridization.

NBO analysis shows that the principal orbital interaction of these tetrel bonds is charge transfer from the lone pair on X in the Lewis base into the empty F-T orbital. Furthermore, the values are related to the type of C hybridization, with the order of sp3 > sp2 > sp. The bond critical point between T and X confirms the existence of the tetrel bond. For both sp and sp3 hybridizations, the tetrel bonds are dominated by electrostatic interaction, while for the sp2 hybridization, both electrostatic and dispersion have similar degrees of magnitude, except for the H2C=CHF···GeH3F complex, which means that those two terms make comparable contributions to the energetic stability of the H2C=CHX complexes.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (21573188).

The authors declare no competing financial interest.

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