Abnormalities of the Halogen Bonds in the Complexes between Y₂CTe (Y = H, F, CH₃) and XF (X = F, Cl, Br, I)

Abstract

In this work, the hydrogen bonds and halogen bonds in the complexes between Y₂CTe (Y = H, F, CH₃) and XF (X = F, Cl, Br, I) have been studied by quantum chemical calculations. We found three interesting abnormalities regarding the interactions. Firstly, the strength of halogen bonds increases in the order of IF < BrF < ClF < F₂. Secondly, the halogen bonds formed by F₂ are very strong, with an interaction energy in the range between −199.8 and −233.1 kJ/mol. Thirdly, all the halogen bonds are stronger than the hydrogen bonds in the systems we examined. All these results are against the general understanding of halogen bonds. These apparent abnormal properties are reconciled with the high polarizability of the Te atom and the strong inducing effect of F on the Te atom of Y₂CTe. These findings provide a new perspective on halogen bonds. Additionally, we also proposed bonding distance-based methods to compare the strength of halogen/hydrogen bonds formed between different donor atoms and the same acceptor atom.

1. Introduction

A halogen bond is formed between an electrophilic region of a halogen atom X (X = F, Cl, Br, and I) in a molecule R-X (R is an electron-withdrawing atom/group) and a nucleophilic region of a molecule Y-R’ [1], denoted as R-X∙∙∙Y-R’. The electrophilic region, or the electron-deficient region of the X atom, is located along the R-X σ-bond, denoted as σ-hole, which is surrounded by a belt of negative electrostatic potential [2]. Nowadays, halogen bonds have received extensive attention due to their important roles in many fields such as supramolecular chemistry, organocatalysis, synthetic coordination chemistry, polymer chemistry, and drug discovery [3,4,5,6,7,8,9,10,11,12,13]. For example, halogen bonding has been a popular and much exploited supramolecular synthon in the crystal field [5,9]. The application of halogen atoms as pharmaceutically active ligand substituents has been widespread in recent medicinal chemistry [10,11].

The properties of halogen bonds are related to their strength, which is not only dependent on the halogen donor atom and the acceptor atom, but is also affected by substituents. Normally, the halogen bond becomes stronger with the halogen donor varying from F to I [1,12,13,14,15,16]. An electron-donating group in the halogen bond acceptor strengthens the halogen bond, while an electron-withdrawing group in the acceptor has a weakening effect [16]. The type of the halogen bond acceptor varies from anions and neutral molecules with lone pairs to π-electron molecules, radicals, metal hydrides, and carbenes [17,18]. Specially, the molecules containing N and O atoms are often taken as the halogen bond acceptor.

It is interesting to study the differences between hydrogen bonds and halogen bonds, since both types of interactions have comparable strength and may coexist in the same systems [19,20,21,22,23,24,25,26,27]. Usually, hydrogen bonds are stronger than halogen bonds, except for when an iodine atom acts as the halogen donor [24,28]. Thus, some studies have tried to make halogen bonds stronger than hydrogen bonds [28,29,30]. When the halogen bond acceptor H₂CO binds with the hydrogen/halogen donor HOBr, the interaction energy of the hydrogen bond is larger by 7 kJ/mol than that of the halogen bond [19]. Inversely, the interaction energy of the halogen bond is larger by 1 kJ/mol than that of the hydrogen bond if H₂CO is changed to H₂CS [28]. This difference is enlarged to 2 kJ/mol when one H atom of H₂CS is replaced by a Li atom [28]. These results indicate that the differences between hydrogen bonds and halogen bonds can be regulated by changing the halogen bond acceptor atoms and/or adding substituents. Nevertheless, these comparisons are not very convincing, because, for HOBr to participate in hydrogen bonding and halogen bonding interactions, the remaining moieties are -OBr and -OH, respectively, meaning that they are not identical. To overcome this difficulty, Li and coauthors designed a molecule called 6-OX-fulvene (X = H, Cl, Br, I), where the moiety of fulvene increases the acidity of the X atom. Then, they examined the interactions between this molecule and ZH₃/H₂Y (Z = N, P, As, and Sb; Y = O, S, Se, and Te) [31]. It was found that the hydrogen bond is weakened with the Lewis base atom growing in size; however, the effect of the same on halogen bonds is very limited [31]. If SbH₃ and H₂Te are selected as the acceptors, the halogen bonds are much stronger than the hydrogen bonds, and the largest difference in their interaction energies is 40 kJ/mol in the SbH₃∙∙∙6-OCl-fulvene complex [31].

H₂CTe is a homologue of H₂CO and H₂CS; thus, it can also work as an acceptor to form hydrogen bonds or halogen bonds. Considering that Te is a semimetal located on the dividing line between metals and non-metals, we expect that the halogen bond formed by it may have different patterns. In this study, we investigated the complexes between Y₂CTe (Y = H, F, and CH₃) and XF (X = H, F, Cl, Br, and I), wherein XF is a hydrogen/halogen bond donor and Y₂CTe is an acceptor. With the strong electronegativity of F, the designated molecules XF are expected to be prominent halogen bond donors. The following questions are addressed by the method of quantum chemical calculations: (1) Whether the halogen bond is stronger than the hydrogen bond. (2) Whether the strength of halogen bond follows the order of F₂ < ClF < BrF < IF. (3) What is the nature of the hydrogen bond and halogen bond in these complexes?

2. Results

2.1. Molecular Electrostatic Potential (MEP) Analyses

It is well known that the MEP diagram of a molecule is helpful to effectively predict noncovalent interactions involving that molecule [32]. Figure 1 shows the MEP maps of two families of molecules: Y₂CTe (Y = F, H, and CH₃) and XF (X = H, F, Cl, Br, and I). The MEP distributions in both families are anisotropic. For Y₂CTe, we focus on the negative areas of the MEPs (blue colored areas). As expected, there are mainly two negative areas in each molecule, which correspond to the lone pairs of the Te atom. Compared with H₂CTe (−78.8 kJ/mol), the minimal MEP value of the Te atom decreases in F₂CTe (−52.5 kJ/mol) but increases in (CH₃)₂CTe (−99.8 kJ/mol), which can be attributed to the electron-withdrawing nature of F atoms and the electron-donating ability of the methyl groups, respectively.

For XF, we focus on the positive areas of the MEPs (red areas). In the case of HF, the atom H exhibits positive electrostatic potential, while F is negative. For dihalogen molecules XF, there is a positive MEP region (σ-hole) at the X atom along the X-F bond. The magnitude of the σ-hole on the halogen atom increases with an increasing atomic mass of X. It is also found that the maximal MEP on the H atom is larger than that on the halogen atoms, including iodine.

2.2. Geometries

For the hydrogen bonding or halogen bonding interactions (Y₂CTe∙∙∙XF), the general geometry of the complexes and the involved parameters are shown in Figure 2. We focus on the Te∙∙∙X distance (R₁), the change in the X-F bond length (∆R₂), and the Te∙∙∙X-F angle (α). The data of the optimized structures are listed in

Table 1. Binding distance (R₁, Å), ΔR₁%; elongation of the X-F bond length (ΔR₂, Å), ΔR₂%; bond angle (α, deg) of the complexes.

	R1	ΔR1%	ΔR2	ΔR2%	α
H2CTe∙∙∙HF	2.518	23.70%	0.015	1.63%	168.6
H2CTe∙∙∙F2	2.151	40.25%	0.359	25.62%	168.8
H2CTe∙∙∙ClF	2.528	36.80%	0.201	12.26%	176.8
H2CTe∙∙∙BrF	2.686	36.05%	0.140	7.96%	177.4
H2CTe∙∙∙IF	2.904	34.00%	0.089	4.64%	177.9
F2CTe∙∙∙HF	2.586	21.64%	0.010	1.08%	179.9
F2CTe∙∙∙F2	2.140	40.56%	0.371	26.48%	170.7
F2CTe∙∙∙ClF	2.647	33.83%	0.137	8.36%	179.7
F2CTe∙∙∙BrF	2.790	33.57%	0.098	5.57%	179.8
F2CTe∙∙∙IF	2.996	31.91%	0.064	3.33%	179.2
(CH3)2CTe∙∙∙HF	2.483	24.76%	0.018	1.95%	170.7
(CH3)2CTe∙∙∙F2	2.176	39.56%	0.343	24.48%	168.0
(CH3)2CTe∙∙∙ClF	2.518	37.05%	0.222	13.54%	178.1
(CH3)2CTe∙∙∙BrF	2.673	36.36%	0.158	8.99%	179.1
(CH3)2CTe∙∙∙IF	2.893	34.25%	0.101	5.26%	180.0

.

As can be seen in the table, all the values of R₁ are much shorter than the sum of the van der Waals radii of the respective atoms (3.3 Å for Te and H, 3.6 Å for Te and F, 4.0 Å for Te and Cl, 4.2 Å for Te and Br, and 4.4 Å for Te and I) [33,34]. This justifies the formation of hydrogen/halogen bonds. Further, the interactions between the electron-donor and acceptor molecules seem to be quite strong because stronger interaction is known to result in shorter bond length (R₁). To compare the relative strength between the halogen bonds between different interaction partners and the hydrogen bond, we define a quantity ΔR₁% in the following equation:

$${\mathsf{\Delta }\mathrm{R}}_1\%=\frac{{\mathrm{R}}_{\mathrm{c}}-{\mathrm{R}}_1}{{\mathrm{R}}_{\mathrm{c}}}\times 100\%$$

(1)

where R_c is the sum of the van der Waals radii of the two atoms representing the critical distance to judge the presence of a hydrogen/halogen bond. After normalization with R_c, the shortening of the Te∙∙∙X distance could be used to evaluate the strength of hydrogen/halogen bonds. Thus, for each of the three molecules (H₂CTe, F₂CTe, and (CH₃)₂CTe), the ΔR₁% are all in the sequential order F₂ > ClF > BrF > IF > HF when they form interaction pairs. This implies that all the halogen bonds are stronger than the hydrogen bonds. Most interestingly, the ΔR₁% values suggest that the halogen bond strength decreases with an increasing size of the halogen atom in the donor molecule XF. This is different from the general understanding of halogen bonds.

The change in the X-F bond length R₂ of a donor could also reflect the interaction strength of the hydrogen/halogen bond. Here, we calculated the change of R₂ relative to the R₂ in the monomer, denoted as ΔR₂%, using the following formula:

$${\mathsf{\Delta }\mathrm{R}}_2\%=\frac{{\mathsf{\Delta }\mathrm{R}}_2}{{\mathrm{R}}_2}\times 100\%$$

(2)

The ΔR₂% represents the elongation percentage of the X-F bond, and the larger ΔR₂% implies more significant weakening of the bond and, thus, stronger interaction. As indicated by ΔR₂%, the value of X-F bond length is larger in the halogen-bonded complex than that in the hydrogen-bonded analogue. This relative elongation in the halogen-bonded complex decreases in the order of F₂ > ClF > BrF > IF. These data are supportive of the conclusions from ΔR₁%.

The Te∙∙∙X-F angle (α) is in the range of 168–180°, confirming a good direction of the hydrogen/halogen bonds. The angles are less than 180° in the majority of the complexs due to the attraction between the Y atom/group in Y₂CTe and XF.

2.3. Energies

Here, we consider the interaction energy to be the most credible criteria to judge the strength of interactions. Therefore, we calculated the interaction energies (E_int) of the various complexes for comparing the hydrogen and the halogen bonds. We used the counterpoise correction method to eliminate the basis set superposition error (BSSE), and the corrected energy is denoted as E_int,BSSE. In addition, the more accurate energy E_int,CBS,BSSE with complete basis set (CBS) was also calculated. The results with and without BSSE correction, as well as with CBS, are all listed in

Table 2. Interaction energies (E_int) corrected with and without BSSE in the complexes at the MP2/aug-cc-pVTZ(PP) level, all in kJ/mol.

		HF	F2	ClF	BrF	IF
H2CTe	Eint	−27.8	−232.6	−107.0	−100.0	−94.8
	Eint,BSSE	−21.1	−220.7	−96.7	−87.0	−81.5
	Eint,CBS,BSSE	−22.3	−225.5	−106.5	−95.6	−89.9
F2CTe	Eint	−21.1	−206.9	−61.2	−66.4	−68.8
	Eint,BSSE	−14.5	−194.4	−52.7	−54.8	−56.4
	Eint,CBS,BSSE	−15.6	−199.8	−60.5	−61.7	−63.6
(CH3)2CTe	Eint	−33.7	−242.2	−128.1	−120.0	−111.8
	Eint,BSSE	−26.3	−228.8	−116.4	−103.6	−94.7
	Eint,CBS,BSSE	−27.7	−233.1	−126.5	−112.5	−103.3

. The main concern of our study is that the changing trends of the interaction energy with the variation of X in XF are the same based on all the three methods. It is worth clarifying that the following discussions about energies in the full text are all according to their absolute values. As shown in Table 2, the interaction energies of hydrogen bonds in all of the three series of complexes are smaller than those of the halogen bonds, indicating that the hydrogen bonds are weaker than all of the halogen bonds. For the strength order of the halogen bonds, both E_int,BSSE and E_int,CBS,BSSE increased in the order of IF < BrF < ClF < F₂ for the series of H₂CTe∙∙∙XF and (CH₃)₂CTe∙∙∙XF complexes. This result is abnormal compared to the common perception that the halogen bond becomes stronger with the halogen donor varying from F to I. For F₂CTe∙∙∙XF complexes, the E_int,BSSE/E_int,CBS,BSSE of ClF, BrF, and IF was close. For all of the three series of the complexes, F₂ molecules formed the strongest halogen bonds. The absolute values of the interaction energy were very large, up to 228.8 kJ/mol for E_int,BSSE and 233.1 kJ/mol for E_int,CBS,BSSE. To compare the interaction energies of the halogen bonds formed by different acceptors (Y₂CTe), when Y is F, an electron-withdrawing atom, the Y₂CTe∙∙∙XF interaction, was weakened and compared to that of H₂CTe. On the contrary, when Y was the electron-donating methyl group, the interaction was strengthened.

To understand the attribution of the interaction energy, we partitioned it into five terms: electrostatic energy (E^es), exchange energy (E^ex), repulsion energy (E^rep), polarization energy (E^pol), and dispersion energy (E^disp), and the data are listed in

Table 3. Electrostatic (E^es), exchange energy (E^ex), repulsion energy (E^rep), polarization (E^pol), and dispersion (E^disp) energies in the complexes, all in kJ/mol.

	Ees	Eex	Erep	Epol	Edisp
H2CTe∙∙∙HF	−33.0	−48.9	90.4	−21.3	−8.3
H2CTe∙∙∙F2	−246.0	−519.1	1097.3	−442.5	−110.3
H2CTe∙∙∙ClF	−255.5	−474.9	985.5	−278.4	−73.4
H2CTe∙∙∙BrF	−251.3	−417.7	865.0	−223.0	−60.1
H2CTe∙∙∙IF	−183.2	−346.0	678.3	−182.8	−47.8
F2CTe∙∙∙HF	−22.8	−38.4	70.8	−16.7	−7.4
F2CTe∙∙∙F2	−242.6	−524.2	1109.5	−423.0	−114.1
F2CTe∙∙∙ClF	−170.5	−344.4	695.7	−169.2	−63.9
F2CTe∙∙∙BrF	−171.7	−312.3	630.0	−148.2	−52.6
F2CTe∙∙∙IF	−129.4	−265.6	510.3	−129.3	−42.3
(CH3)2CTe∙∙∙HF	−46.2	−64.5	118.7	−26.2	−8.1
(CH3)2CTe∙∙∙F2	−253.4	−533.8	1116.9	−457.1	−101.5
(CH3)2CTe∙∙∙ClF	−287.7	−522.2	1080.9	−315.4	−72.1
(CH3)2CTe∙∙∙BrF	−287.6	−468.2	966.8	−253.4	−61.2
(CH3)2CTe∙∙∙IF	−211.6	−391.0	763.3	−205.4	−50.0

. Obviously, E^ex is the largest attractive term in each complex; thus, it plays the most important role in the stabilization of hydrogen/halogen bonds [35,36]. This term increases in the order of HF < IF < BrF < ClF < F₂, which is consistent with the results of orbital interaction discussed in the following section. The large E^ex of each complex suggests a strong orbital interaction between the two respective monomers. For the repulsive term, E^rep was very large and even exceeds 1000 kJ/mol in each F₂-related complex. This can be attributed to the much shorter Te∙∙∙X distances. It is seen that E^rep was almost twice as much as E^ex and both terms have a good linear relationship (Figure S1), confirming their dependency each other.

Now, we examine the three attractive terms (E^es, E^pol, and E^disp) in Table 3 in some detail (intuitively in Figure S2). For the hydrogen bond complex Y₂CTe∙∙∙HF, E^es was the largest attractive interaction among the three terms, followed by E^pol. For the interaction energies of halogen bonds formed by ClF, BrF, or IF with all the three acceptors Y₂CTe, the contributions of electrostatic and polarization interactions are comparable. However, for the interaction energies of the halogen bonds formed by F₂ with the Y₂CTe, the polarization interaction is the dominating contribution. This may be attributed to the special property of F, namely the largest electronegativity in the periodic table, thus possessing a very strong inducing ability.

2.4. Atoms in Molecules (AIM) Analyses

The hydrogen/halogen bonds can be characterized by the Te∙∙∙X bond critical points (BCPs, Figure S3). The most important properties of each bond critical point are summarized in

Table 4. Electron density (ρ), Laplacian (∇²ρ), and total energy density (H) at the intermolecular BCP in the complexes (all values in a.u.).

	ρ	∇2ρ	H
H2CTe∙∙∙HF	0.022	0.032	−0.003
H2CTe∙∙∙F2	0.095	0.101	−0.036
H2CTe∙∙∙ClF	0.079	0.024	−0.027
H2CTe∙∙∙BrF	0.066	0.033	−0.020
H2CTe∙∙∙IF	0.052	0.041	−0.013
F2CTe∙∙∙HF	0.019	0.032	−0.001
F2CTe∙∙∙F2	0.096	0.112	−0.036
F2CTe∙∙∙ClF	0.060	0.058	−0.015
F2CTe∙∙∙BrF	0.052	0.053	−0.012
F2CTe∙∙∙IF	0.042	0.049	−0.008
(CH3)2CTe∙∙∙HF	0.025	0.031	−0.004
(CH3)2CTe∙∙∙F2	0.091	0.088	−0.033
(CH3)2CTe∙∙∙ClF	0.082	0.013	−0.029
(CH3)2CTe∙∙∙BrF	0.069	0.024	−0.022
(CH3)2CTe∙∙∙IF	0.054	0.036	−0.015

, where ρ refers to the electron density, ∇²ρ its Laplacian, and H the energy density [37,38,39]. Generally, the larger electron density ρ reflects the stronger interaction. For all the investigated systems, ρ increases in the sequential order of HF < IF < BrF < ClF < F₂, in agreement with the order of interaction energies (Table 2). For the Laplacian, it was seen that ∇²ρ > 0 for all the complexes, demonstrating that the interactions studied were closed shell interaction. The energy density H is a more sensitive parameter than ∇²ρ. The negative values of H further demonstrate that the interactions are partially covalent in nature. In the complexes involving (CH₃)₂CTe, there are also BCPs between the methyl H and the halogen X in HX or XFs (Figure S3), indicating the presence of C-H∙∙∙F/X hydrogen bonds. The interaction energies of the C-H∙∙∙F/X hydrogen bonds were estimated by E = 0.5V(r) [40,41], where V(r) is the potential energy density at a BCP in each case. The corresponding data are −5.6, −17.8, −10.3, −9.9, and −8.1 kJ/mol for (CH₃)₂CTe∙∙∙HF, (CH₃)₂CTe∙∙∙F₂, (CH₃)₂CTe∙∙∙ClF, (CH₃)₂CTe∙∙∙BrF, and (CH₃)₂CTe∙∙∙IF, respectively. Clearly, these hydrogen bonds contributed to the stability of the complexes; however, their shares in the total interaction energies (Table 2) are small. Subtracting them from the total interaction energies, the residual results still have the same change trend with the total interaction energy. Thus, the presence of C-H∙∙∙F/X hydrogen bonds does not affect the abnormality of halogen bonds.

2.5. Natural Bond Orbital (NBO) Analyses

The charge transfers (CTs) from Y₂CTe to XF are listed in

Table 5. Charge transfer (CT, e), second-order perturbation energy (E², kJ/mol), and dipole moment (μ, D) in the complexes.

	CT	E2	μ
H2CTe∙∙∙HF	0.043	70.0	3.17
H2CTe∙∙∙F2	0.893	-	10.52
H2CTe∙∙∙ClF	0.511	781.6	8.23
H2CTe∙∙∙BrF	0.414	761.4	7.87
H2CTe∙∙∙IF	0.322	636.6	7.81
F2CTe∙∙∙HF	0.031	51.0	2.88
F2CTe∙∙∙F2	0.843	-	9.53
F2CTe∙∙∙ClF	0.334	462.3	5.62
F2CTe∙∙∙BrF	0.293	417.7	5.93
F2CTe∙∙∙IF	0.242	334.3	6.34
(CH3)2CTe∙∙∙HF	0.056	93.3	4.76
(CH3)2CTe∙∙∙F2	0.943	-	11.73
(CH3)2CTe∙∙∙ClF	0.579	711.7	10.37
(CH3)2CTe∙∙∙BrF	0.462	696.9	9.96
(CH3)2CTe∙∙∙IF	0.350	613.1	9.84

, which are calculated as the sum of the charge on all atoms in Y₂CTe in the complexes. The charge transfer reflects the electrons bias from electron donor (Y₂CTe) to electron acceptor (XF), providing information about the interaction strength in one aspect. As can be seen, the CTs are all larger than 0.2 e in the halogen bonds and even exceed 0.8 e in the F₂ complexes. On the contrary, the hydrogen-bonded complexes have much smaller CTs than the halogen-bonded analogues. Additionally, for all three of the series of complexes, the CT value decreases in the order F₂ > ClF > BrF > IF > HF, which is the same as the interaction strength order. Besides, when the Y is the electron-withdrawing atom F in Y₂CTe, the CT becomes smaller than that in H₂CTe. When the Y is the electron-donating methyl group, the CT increases.

There is an orbital interaction between the lone pair orbital on the Te atom of Y₂CTe and the anti-bonding orbital of the X-F bond (Lp_Te→σ^*x-_F), and this orbital interaction can be measured with the second-order perturbation energy (E²), which is also listed in Table 5. This orbital interaction is not detected in the F₂-containing complexes since the F-F bond is taken as two subunits in the NBO analysis. The E² has a consistent change order with the charge transfer. This orbital interaction is strong; therefore, it makes an important contribution to the formation of hydrogen/halogen bond. We also calculated the dipole moments of the complexes (Table 5). It was found that the order of the dipole moment is consistent with the interaction energy. Further, the relationship between the CTs and the population of the σ*x-_F orbital was analyzed, and positive correlation was found (Figure S4). This suggests that the main destination/receiver of the CT is the σ*x-_F orbital in each complex.

3. Discussion

Hydrogen bonds and halogen bonds are two important noncovalent interactions, and they often coexist; thus, it is interesting to compare their strength. Generally speaking, hydrogen bonds are considered to be stronger than halogen bonds [28]. Interestingly, in the present study, using Y₂CTe (Y = H, F, and CH₃) as electron donors, we found that their halogen bonding interactions with dihalogen molecules XF (X = F, Cl, Br, and I) are stronger than their hydrogen bonding interactions with HF. This apparent abnormality was also seen in a previous study on the interactions between PH₃/AsH₃/H₂Te and 6-OX-fulvene (X = H, Cl, Br, I) [31]. The second abnormality found in this work was that, when the X changes from F to I, the halogen bond becomes weaker, in contrast to the normal understanding that stronger halogen bonds accompany heavier halogen donors [16]. The abnormalities can be explained by the high polarizability of the Te atom, which is easily polarized when the electronegative XF approaches it. The greater the electronegativity of the approaching atom, the greater the polarization of the Te atom. Therefore, when the X atom of XF varies from I to F, the dipole moment of the complex increases, as seen in Table 5, and the polarization energy (the major contribution to the interaction energy) also increases. Based on the data in Table 3 and Table 5, a near positive correlation between the polarization energy and the dipole moment of the complex is found (Figure S5).

Another surprising result was that F₂ participates in the strongest halogen bond with the interaction energy up to −233.1 kJ/mol in the (CH₃)₂CTe∙∙∙F₂ complex. Such large interaction energy is abnormal because it shows the least MEP at the end of the X atom among the four XF molecules. The apparent contradiction can be reconciled as follows. The F atom of F₂, due to it having the highest electronegativity among the halogens, would cause the largest polarization on the Te atom and, thus, the largest dipole moment of the Y₂CTe∙∙∙XF complex. This is evidenced by the largest polarization energies being seen in the three Y₂CTe∙∙∙F₂ complexes. The polarization mechanism is also consistent with the charge transfer data, which are the biggest in the Y₂CTe∙∙∙F₂ complexes, even as big as 0.943e in the complex of (CH₃)₂CTe∙∙∙F₂. Such big charge transfers (>0.8e) mean that the molecule F₂ holds nearly an extra electron in each of the three complexes, similar to the process of becoming an anion.

In order to test if the above abnormal results are found only for Y₂CTe, the Te atom of H₂CTe was replaced by O, S, and Se. The corresponding interaction energies are listed in

Table 6. Interaction energies (E_int,BSSE, kJ/mol) of complexes between H₂CZ (Z = O, S, Se, and Te) and XF (X = H, F, Cl, Br, and I) at the MP2/aug-cc-pVTZ(PP) level.

	HF	F2	ClF	BrF	IF
H2CO	−34.4	−5.9	−25.2	−34.4	−42.3
H2CS	−26.6	−7.3	−52.2	−60.6	−64.0
H2CSe	−24.6	−171.7	−64.7	−68.2	−69.6
H2CTe	−21.1	−220.7	−96.7	−87.0	−81.5

. For the lighter chalcogen atoms O and S, the halogen bond strength increases in the order of F₂ < ClF < BrF < IF, which is the “normal” understanding of halogen bonds. For the heavier Se as the electron donor, the halogen bonds formed by ClF, BrF, and IF turned out to be comparable, while that formed by F₂ increased tremendously. This complicated situation is explained as follows. On one hand, a Se atom with a larger radius is more easily polarized than O and S. On the other hand, it is not as easily polarized as Te. Thus, only the most electronegative F₂ is able to assert marked influence on the electron distribution of H₂CSe, making it the strongest interaction in the H₂CSe∙∙∙XF complexes.

As discussed above, the size/polarizability of the chalcogen atoms in H₂CZ (Z = O, S, Se, and Te) plays a very important role in the strength of halogen bonds. The data in Table 6 demonstrate that, for a given XF (X = F, Cl, Br, and I), the strength of its halogen bond with H₂CZ increases monotonously when Z varies from O to Te. On the contrary, the strength of the hydrogen bond between HF and H₂CZ decreases monotonously. As a result, for H₂CO, only IF forms a stronger halogen bond than the hydrogen bond. For H₂CS, each dihalogen molecule, excluding F₂, participates in a stronger halogen bond than the hydrogen bond formed by HF. For H₂CSe and H₂CTe, all the dihalogen molecules form stronger halogen bonds than hydrogen bonds formed by HF.

The above discussions about the interaction strength of halogen/hydrogen bonds are based on their interaction energies, often regarded as golden criteria. Practically, other parameters such as electrostatic potential (MEP), halogen/hydrogen bond length (R₁), and donor bond length (R₂) are often used to compare the interaction strength. MEP sometimes provides correct indications. For example, the MEP order is Cl < Br < I at the end of X atom in XF, and the halogen bond strength order is ClF < BrF < IF in the F₂CTe∙∙∙XF complexes. However, the F has the least MEP at the end of the X atom among the four XF molecules, but it forms the strongest interaction with F₂CTe. Clearly, MEP cannot always provide correct results because it only contains the information of isolated molecules. For R₁ and R₂, due to the different radii of the halogen atoms, we defined two quantities, ΔR₁% and ΔR₂%, to compare the halogen/hydrogen bond strength. The correlations between the two quantities and the respective interaction energies are plotted in Figure 3 (the trend comparisons are shown in Figure S6). Undoubtedly, they are all positively correlated, suggesting that both ΔR₁% and ΔR₂% can be used to compare the halogen/hydrogen bond strength qualitatively. Quantitatively, ΔR₂% is a better choice.

4. Computational Methods

All calculations were carried out with the Gaussian 09 program [42]. The geometries of all the monomers and complexes were optimized at the MP2 level with the aug-cc-pVTZ basis set for all atoms except I and Te, where the aug-cc-pVTZ-PP basis set was adopted to account for relativistic corrections [43]. For all atoms in all the complexes, collectively, aug-cc-pVTZ(PP) represents the basis set used in this work. The extrema of molecular electrostatic potentials (MEPs) were calculated on the 0.001 a.u. isodensity surface at the MP2/aug-cc-pVTZ(PP) level using the WFA-SAS program [32]. The interaction energy (E_int) of a complex was computed as the difference between the energy of the complex and the sum of the energies of the monomers with their geometries frozen in the optimized complex. For this supermolecular method of calculating the MP2 interaction energy, the dispersion correction was taken into account, since MP2 contains certain correlation terms such as the uncoupled Hartree-Fock (UCHF) dispersion energy, the corresponding Hartree-Fock exchange-dispersion energy, and a deformation-correlation term [44]. Interaction energies were corrected for basis set superposition error (BSSE) using the counterpoise procedure (CP) proposed by Boys and Bernardi [45]. The two-point extrapolated energies with a complete basis set (CBS) proposed by Halkier et al. [46,47] were obtained with two basis sets of aug-cc-pVDZ(PP) and aug-cc-pVTZ(PP). The localized molecular orbital-energy decomposition analysis was used to decompose the interaction energy into five terms of electrostatic, exchange, repulsion, polarization, and dispersion at the MP2/aug-cc-pVTZ(PP) level with the GAMESS program [48]. The dispersion energy was obtained as a difference between the MP2 and CCSD(T) energy in the GAMESS program. The AIM2000 package [49] was used to assess the topological parameters at each bond critical point (BCP), including electron density, as well as its Laplacian, and energy density. Using the natural bond orbital (NBO) method [50] within the Gaussian 09 program, the charge transfer and second-order perturbation energy were obtained.

5. Conclusions

Quantum chemical calculations have been performed to study the interactions between Y₂CTe (Y = H, F, and CH₃) and XF (X = H, F, Cl, Br, and I). The results show that the electron-withdrawing groups F in F₂CTe weaken the interactions, while the electron-donating methyl groups in (CH₃)₂CTe strengthen them. More importantly, we found three abnormalities regarding halogen bonds in this work. The first one is that the strength of halogen bond increases in the sequential order IF < BrF < ClF < F₂ in H₂CTe∙∙∙XF and (CH₃)₂CTe∙∙∙XF complexes. This is contrary to the normal understanding that the stronger halogen bonds accompany heavier halogen donors. The second one is that the halogen bonds formed by F₂ are very strong, even up to −233.1 kJ/mol with (CH₃)₂CTe. Contrary to this, the halogen bonds formed by F-R are normally considered to be very weak or even negligible. The last one is that all halogen bonds are stronger than the hydrogen bonds in the complexes, which is abnormal compared with the majority of previous studies. These abnormalities are discussed in the context of the high polarizability of the Te atom in the halogen acceptors. Because the Te atom is easily polarized when the electronegative XF approaches it, the greater the electronegativity of the X atom, the greater the polarization of the Te atom. Particularly, the F atom has the largest electronegativity in the periodic table and possesses a very strong inducing ability. Consequently, F-F forms tremendously strong interactions with Y₂CTe.