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 H
2CO 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 H
2CO is changed to H
2CS [
28]. This difference is enlarged to 2 kJ/mol when one H atom of H
2CS 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 ZH
3/H
2Y (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 SbH
3 and H
2Te 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 SbH
3∙∙∙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?
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 Y
2CTe (Y = H, F, and CH
3) 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 PH
3/AsH
3/H
2Te 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 Y
2CTe, the Te atom of H
2CTe was replaced by O, S, and Se. The corresponding interaction energies are listed in
Table 6. For the lighter chalcogen atoms O and S, the halogen bond strength increases in the order of F
2 < 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 F
2 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 F
2 is able to assert marked influence on the electron distribution of H
2CSe, making it the strongest interaction in the H
2CSe∙∙∙XF complexes.
As discussed above, the size/polarizability of the chalcogen atoms in H
2CZ (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 H
2CZ increases monotonously when Z varies from O to Te. On the contrary, the strength of the hydrogen bond between HF and H
2CZ decreases monotonously. As a result, for H
2CO, only IF forms a stronger halogen bond than the hydrogen bond. For H
2CS, each dihalogen molecule, excluding F
2, participates in a stronger halogen bond than the hydrogen bond formed by HF. For H
2CSe and H
2CTe, 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 (R
1), and donor bond length (R
2) 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 F
2CTe∙∙∙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 F
2CTe. Clearly, MEP cannot always provide correct results because it only contains the information of isolated molecules. For R
1 and R
2, due to the different radii of the halogen atoms, we defined two quantities, ΔR
1% and ΔR
2%, 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 ΔR
1% and ΔR
2% can be used to compare the halogen/hydrogen bond strength qualitatively. Quantitatively, ΔR
2% 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.