Skip to main content
NCBI home page
ACS Omega logoLink to ACS Omega
. 2020 Nov 12;5(46):30210–30225. doi: 10.1021/acsomega.0c04682

Intermolecular Interactions Involving Heavy Alkenes H2Si=TH2 (T = C, Si, Ge, Sn, Pb) with H2O and HCl: Tetrel Bond and Hydrogen Bond

Yishan Chen 1,*, Fan Wang 1
PMCID: PMC7689927  PMID: 33251455

Abstract

graphic file with name ao0c04682_0014.jpg

The intermolecular interactions between the heavy alkenes H2Si=TH2 (T = C, Si, Ge, Sn, Pb) and H2O or HCl have been explored at the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVDZ level. The various hydrogen bond (HB) and tetrel bond (TB) complexes can be located on the basis of molecular electrostatic potential maps of the isolated monomers. The competition between TB and HB interactions has been investigated through the relaxed potential energy surface scan. The results indicate that the HB complexes become more and more unstable relative to the TB complexes with the increase of the T atomic number, and cannot even retain as a minimum in some cases, for H2Si=TH2···H2O systems. In contrast, the HB complexes are generally more stable than TB complexes, and the TB complexes exhibit rather weak binding strength, for H2Si=TH2···HCl systems. The majority of the TB complexes formed between H2Si=TH2 and H2O possesses very strong binding strength with covalent characteristics. The noncovalent TB complexes can be divided into two types on the basis of the orbital interactions: π-hole complexes, with binding angles ranging from 91 to 111°, and hybrid σ/π-hole complexes, with binding angles ranging from 130 to 165°. The interplay between different molecular interactions has been explored, and an interesting result is that the covalent TB interaction is significantly abated and becomes noncovalent because of the competitive effect.

1. Introduction

Noncovalent interactions are a central issue of supermolecular chemistry and have attracted continuous attention from experimental and theoretical chemistry community.1−3 Hydrogen bonds (HBs) are the first widely used noncovalent interaction in supermolecular systems,4 and another important noncovalent interaction is the halogen bond.5−11 A region of lower electronic density on the extension of a bond is called a σ-hole,12 which was first employed to clarify the formation of halogen bond, and then, this concept was expanded to explain the other types of noncovalent interactions, such as tetrel,13−35 pnicogen,36 and chalcogen37 bonds. Similarly, a region of a lower electronic density above and below a planar portion of a molecule is called a π-hole,38 which was also used to clarify the noncovalent interactions.

Since the first stable heavy alkene with a Sn=Sn double bond was successfully synthesized and reported in 1973,39 plenty of experimental studies have been carried out in this area,40−51 and some theoretical studies about the mechanism of their reactions have been performed.52−56 However, a comprehensive and comparative study of the noncovalent interactions involving heavy alkenes is still absent. Besides the lone pair, the π-system such as an alkene or aromatic compound is a common type of electron donor for noncovalent interaction. Because ethene is a well-known electron donor for HB,57 a natural and logical question arises: are the heavy alkenes also effective as electron donors for forming HB with other electron acceptors? On the other hand, the heavy alkenes can easily react with water or alcohol without a catalysis to form addition products,58 which indicates that the heavy alkenes are highly electrophilic. Once again, the second question arises: can the heavy alkenes act as electron acceptors for forming the tetrel bond (TB) with other electron donors? This TB interaction involves heavy alkenes in which both of tetrel atoms are sp2 hybridization, and this study can be expected to provide some new insights into the TB interaction.

In this study, we select H2O and HCl as the probe molecules to investigate the dual behavior of the selected heavy alkenes H2Si=TH2 (T = C, Si, Ge, Sn, Pb) in HB and TB interactions. H2O and HCl are well known for their dual behavior in HB interaction, and both of them are strong electron acceptors when they act as proton donors. However, on the other hand, H2O is a considerably better electron donor than HCl when they act as proton acceptors.57 We first plot molecular electrostatic potential (MEP) maps of H2Si=TH2 in order to find the possible binding modes for the complexes formed between H2Si=TH2 and H2O or HCl, and then, the geometries and binding strength of the complexes are discussed in detail. Furthermore, the competition between TB and HB interactions in the selected systems is clarified through the relaxed potential energy surface scan. There is another important issue. Are the TB interactions in theses complexes σ-hole or π-hole interactions? We answer this question by investigating the orbital interaction involved in the complexes. It has been well known that the strength of a molecular interaction can be enhanced or weakened through synergistic or competitive interplay with another molecular interaction,59−69 and finally, we explore the change in binding pattern of the selected complexes because of the interplay between different noncovalent interactions.

2. Computational Methods

The geometries of all the monomers and complexes investigated in this study were fully optimized at the MP2 level of theory using the Gaussian 09 programs.70 The aug-cc-pVDZPP basis set, which uses pseudopotentials to describe the inner core orbitals,71 was applied to Sn and Pb atoms, whereas aug-cc-pVDZ was used for else atoms. The vibrational frequencies were calculated for all the optimized geometries at the same level. As a comparison, the geometries of monomers and binary complexes were reoptimized at the MP2/aug-cc-pVTZ level. Single-point energy calculations were performed at the CCSD(T)/aug-cc-pVTZ level to obtain more accurate energies. Binding energy is defined as the difference between the energy of the complex and the sum of the monomers in their optimzed geometries. Interaction energy is defined as the difference between the energy of the complex and the sum of the monomers retaining their internal geometries as in the complex. Basis set superposition error correction was carried out following the counterpoise method.72 The relaxed potential energy surface scans were performed for some selected complexes at the MP2/aug-cc-pVDZ level. Natural bond orbital (NBO) analysis73 was performed via the procedures contained within Gaussian 09, and atoms in molecules (AIM) analysis74 and MEP calculation were carried out using the Multiwfn program.75 The MEP maps were generated on a 0.001 a.u. isodensity surface.

3. Results and Discussion

3.1. Monomers: Geometries and MEP Surfaces

The optimized geometries and NBO analysis results [natural charge and Wiberg bond index (WBI) of Si=T bond] of the heavy alkenes (1–5) are illustrated in Figure 1. The structure of silene (1) is essentially planar, while the other alkenes (2–5) are trans-bent, which is consistent with the experimental reports.46 The dihedral D(H–Si–T–H) increases with the increase of the T atomic number, indicating that the degree of nonplanarity of H2Si=TH2 becomes larger for the heavier T atom. The values of WBI of Si=T bond are smaller than 2 for all the alkenes, as displayed in Figure 1, and the WBI value of the homonuclear disilene (2) is closer to 2 than the other heteronuclear alkenes.

Figure 1.

Figure 1

Open in a new tab

Optimized geometries of the heavy alkenes, distances in Å, and natural charges in e: top view (left) and side view (right).

The framework of the present study is based on the MEP surface analysis for the isolated monomers. As illustrated in Figure 2, the MEP maps of the heavy alkenes clearly elucidate their dual behavior. The positive areas of electrostatic potential imply that these alkenes can act as an electron acceptor (Lewis acid), while the negative regions suggest that these molecules can also serve as an electron donor (Lewis base). In this study, we select H2O and HCl as the probe molecules to explore the binding sites and strengths for the complexes formed between the heavy alkenes and H2O or HCl. As shown in Figure 3, H2O and HCl also exhibit the dual behavior. The hydrogen atoms in H2O and HCl can be expected to act as an electron acceptor to form the HB complexes with the alkenes, while the oxygen and chlorine atoms in H2O and HCl can be expected to serve as an electron donor to form the TB complexes. The HB complex (6) formed between H2O and HCl is also displayed in Figure 3 and will be discussed in Section 3.6.

Figure 2.

Figure 2

Open in a new tab

MEP surfaces of the heavy alkenes, VS,max and VS,min in kcal mol–1: side view (left), top view (middle), and bottom view (right).

Figure 3.

Figure 3

Open in a new tab

Optimized geometries of H2O, HCl, and complex 6, distances in Å, and natural charges in e; MEP surfaces, VS,max and VS,min in kcal mol–1.

According to the distribution of the most positive (VS,max) and negative (VS,min) potentials on the MEP maps, the approximate binding sites of HB and TB interactions for the alkenes are illustrated in Figure 2. It should be noted that Figure 2 just displays the rough locations of VS,max and VS,min, and their accurate locations will be illustrated and discussed in Section 3.3. H2Si=CH2 is a molecule with C2v symmetry. The two identical TB binding sites with planar symmetry are located around the Si atom for H2Si=CH2, while the two identical HB binding sites with planar symmetry are located around the C atom for it. H2Si=SiH2 is of C2h symmetry, and it has two identical TB binding sites with central symmetry. Similarly, two identical HB binding sites with central symmetry can be located for H2Si=SiH2. H2Si=GeH2, H2Si=SnH2, and H2Si=PbH2 are all Cs symmetry, and they possess more binding modes than H2Si=CH2 and H2Si=SiH2. In contrast with H2Si=SiH2, H2Si=GeH2 has two different TB binding sites which are distinguished as type-A and type-B TB binding sites. Similarly, the two different HB binding sites are named as type-A and type-B HB binding sites for H2Si=GeH2. The binding sites of H2Si=SnH2 and H2Si=PbH2 are similar to those of H2Si=GeH2 except that H2Si=SnH2 and H2Si=PbH2 exhibit a third (referred as type-C) TB binding site.

3.2. Computational Levels: A Comparison

The previous studies indicate that the interaction energies of complexes calculated at the MP2/aug-cc-pVTZ level are very similar to those at the CCSD(T)/aug-cc-pVTZ level in some cases. However,76 in other cases, the MP2/aug-cc-pVTZ level overestimates the interaction energies with respect to the CCSD(T)/aug-cc-pVTZ values.77 Furthermore, it has been certified that the interaction energies at the MP2/aug-cc-pVDZ level are close to the CCSD(T)/aug-cc-pVTZ results for some intermolecular interactions.78 Considering that the extensive study of intermolecular interactions involving the heavy alkenes has not been reported before, it is necessary to investigate the performance of MP2/aug-cc-pVTZ and MP2/aug-cc-pVDZ levels by comparing the calculated energies at these two levels with those at the CCSD(T)/aug-cc-pVTZ level. The binding and interaction energies at the four different computational levels are listed in Table 1. The four levels are designated as L1 (MP2/aug-cc-pVDZ), L2 (CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVDZ), L3 (MP2/aug-cc-pVTZ), and L4 (CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ), respectively.

Table 1. Binding (Eb) and Interaction Energies (Eint) for Binary Complexes at Various Computational Levels, in kcal mol–1.

    Eba
 Einta
complex binding mode L1 L2 L3 L4 L12 L34 L1 L2 L3 L4 L12 L34
7 (1 + H2O) TB –2.57 –2.69 –3.37 –2.14 0.12 –1.23 –2.67 –2.80 –3.93 –2.60 0.13 –1.33
8 (1 + H2O) HB –2.98 –3.03 –3.49 –3.01 0.05 –0.47 –3.05 –3.15 –3.56 –3.08 0.10 –0.48
9 (1 + HCl) TB –0.72 –0.75 –0.95 –0.72 0.03 –0.23 –0.73 –0.76 –0.96 –0.72 0.03 –0.24
10 (1 + HCl) HB –4.11 –3.53 –4.61 –3.51 –0.58 –1.10 –4.34 –3.91 –4.87 –3.67 –0.43 –1.20
11 (2 + H2O) TB –2.07 –2.33 –3.08 –2.06 0.26 –1.03 –4.03 –3.73 –7.82 –5.49 –0.30 –2.33
12 (2 + H2O) HB –1.87 –1.91 –2.29 –1.89 0.04 –0.40 –1.90 –2.04 –2.33 –2.05 0.14 –0.28
13 (2 + HCl) TB –0.82 –0.88 –0.99 –0.87 0.06 –0.12 –0.85 –0.82 –1.03 –0.76 –0.03 –0.27
14 (2 + HCl) HB –2.76 –2.31 –3.22 –2.28 –0.45 –0.93 –2.88 –2.61 –3.35 –2.51 –0.27 –0.84
15 (3 + H2O) type-A TB –2.75 –4.10 –6.08 –4.34 1.35 –1.75 –19.43 –21.47 –22.84 –20.94 2.04 –1.90
16 (3 + H2O) type-B TB –1.96 –1.61 –2.16 –1.97 –0.35 –0.19 –3.03 –2.49 –2.79 –2.07 –0.54 –0.72
17 (3 + H2O) type-A HB –1.79 –1.85 –2.15 –1.76 0.06 –0.40 –1.82 –1.97 –2.20 –1.89 0.15 –0.31
18 (3 + H2O) type-B HB –1.65 –1.71 –2.12 –1.69 0.06 –0.43 –1.69 –1.82 –2.16 –1.80 0.13 –0.36
19 (3 + HCl) type-A TB –0.91 –0.94 –1.08 –0.89 0.03 –0.18 –0.94 –0.91 –1.12 –0.79 –0.03 –0.33
20 (3 + HCl) type-B TB –0.86 –0.88 –0.97 –0.81 0.02 –0.16 –0.89 –0.86 –1.00 –0.71 –0.03 –0.29
21 (3 + HCl) type-A HB –2.69 –2.23 –3.11 –2.15 –0.46 –0.96 –2.81 –2.52 –3.24 –2.34 –0.29 –0.90
22 (3 + HCl) type-B HB –2.53 –2.09 –3.04 –2.07 –0.44 –0.97 –2.64 –2.36 –3.16 –2.22 –0.28 –0.94
23 (4 + H2O) type-A TB –8.90 –10.20 –12.71 –10.43 1.30 –2.28 –26.89 –28.83 –31.13 –28.47 1.94 –2.66
24 (4 + H2O) type-B TB –3.82 –3.09 –4.51 –3.05 –0.73 –1.45 –12.89 –13.35 –14.38 –13.21 0.46 –1.17
25 (4 + H2O) type-C TB –5.72 –5.11 –6.49 –5.05 –0.61 –1.44 –12.33 –12.40 –13.60 –11.65 0.07 –1.95
26 (4 + H2O) type-B HB –1.64 –1.56 –1.91 –1.52 –0.08 –0.39 –1.70 –1.69 –1.95 –1.57 –0.01 –0.38
27 (4 + HCl) type-A TB –0.98 –1.04 –1.27 –0.96 0.06 –0.31 –1.01 –1.01 –1.31 –0.88 0.00 –0.43
28 (4 + HCl) type-B TB –1.35 –1.34 –1.56 –1.26 –0.01 –0.31 –1.40 –1.37 –1.64 –1.17 –0.03 –0.47
29 (4 + HCl) type-C TB –0.55 –0.62 –0.73 –0.53 0.07 –0.20 –0.58 –0.69 –0.77 –0.56 0.11 –0.21
30 (4 + HCl) type-A HB –2.75 –2.11 –3.11 –2.07 –0.64 –1.04 –2.89 –2.43 –3.26 –2.24 –0.46 –1.02
31 (4 + HCl) type-B HB –2.19 –1.79 –2.63 –1.71 –0.40 –0.93 –2.29 –2.03 –2.73 –1.84 –0.26 –0.89
32 (4 + HCl) DB –1.27 –1.48 –1.71 –1.42 0.21 –0.29 –1.41 –1.56 –1.82 –1.42 0.15 –0.40
33 (5 + H2O) type-A TB –18.33 –19.39 –22.23 –19.47 1.05 –2.76 –31.52 –33.84 –36.90 –34.13 2.32 –2.77
34 (5 + H2O) type-B TB –4.74 –4.35 –4.83 –4.19 –0.39 –0.64 –10.76 –11.22 –11.48 –10.51 0.46 –0.97
35 (5 + H2O) type-C TB –6.28 –5.94 –6.62 –5.78 –0.34 –0.84 –10.74 –11.02 –11.43 –9.97 0.28 –1.46
36 (5 + HCl) type-A TB –1.43 –1.37 –1.90 –1.16 –0.06 –0.74 –1.51 –1.42 –2.03 –1.15 –0.09 –0.88
37 (5 + HCl) type-A TB –1.27 –1.32 –1.65 –1.11 0.05 –0.53 –1.32 –1.34 –1.72 –1.06 0.02 –0.66
38 (5 + HCl) type-B TB –1.58 –1.60 –1.86 –1.48 0.01 –0.37 –1.71 –1.73 –1.99 –1.43 0.02 –0.56
39 (5 + HCl) type-C TB –0.64 –0.75 –0.85 –0.57 0.11 –0.28 –0.76 –0.91 –1.06 –0.69 0.15 –0.37
40 (5 + HCl) type-A HB –2.77 –2.20 –3.11 –2.12 –0.57 –0.99 –2.97 –2.56 –3.29 –2.28 –0.41 –1.01
41 (5 + HCl) type-B HB –1.72 –1.49 –2.01 –1.17 –0.23 –0.84 –1.82 –1.68 –2.08 –1.27 –0.14 –0.81
42 (5 + HCl) DB –1.54 –1.64 –2.00 –1.56 0.10 –0.45 –1.81 –1.89 –2.24 –1.69 0.08 –0.55
Open in a new tab
a

L1: MP2/aug-cc-pVDZ; L2: CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVDZ; L3: MP2/aug-cc-pVTZ; L4: CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ; L12: the difference between L1 and L2 levels; L134: The difference between L3 and L4 levels.

The deviation between L1 and L2 levels is smaller than that between L3 and L4 levels in most cases. For example, the binding energies for complex 7 at the L1 and L2 levels are −2.57 and −2.69 kcal mol–1, respectively, and those values at the L3 and L4 levels are −3.37 and −2.14 kcal mol–1, respectively. Complex 7 is not a special example: the average absolute deviation of binding energies between L1 and L2 levels is 0.32 kcal mol–1 for all the 36 complexes, whereas this value climbs up to 0.77 kcal mol–1 for L3 and L4 levels. Similarly, the average absolute deviation of interaction energies between L1 and L2 levels is 0.34 kcal mol–1 for all the 36 complexes, whereas this value climbs up to 0.90 kcal mol–1 for L3 and L4 levels, which means that the MP2/aug-cc-pVDZ level exhibits a better performance in calculating the energies for these complexes than MP2/aug-cc-pVTZ level. The differences in binding and interaction energies between L1 and L2 levels (L12), or between L3 and L4 levels (L34), are also listed in Table 1. It can be observed that nearly half of the L12 values (20 of 36 complexes) for binding energies are positive, suggesting that the distribution of deviation between L1 and L2 levels is random. In contrast, all the 36 L34 values for binding energies are negative, implying that the MP2/aug-cc-pVTZ level systematically overestimates the binding energies with respect to the CCSD(T)/aug-cc-pVTZ values. Similarly, nearly half of the L12 values (19 of 36) for interaction energies are positive, whereas all the L34 values for interaction energies are negative, indicating that the MP2/aug-cc-pVTZ level also systematically overestimates the interaction energies.

It can also be found that the L2 values are more negative than L4 values for most complexes, which means that the geometries of complexes optimized at the MP2/aug-cc-pVDZ level are generally more stable than those at the MP2/aug-cc-pVTZ level. The binding distances of complexes optimized at the L1 and L3 levels are collected in Table 2. The L1 values are larger than L3 values for most complexes, indicating that the complexes optimized at the MP2/aug-cc-pVTZ level are generally overbound with respect to those at the MP2/aug-cc-pVDZ level, in agreement with the systematic overestimate of energies at the MP2/aug-cc-pVTZ level. On the basis of the analysis above, it can be concluded that the MP2/aug-cc-pVDZ level is more reasonable than the MP2/aug-cc-pVTZ level for describing the geometries and energies of the complexes studied in this paper. The geometries at the MP2/aug-cc-pVDZ level and the energies at the CCSD(T)/aug-cc-pVTZ level are used in the following discussion.

Table 2. Binding Distance at MP2/aug-cc-pVDZ and MP2/aug-cc-pVTZ (in Parentheses) Levels (R, in Å), Second-Order Perturbation Stabilization Energy (E(2), in kcal mol–1), Wiberg Bond Index (WBISi=T), Electron Density (ρ, in a.u.), and Energy Density (H, in a.u.) of Bond Critical Points for Binary Complexes.

complex binding interaction R orbital interaction E(2) σ*/π* qCT WBISi=T ρ H
7 (1 + H2O) TB 2.776 (2.403) LP(O) → π*(Si=C) 11.07   0.0222 1.6555 0.0174 –0.0019
8 (1 + H2O) HB 2.371 (2.328) π(Si=C) → σ*(H–O) 7.09   –0.0108 1.7049 0.0143 0.0005
9 (1 + HCl) TB 3.706 (3.636) LP(Cl) → π*(Si=C) 2.23   0.0070 1.7411 0.0051 0.0005
10 (1 + HCl) HB 2.186 (2.158) π(Si=C) → σ*(H–Cl) 16.95   –0.0381 1.6756 0.0204 –0.0001
11 (2 + H2O) TB 2.361 (2.140) LP(O) → π*(Si=Si) 29.25 0.16 0.0770 1.6268 0.0338 –0.0103
      LP(O) → σ*(Si=Si) 4.79          
12 (2 + H2O) HB 2.942 (2.917) π(Si=Si) → σ*(H–O) 5.38   –0.0107 1.9104 0.0098 0.0001
13 (2 + HCl) TB 3.692 (3.638) LP(Cl) → π*(Si=Si) 2.01 0.57 0.0105 1.8863 0.0054 0.0005
      LP(Cl) → σ*(Si=Si) 1.14          
14 (2 + HCl) HB 2.817 (2.805) π(Si=Si) → σ*(H–Cl) 13.41   –0.0397 1.8834 0.0129 –0.0003
15 (3 + H2O) TB 2.008 (1.946)       0.1377 0.9964 0.0549 –0.0155
  DB 1.895 (1.855) σ(H–Ge) → σ*(H–O) 4.94       0.0190 –0.0005
16 (3 + H2O) TB 2.575 (2.690) LP(O) → π*(Si=Ge) 20.80 0.14 0.0523 1.6403 0.0263 –0.0028
      LP(O) → σ*(Si=Ge) 2.97          
17 (3 + H2O) HB 2.927 (2.909) π(Si=Ge) → σ*(H–O) 5.65   –0.0112 1.8496 0.0101 0.0001
18 (3 + H2O) HB 2.900 (2.847) π(Si=Ge) → σ*(H–O) 5.87   –0.0109 1.8516 0.0104 0.0001
19 (3 + HCl) TB 3.643 (3.554) LP(Cl) → π*(Si=Ge) 2.74 0.45 0.0128 1.8262 0.0059 0.0005
      LP(Cl) → σ*(Si=Ge) 1.23          
20 (3 + HCl) TB 3.692 (3.591) LP(Cl) → π*(Si=Ge) 1.91 0.87 0.0122 1.8244 0.0057 0.0005
      LP(Cl) → σ*(Si=Ge) 1.66          
21 (3 + HCl) HB 2.783 (2.801) π(Si=Ge) → σ*(H–Cl) 13.97   –0.0409 1.8221 0.0134 –0.0004
22 (3 + HCl) HB 2.802 (2.745) π(Si=Ge) → σ*(H–Cl) 13.60   –0.0390 1.8259 0.0132 –0.0004
23 (4 + H2O) TB 1.969 (1.908)       0.1016 0.8202 0.0596 –0.0149
  DB 1.522 (1.485) σ(H–Sn) → σ*(H–O) 30.11       0.0377 –0.0065
24 (4 + H2O) TB 2.370 (2.323) LP(O) → LP*(Sn) 56.98   0.0868 1.0046 0.0440 –0.0043
25 (4 + H2O) TB 2.379 (2.334) LP(O) → π*(Si=Sn) 36.94   0.0635 1.1142 0.0428 –0.0040
26 (4 + H2O) HB 3.225 (3.177) π(Si=Sn) → σ*(H–O) 3.25   –0.0058 1.6729 0.0086 0.0002
27 (4 + HCl) TB 3.610 (3.500) LP(Cl) → π*(Si=Sn) 3.32 0.39 0.0149 1.6664 0.0063 0.0005
      LP(Cl) → σ*(Si=Sn) 1.29          
28 (4 + HCl) TB 3.662 (3.571) LP(Cl) → π*(Si=Sn) 1.68 2.08 0.0196 1.6444 0.0070 0.0004
      LP(Cl) → σ*(Si=Sn) 3.50          
29 (4 + HCl) TB 4.016 (3.871) LP(Cl) → π*(Si=Sn) 1.29   0.0058 1.6775 0.0045 0.0005
30 (4 + HCl) HB 2.665 (2.674) π(Si=Sn) → σ*(H–Cl) 17.42   –0.0472 1.6325 0.0153 –0.0008
31 (4 + HCl) HB 3.039 (3.026) π(Si=Sn) → σ*(H–Cl) 10.43   –0.0317 1.6828 0.0109 –0.0002
32 (4 + HCl) DB 1.977 (1.970) σ(H–Sn) → σ*(H–Cl) 2.84   –0.0057 1.6837 0.0126 0.0001
33 (5 + H2O) TB 1.952 (1.887) LP(O) → LP*(Si) 141.43   0.0655 0.7710 0.0619 –0.0146
  DB 1.396 (1.331) σ(H–Pb) → σ*(H–O) 53.31       0.0495 –0.0125
34 (5 + H2O) TB 2.506 (2.453) LP(O) → LP*(Pb) 42.87   0.0676 0.8681 0.0390 –0.0016
35 (5 + H2O) TB 2.510 (2.459) LP(O) → LP*(Pb) 42.29   0.0523 0.9546 0.0382 –0.0013
36 (5 + HCl) TB 3.436 (3.241) LP(Cl) → π*(Si=Pb) 7.65 0.10 0.0198 1.4490 0.0088 0.0003
      LP(Cl) → σ*(Si=Pb) 0.73          
37 (5 + HCl) TB 3.477 (3.308) LP(Cl) → π*(Si=Pb) 4.26 0.49 0.0212 1.4376 0.0076 0.0004
      LP(Cl) → σ*(Si=Pb) 2.07          
38 (5 + HCl) TB 3.564 (3.568) LP(Cl) → π*(Si=Pb) 3.60 1.09 0.0255 1.3923 0.0086 0.0006
      LP(Cl) → σ*(Si=Pb) 3.92          
39 (5 + HCl) TB 3.910 (3.686) LP(Cl) → π*(Si=Pb) 1.75   0.0095 1.4226 0.0047 0.0005
40 (5 + HCl) HB 2.614 (2.631) π(Si=Pb) → σ*(H–Cl) 20.37   –0.0532 1.3948 0.0168 –0.0010
41 (5 + HCl) HB 3.032 (3.035) π(Si=Pb) → σ*(H–Cl) 7.21   –0.0198 1.4649 0.0094 0.0001
42 (5 + HCl) DB 1.850 (1.829) σ(H–Pb) → σ*(H–Cl) 5.19   –0.0123 1.4591 0.0164 –0.0005
Open in a new tab

3.3. Complexes: Geometries, Energies, and Binding Modes

The optimized geometries of all the 36 complexes (7–42) are illustrated in Figures 4–8, and the corresponding monomers (1–5) with the accurate locations of VS,max and VS,min are also displayed in these figures as a comparison. The results of NBO and AIM analysis for these complexes are listed in Table 2.

Figure 4.

Figure 4

Open in a new tab

Locations of VS,max and VS,min shown as purple balls around H2Si=CH2 and optimized geometries of complexes formed between H2Si=CH2 and H2O or HCl, distances in Å, angles in °, VS,max and VS,min in kcal mol–1, and interaction energies (in parenthesis) in kcal mol–1.

Figure 8.

Figure 8

Open in a new tab

Locations of VS,max and VS,min shown as purple balls around H2Si=PbH2 and optimized geometries of complexes formed between H2Si=PbH2 and H2O or HCl, distances in Å, angles in °, VS,max and VS,min in kcal mol–1, and interaction energies (in parenthesis) in kcal mol–1.

As mentioned before, the MEP map of 1 predicts that the TB and HB binding sites should be distributed around Si and C atoms, respectively. We indeed located the TB and HB binding complexes involving 1 for both H2O and HCl, as shown in Figure 4. The binding distance of the TB complex (7) formed between 1 and H2O is 2.776 Å, with binding energy as high as −2.69 kcal mol–1, which is very similar to the TB complex formed between SiF4 and H2O both in binding distance (2.785 Å) and energy (−2.71 kcal mol–1).79 The corresponding HB complex (8) possesses a more negative binding energy (−3.03 kcal mol–1), suggesting that the HB interaction is stronger than TB interaction for the 1···H2O system. A previous study indicates that the HB binding energy for the complex formed between ethene and H2O is −2.02 kcal mol–1,80 which is more positive than that for 8, implying that the electron-donating ability of C atom in ethene is weaker than that in 1. This should be attributed to the polarity of the Si=C bond in 1, which make the C atom in 1 more negatively charged than that in ethene. The TB complex (9) formed between 1 and HCl exhibits a obviously weaker TB interaction than that in 7, with Eb = −0.75 kcal mol–1, which is consistent with that the absolute value of VS,min(−10.1 kcal mol–1) in HCl is much smaller than that (−32.3 kcal mol–1) in H2O as shown in Figure 3. On the other hand, the HB complex (10) presents a stronger HB interaction than that in 8, with Eb = −3.53 kcal mol–1, and once again, which is consistent with that the value of VS,max (45.3 kcal mol–1) in HCl is larger than that (43.0 kcal mol–1) in H2O.

As shown in Figure 2, the O–Si–C and Cl–Si–C angles in complexes 7 and 9 are 101.2 and 110.7°, respectively, which deviate 20–30° from the location of VS,max in 1 [θ(Vmax–Si–C) = 132.5°]. In contrast, the H–C–Si angles in complexes 8 and 10 are 88.9 and 95.6°, respectively, and both of them are close to the location of VS,min in 1 [θ(Vmin–C–Si) = 94.2°].

The NBO analysis indicates that the orbital interaction for the TB complexes (7 and 9) is exclusively the LP → π* interaction, and as expected, the orbital interaction for the HB complexes (8 and 10) is π → σ*, with the stretch of the covalent H–O and H–Cl bonds in these two complexes compared with the isolated H2O and HCl molecules. The values of charge transfer from H2O and HCl to 1 are also listed in Table 2. A positive value means the direction of charge transfer is from H2O and HCl to 1, whereas a negative value means the reverse direction. The values of the TB and HB complexes are positive and negative, respectively, in agreement with the direction of charge transfer in these complexes. The values of WBISi=C range from 1.6555 to 1.7411 for these four complexes, and they are all smaller than that (1.7600) for the isolated monomer 1.

The AIM analysis also confirms the existence of the TB and HB interactions in these complexes, and the electron densities (ρ) at the corresponding bond critical points are listed in Table 2. There exists a linear relationship between interaction energies (Eint) and ρ for all the 36 complexes, with correlation coefficient R2 = 0.972, as shown in Figure 9. The energy density (H) is another useful parameter because its value can be used to distinguish the type of interaction: a positive value means a purely closed shell interaction, while a negative suggests a covalent interaction.81 The H value for complex 7 is negative, suggesting that 7 has partially covalent character.

Figure 9.

Figure 9

Open in a new tab

Correlation between the interaction energies and ρ for binary complexes.

The binding energy (−2.33 kcal mol-1) of the TB complex (11) formed between 2 and H2O is more positive than that (−2.69 kcal mol-1) of 7. This seems somewhat surprising, considering that the binding distance (2.361 Å) in 11 is obviously smaller than that (2.776 Å) in 7, and the electron density (0.0338 a.u.) for 11 is also nearly twice as much as that (0.0174 a.u.) for 7. Additionally, 11 possesses a more negative H value than that of 7, suggesting that 11 has stronger covalent character than 7. These seemingly contradictory results can be clarified by investigating the difference between binding and interaction energies, which is the deformation energy, reflecting the energy cost of monomer to achieve the binding geometry from the minimum geometry. A stronger interaction generally leads to a greater deformation of the monomer, which makes the binding energy more positive, and therefore, the interaction strength should not be evaluated simply on the basis of the binding energy, especially for the complexes with great deformation energies. In fact, the interaction energy is more reasonable for evaluating the interaction strength, as displayed in Figure 9. The interaction energy (−3.73 kcal mol–1) of 11 is more negative than that (−2.80 kcal mol–1) of 7, which makes sense.

It should be noted that although the bond length seems a reasonable parameter for evaluating the binding strength in this case, the previous study indicates that the stronger bond is not always the shorter bond.82 It also should be noted that although binding energy is widely used as the bond strength descriptor, some examples have been shown that the binding energy has the limitation of describing the intrinsic strength of a bond because it includes the geometry relaxation of the fragments as well as the reorganization of the electron density,83−85 and the intrinsic bond strength based on the local mode force constants is suggested to measure the bond strength.86,87

In contrast with the 1···H2O system for which the HB complex is more stable than TB complex, the HB complex (12) formed between 2 and H2O is less stable, with more positive binding (−1.91 kcal mol–1) and interaction (−2.04 kcal mol–1) energies, than the corresponding TB complex 11. Like the 1···HCl system, the TB complex (13) formed between 2 and HCl exhibits a rather weak binding strength, with Eb = −0.88 kcal mol–1, and it is less stable than the corresponding HB complex 14, with Eb = −2.31 kcal mol–1.

The location of VS,max in 2 exhibits a more serious deviation from the Si=T bond compared with 1, with the Vmax–Si–Si angle as high as 154.1°, as displayed in Figure 5. In addition, unlike 1 in which VS,min is located right above the C atom, VS,min in 2 is located over the center of the Si=Si bond, with θ(Vmin–Si–Si) = 68.9°. The O–Si–C angle in complex 11 is 129.6°, which deviates 24.5° from the location of VS,max in 2, and the Cl–Si–C angle in complex 13 is 140.6°, with an angle deviation of 13.5°. The H–C–Si angles in the HB complexes 12 and 14 are 71.8 and 72.9°, respectively, and both of them are close to the corresponding VS,min location, as discovered in the HB complexes involving 1.

Figure 5.

Figure 5

Open in a new tab

Locations of VS,max and VS,min shown as purple balls around H2Si=SiH2 and optimized geometries of complexes formed between H2Si=SiH2 and H2O or HCl, distances in Å, angles in °, VS,max and VS,min in kcal mol–1, and interaction energies (in parenthesis) in kcal mol–1.

Unlike the complexes 7 and 9 for which the orbital interaction is exclusively the LP → π* interaction, the LP → σ* interaction is also involved in the complexes 11 and 13 besides the LP → π* interaction. As shown in Table 2, the E(2) values of LP → π* and LP → σ* interactions for the complex 11 are 29.25 and 4.79 kcal mol–1, which means that the major interaction is LP → π* and the LP → σ* is a minor interaction for 11. The complex 13 exhibits a similar result, but these two E(2) values of 13 are obviously smaller than those of 11, and the σ*/π* (the ratio of E(2) for LP → σ* to that for LP → π*) value is larger for 13 (0.57) than that for 11 (0.16). The relation between the σ*/π* value and binding pattern will be discussed in Section 3.5.

As displayed in Figure 2, the MEP map predicts that the monomer 3 should have two different TB binding sites and two different HB binding sites. Figure 6 shows that these two expected TB binding sites (named as type-A and type-B) are very similar. The type-A TB binding site is around the Si atom, with VS,max = 19.2 kcal mol–1 and θ(Vmax–Si–Ge) = 159.6°, and the type-B site is around the Ge atom, with VS,max = 18.4 kcal mol–1 and θ(Vmax–Ge–Si) = 157.1°. This similarity strongly implies that the type-A and type-B TB complexes should be very similar, but the two TB complexes formed between 3 and H2O exhibit completely different binding behavior.

Figure 6.

Figure 6

Open in a new tab

Locations of VS,max and VS,min shown as purple balls around H2Si=GeH2 and optimized geometries of complexes formed between H2Si=GeH2 and H2O or HCl, distances in Å, angles in °, VS,max and VS,min in kcal mol–1, and interaction energies (in parenthesis) in kcal mol–1.

The type-A TB complex (15) is a highly strained geometry, with deformation energy as high as 17.37 kcal mol–1, and H2O is almost perpendicular to the Si=Ge bond in this complex. The NBO analysis indicates that the monomer 3 and H2O are within a unit for the complex 15, and therefore, the E2 value of TB interaction for 15 is not listed in Table 2. This result suggests that the TB interaction for 15 is totally covalent, in agreement with the short O–Si distance (2.008 Å) and the large electron density (0.0549). A negative energy density value (−0.0155) also confirms that the TB interaction is covalent. Additionally, the Si=Ge bond is obviously stretched from 2.225 Å in monomer to 2.411 Å in the complex, implying that the Si=Ge double bond has been broken for 15, in agreement with the value (0.9964) of WBISi=T. Therefore, 15 should be the intermediate state of the nucleophilic reaction between 3 and H2O. In fact, this phenomenon is not strange, because the difference between a covalent bond and a hole interaction is essentially a matter of degrees, as pointed out by the previous studies.88 The O–Si–Ge angle in complex 15 is 98.0°, which seriously deviates from the location of type-A VS,max in 3. This is also not surprising, because it is impossible to predict the binding site even if in a roughly accurate way for the so-strained complex as 15 simply on the basis of the MEP map of the isolated monomer.

Besides the TB interaction, the NBO and AIM analysis indicates that the dihydrogen bond (DB) interaction also occurs in 15 as a secondary interaction, with H···H distance as long as 1.895 Å. Although the DB interaction is discovered in the complex 15, a pure DB binding geometry cannot be located for the 3···H2O or 3···HCl system. The type-B TB complex (16) is similar to the complex 11 in many ways, and we will not discuss it anymore.

The two TB complexes (19 and 20) formed between 3 and HCl are not the true minima with one imaginary frequency, respectively. Although these two complexes are not the true minima, the NBO and AIM analysis confirms the existence of TB interaction for them, as listed in Table 2. The binding patterns of 19 and 20 are very similar to each other and are also similar to that of 13, with an angle deviation of about 13° from the corresponding location of VS,max in the monomer.

The two expected HB binding sites are also illustrated in Figure 6. The type-A HB binding site is slightly closer to the Si atom, with VS,min = −10.2 kcal mol–1 and θ(Vmin–Si–Ge) = 71.7°, and the type-B site is slightly closer to the Ge atom, with VS,min = −9.4 kcal mol–1 and θ(Vmin–Ge–Si) = 71.5°. The type-A HB complexes (17 and 21) are more stable than the corresponding type-B complexes (18 and 22), respectively, with more negative binding and interaction energies, which is consistent with the fact that the value of type-A VS,min is more negative than that of type-B. The binding sites can be predicted by the MEP map of 3 in an accurate way for these four HB complexes, with angle deviations within 3°.

The expected binding sites of 4 are similar to those of 3, but 4 exhibits a third (named as type-C) TB binding site, as shown in Figure 2, and the specific locations of these binding sites for 4 are displayed in Figure 7.

Figure 7.

Figure 7

Open in a new tab

Locations of VS,max and VS,min shown as purple balls around H2Si=SnH2 and optimized geometries of complexes formed between H2Si=SnH2 and H2O or HCl, distances in Å, angles in °, VS,max and VS,min in kcal mol–1, and interaction energies (in parenthesis) in kcal mol–1.

The binding behavior of the type-A TB complex (23) formed between 4 and H2O is similar to that of 15, but the DB interaction in 23 is much stronger than that in 15, with an obviously shorter H···H distance of 1.522 Å and E(2) value as high as 30.11 kcal mol–1. As is evident in Table 2, the value of charge transfer (0.1016) for 23 is obviously smaller than that (0.1377) for 15, although 23 possesses a stronger TB interaction, with a shorter O–Si distance (1.969 Å) and a larger electron density (0.0596). This should be ascribed to the strong DB interaction in 23, because the direction of charge transfer is from 3 to H2O for the DB interaction, which is opposite to that for the TB interaction. In fact, it is the bidirectional transfer of charge that leads to a synergistic effect between the DB and TB interactions, which is responsible for the very strong DB interaction in 23. This cooperative effect also exists in 15, but to a lesser degree. Similar to the 3···H2O system, a pure DB binding geometry cannot be located for 4 and H2O, but the DB complex (32) can be obtained for 4 and HCl, with H···H distance as long as 1.977 Å. The DB interaction in 32 is obviously weak than that in 23 because of the absence of a synergistic effect.

The type-B TB complex (24) is a rather strained geometry, with deformation energy as high as 10.26 kcal mol–1. The NBO analysis suggests that the Si=Sn double bond in 24 should be broken, with WBISi=Ge = 1.0046, and the orbital interaction is LP(O) → LP*(Sn), with E(2) = 56.98 kcal mol–1. Therefore, similar to the covalent complexes 15 and 23, the TB interaction in 24 corresponds to a nucleophilic attack at the Sn atom. The type-C TB complex (25) is very similar to 24 and is also the intermediate state of the nucleophilic reaction. It should be noted that the water molecules are almost perpendicular to the Si=T bonds for all the four covalent complexes (15, 23, 24, and 25). This is because the orbitals involved in the corresponding nucleophilic reactions are π* or LP*, which are almost perpendicular to the Si=T bonds. It is the orbitals involved in the nucleophilic reactions not the MEP maps of the isolated monomers that are responsible for the final geometries of these covalent complexes. The MEP maps fail to predict the binding pattern for these covalent complexes, which should attribute to the kinetic aspect of chemical bonding. Ruedenberg’s seminal work have shown that a pure electrostatic model may underestimate the important role of the lowering of the kinetic energy associated with electron delocalization upon covalent bond formation.89,90

As shown in Figure 7, the two expected TB binding sites (type-A and type-B) of 4 are similar to those of 3. The type-A TB site is around the Si atom, with VS,max = 17.8 kcal mol–1 and θ(Vmax–Si–Sn) = 165.1°, and the type-B site is around the Sn atom, with VS,max = 28.2 kcal mol–1 and θ(Vmax–Sn–Si) = 153.0°. Additionally, the type-C site is around the Sn atom and is almost perpendicular to the Si=Sn bond, with VS,max = 13.6 kcal mol–1 and θ(Vmax–Sn–Si) = 96.3°. As expected, the binding geometries of type-A and type-B TB complexes (27 and 28) formed between 4 and HCl are similar to those of 19 and 20. The type-C TB complex (29) is not a true minimum with one imaginary frequency, and its binding strength is very weak, but the NBO and AIM analyses confirm the existence of TB interaction for it, as listed in Table 2. The binding sites can be predicted by the MEP map of 4 in a relatively accurate way for these three TB complexes, with angle deviations within 7°.

The two expected HB binding sites for 4 are also illustrated in Figure 7. The type-A HB site is obviously closer to the Si atom than the Sn atom, with VS,min = −9.1 kcal mol–1 and θ(Vmin–Si–Sn) = 80.9°, and the type-B site is slightly closer to the Si atom, with VS,min = −7.3 kcal mol–1 and θ(Vmin–Si–Sn) = 66.7°. It is somewhat surprising that the type-A HB complex formed between 4 and H2O cannot be located, and only the type-B HB complex (26) can be located for H2O. This issue will be discussed in detail in Section 3.4. Both the two HB complexes can be located for HCl, and the type-A HB complex (30) is more stable than the type–B complex (31), in agreement with that the value of type-A VS,min is more negative than that of type-B. In fact, there exists a linear relationship between interaction energies (Eint) and VS,min for all the eight HB complexes involving HCl, with correlation coefficient R2 = 0.973, as shown in Figure 10. The binding sites can be predicted by the MEP map of 4 in an accurate way for the three HB complexes, with angle deviations within 3°.

Figure 10.

Figure 10

Open in a new tab

Correlation between the interaction energies and VS,min for HB complexes involving HCl.

As shown in Figure 8, the binding patterns of the complexes involving 5 are generally similar to those involving 4 except for two major differences. First, there exist two different type-A TB complexes (36 and 37) formed between 5 and HCl, and we will discuss this issue in Section 3.5. Second, unlike 4 for which the type-B HB complex involving H2O can be located, neither type-A nor type-B HB complex involving H2O can be located for 5, and this difference will be clarified in the following section.

3.4. Competition between TB and HB Interactions: Potential Energy Surfaces

As discussed before, there exist various binding modes for the complexes of the heavy alkenes with H2O and HCl. These complexes mainly involve in the TB and HB interactions, and these interactions exhibit different binding strengths. Previous studies have confirmed that both HB and TB bonding result from a complex interplay of electronic effects which determine their covalent and/or ionic character.91,92 In this section, we will explore the competition between TB and HB interactions by investigating the potential energy surfaces around DB and HB binding sites. The relaxed potential energy surface scans have been performed for some selected systems. The results of these scans are displayed in Figure 11, which provide some interesting and instructive information. The scans gradually move from a HB binding area to a TB area with the increase in θ step by step.

Figure 11.

Figure 11

Open in a new tab

Relaxed potential energy surface scans for selected systems: (a) H2Si=CH2···H2O; (b) H2Si=GeH2···H2O; (c) H2Si=PbH2···H2O; (d) H2Si=GeH2···HCl; and (e) H2Si=PbH2···HCl.

Figure 11a indicates that the TB complex is separated from the HB complex by a very small energy barrier and the global minimum is the HB complex for the 1···H2O system, suggesting that the TB complex can easily transform into the HB complex for the 1···H2O system. As shown in Figure 11b, unlike the 1···H2O system, the type-B TB complex is separated from the type-B HB complex by a relatively large energy barrier, and the TB complex is more stable than HB complex for the 3···H2O system. Figure 11c discloses the absence of the type-A HB complex for the 5···H2O system, as mentioned before. The absence of the type-A HB complex for 4···H2O and 5···H2O systems should be attributed to the occurrence of the type-C TB binding site for 4 and 5, because a trial to locate the type-A HB geometry always leads to the type-C TB geometry for 4···H2O and 5···H2O systems. As illustrated in Figures 7 and 8, the location of type-A HB binding site is very close to that of type-C TB site for 4 and 5, and therefore, there exists a strong competition between type-A HB and type-C TB geometries, which makes the type-A HB geometry unstable and collapse to the type-C TB geometry. Similar competition also exists for the type-B HB and type-B TB geometries, but to a lesser extent, because the distance between type-B HB and type-B TB binding sites is relatively large. The type-B HB geometry can retain for 4, with the type-B HB VS,min as much as −7.3 kcal mol–1, but the type-B HB geometry cannot retain for 5, with a very small type-B HB VS,min of −3.9 kcal mol–1. This postulation is confirmed by that a trial to locate the type-B HB geometry always leads to the type-B TB geometry for 5···H2O systems. In contrast, all the HB complexes can retain for HCl, because HCl is a rather weak electron donor and the TB geometry is not a strong competitor to the HB geometry for the systems involving HCl, as discussed below.

Unlike the H2Si=TH2···H2O systems, for which the HB complexes become more and more unstable relative to the TB complexes with the increase of the T atomic number, as displayed in Figure 11a–c, the HB complexes are generally more stable than TB complexes for H2Si=TH2···HCl systems. Figure 11d confirms that the type-A TB geometry is unstable for the 3···HCl system. As mentioned before, the type-A TB complex 19 is not a true minimum with one imaginary frequency, and the vibrational mode of the frequency leads to the HB geometry. Figure 11e indicates that the type-A TB complex is separated from the type-A HB complex by a very small energy barrier for the 5···HCl system, and the TB area corresponds to a very flat potential energy surface.

3.5. σ-Hole or π-Hole: Hybrid σ/π-Hole?

The terms “σ-hole” and “π-hole” were coined in 2007 and 2010, respectively. A region of lower electronic density on the extension of a bond is called a σ-hole, and a region of a lower electronic density above and below a planar portion of a molecule is called a π-hole. However, such definitions may cause confusion in some cases, and therefore, we will classify these two holes on the basis of the orbital interaction: the interaction involving the charge transfer of LP → σ* is classified as a σ-hole interaction, and the interaction involving the charge transfer of LP → π* is classified as a π-hole interaction. As listed in Table 2, there exist some complexes involving both of LP → σ* and LP → π* interactions, which can be called hybrid σ/π-hole as proposed by the previous study.93 The noncovalent TB complexes can be divided into two types according to the orbital interactions: (1) π-hole complexes (7, 9, 29, and 39), with binding angles ranging from 91 to 111°; and (2) hybrid σ/π-hole complexes (11, 13, 16, 19, 20, 27, 28, 36, 37, and 38), with binding angles ranging from 130 to 165° and σ*/π* values ranging from 0.1 to 2.1. It can be concluded that the σ*/π* value should increase with the increase in the binding angle for the same binding site, because the σ* orbital is parallel to the Si=T bond and the π* orbital is approximately perpendicular to the Si=T bond. This postulation is confirmed by the two different type-A complexes (36 and 37) formed between 5 and HCl: 36 possess a small binding angle of 149.5°, with a small σ*/π* value of 0.10, and 37 possess a large binding angle of 165.4°, with a large σ*/π* value of 0.49.

3.6. Cooperative Effect: Change of Binding Pattern

As clarified before, the binding sites can be located on the basis of MEP maps of the isolated H2Si=TH2 molecules in a relatively accurate way for H2Si=TH2···HCl systems, but the H2Si=TH2···H2O systems generally exhibit different binding behavior because of the strong nucleophilic ability of H2O. The cooperative effect is an important issue for noncovalent interaction because it can modulate the strength of interaction. The strength of a molecular interaction can be enhanced or weakened through synergistic or competitive interplay with another molecular interaction. In this section, we will investigate the change in the binding pattern of the selected systems under the influence of the competitive effect, which mitigates the electron-donating ability of H2O. As a comparison, we will also explore the synergistic effect. The corresponding ternary complexes are displayed in Figure 12.

Figure 12.

Figure 12

Open in a new tab

Optimized geometries of ternary complexes, distances in Å, angles in °.

Unlike H2Si=TH2···HCl systems for which the TB complexes exhibit rather weak binding strength, the TB complexes formed between H2Si=TH2 and H2O possess very strong binding strength with covalent characteristics in many cases. Ternary complexes 43 and 44 indicate that the competitive effect can exert a significant influence on the binding pattern of the covalent TB complexes, such as 15, 23, and 24. As mentioned before, 15 is a highly strained TB binding geometry and obviously has covalent characteristics, with a very short binding distance of 2.008 Å and a binding angle of 98.0°. However, the TB interaction in 43 has been significantly abated and became noncovalent, with a long binding distance of 2.951 Å. This should ascribe to the existence of a competitive HB interaction in 43. As displayed in Figure 3, the HB interaction between H2O and HCl make the VS,min value around the O atom become more positive (−18.4 kcal mol–1) compared with that (−32.3 kcal mol–1) of the isolated H2O molecule, which can explain the abated nucleophilic ability of H2O. It can also be observed that the TB binding angle in 43 is 142.5°, which is similar to that of the weak TB binding complex 19, suggesting that the TB binding behavior of H2O becomes similar to that of HCl because of the competitive effect. Similar results can be found for 44, in which the competitive effect results from two different TB interactions, and compared with 23 and 24, both of the two TB interactions in 44 have been abated, with the larger binding distances and angles.

The synergistic effect between two different HB interactions is reflected in 45, with a shortened H2O···HCl distance as long as 1.769 Å (this distance is 1.855 Å for 6 as displayed in Figure 3). However, in fact, the geometry of 45 resulting from that the nucleophilic ability of H2O is weakened because of the HB interaction between H2O and HCl. As mentioned before, the type-A HB complex cannot be formed between 4 and H2O, because H2O possesses a rather strong nucleophilic ability and always leads to the intermediate state of the nucleophilic reaction. However, in 45, the HB binding mode can retain because H2O exhibits a relatively weak nucleophilic ability. The geometry of 46 discloses the influence of the synergistic effect between HB and TB interactions on the binding pattern of HCl. Figure 3 indicates that the HB interaction between H2O and HCl makes the VS,min value around the Cl atom become more negative (−20.9 kcal mol–1) compared with that (−10.1 kcal mol–1) of the isolated HCl molecule, which means that the electron-donating ability of HCl is strengthened because of the HB interaction. As discussed before, the type-A TB geometry is not a true minimum with an imaginary frequency for the 3···HCl system. However in 46, the type-A TB binding mode can retain without imaginary frequency because HCl possesses a stronger electron-donating ability compared with the isolated HCl. 47 is another example of the synergistic effect between HB and TB interactions, and compared with 1 and 4, both of the TB and HB interactions in 47 have been enhanced, with the shorter TB and HB binding distances.

4. Conclusions

In this study, we select H2O and HCl as the probe molecules to investigate the dual behavior of the selected heavy alkenes H2Si=TH2 (T = C, Si, Ge, Sn, Pb) in HB and TB interactions. The various HB and TB complexes formed between H2Si=TH2 and H2O or HCl have been located on the basis of MEP maps of the isolated monomers, and the DB complexes are also found for some systems. The HB complexes become more and more unstable relative to the TB complexes with the increase of the T atomic number, and even cannot retain as a minimum in some cases, for H2Si=TH2···H2O systems. In contrast, the HB complexes are generally more stable than TB complexes, and the TB complexes exhibit rather weak binding strength, for H2Si=TH2···HCl systems. The majority of the TB complexes formed between H2Si=TH2 and H2O possess very strong binding strength with covalent characteristics. The binding sites can be predicted by the MEP maps of the isolated monomers in an accurate way for the HB complexes, and for the noncovalent TB complexes, their binding sites can also be predicted in a relatively accurate way, but for the covalent TB complexes, their binding behavior is mainly determined by the orbitals involved in the nucleophilic attack and not the MEP maps of the isolated monomers. The noncovalent TB complexes can be divided into two types on the basis of the orbital interactions: π-hole complexes, with binding angles ranging from 91 to 111°, and hybrid σ/π-hole complexes, with binding angles ranging from 130 to 165°. We explore the change in the binding pattern of the selected complexes because of the interplay between different noncovalent interactions, and an interesting result is that the covalent TB interaction is significantly abated and becomes noncovalent because of the competitive effect.

Acknowledgments

This work was supported by the Scientific Research Funds from the Educational Department of Yunnan Province, China, grant nos. 2015Y434 and 2020J0634.

The authors declare no competing financial interest.

References

  1. Wheeler S. E.; Seguin T. J.; Guan Y.; Doney A. C. Noncovalent Interactions in Organocatalysis and the Prospect of Computational Catalyst Design. Acc. Chem. Res. 2016, 49, 1061–1069. 10.1021/acs.accounts.6b00096. [DOI] [PubMed] [Google Scholar]
  2. Vallavoju N.; Sivaguru J. Supramolecular photocatalysis: combining confinement and non-covalent interactions to control light initiated reactions. Chem. Soc. Rev. 2014, 43, 4084–4101. 10.1039/c3cs60471c. [DOI] [PubMed] [Google Scholar]
  3. Georgakilas V.; Tiwari J. N.; Kemp K. C.; Perman J. A.; Bourlinos A. B.; Kim K. S.; Zboril R. Noncovalent functionalization of graphene and graphene oxide for energy materials, biosensing, catalytic, and biomedical applications. Chem. Rev. 2016, 116, 5464–5519. 10.1021/acs.chemrev.5b00620. [DOI] [PubMed] [Google Scholar]
  4. Scheiner S.Hydrogen Bonding, A Theoretical Perspective; Oxford University Press: New York, 1997. [Google Scholar]
  5. Politzer P.; Murray J. S.; Clark T. Halogen bonding: an electrostatically-driven highly directional noncovalent interaction. Phys. Chem. Chem. Phys. 2010, 12, 7748–7757. 10.1039/c004189k. [DOI] [PubMed] [Google Scholar]
  6. Sarwar M. G.; Dragisic B.; Sagoo S.; Taylor M. S. A tridentate halogen-bonding receptor for tight binding of halide anions. Angew. Chem., Int. Ed. 2010, 49, 1674–1677. 10.1002/anie.200906488. [DOI] [PubMed] [Google Scholar]
  7. Kilah N. L.; Wise M. D.; Serpell C. J.; Thompson A. L.; White N. G.; Christensen K. E.; Beer P. D. Enhancement of anion recognition exhibited by a halogen-bonding rotaxane host system. J. Am. Chem. Soc. 2010, 132, 11893–11895. 10.1021/ja105263q. [DOI] [PubMed] [Google Scholar]
  8. Hernandes M. Z.; Cavalcanti S. M. T.; Moreira D. R. M.; de Azevedo W. F. Jr.; Leite A. C. L. Halogen atoms in the modern medicinal chemistry: hints for the drug design. Curr. Drug Targets 2010, 11, 303–314. 10.2174/138945010790711996. [DOI] [PubMed] [Google Scholar]
  9. Metrangolo P.; Meyer F.; Pilati T.; Resnati G.; Terraneo G. Halogen bonding in supramolecular chemistry. Angew. Chem., Int. Ed. 2008, 47, 6114–6127. 10.1002/anie.200800128. [DOI] [PubMed] [Google Scholar]
  10. Politzer P.; Murray J. S.; Concha M. C. Halogen bonding and the design of new materials: organic bromides, chlorides and perhaps even fluorides as donors. J. Mol. Model. 2007, 13, 643–650. 10.1007/s00894-007-0176-9. [DOI] [PubMed] [Google Scholar]
  11. Varadwaj P. R.; Varadwaj A.; Marques H. M. Halogen bonding: A halogen-centered noncovalent interaction yet to be understood. Inorganics 2019, 7, 40. 10.3390/inorganics7030040. [DOI] [Google Scholar]
  12. Clark T.; Hennemann M.; Murray J. S.; Politzer P. Halogen bonding: the sigma-hole. Proceedings of “Modeling interactions in biomolecules II”, Prague, September 5th-9th, 2005. J. Mol. Model. 2007, 13, 291–296. 10.1007/s00894-006-0130-2. [DOI] [PubMed] [Google Scholar]
  13. Scheiner S. The ditetrel bond: noncovalent bond between neutral tetrel atoms. Phys. Chem. Chem. Phys. 2020, 22, 16606–16614. 10.1039/d0cp03068f. [DOI] [PubMed] [Google Scholar]
  14. Murray J. S.; Lane P.; Politzer P. Expansion of the σ-hole concept. J. Mol. Model. 2009, 15, 723–729. 10.1007/s00894-008-0386-9. [DOI] [PubMed] [Google Scholar]
  15. Wei Y.; Li Q.; Scheiner S. The π-Tetrel Bond and its Influence on Hydrogen Bonding and Proton Transfer. ChemPhysChem 2018, 19, 736–743. 10.1002/cphc.201701136. [DOI] [PubMed] [Google Scholar]
  16. Li Q.; Guo X.; Yang X.; Li W.; Cheng J.; Li H.-B. A σ-hole interaction with radical species as electron donors: does single-electron tetrel bonding exist?. Phys. Chem. Chem. Phys. 2014, 16, 11617–11625. 10.1039/c4cp01209g. [DOI] [PubMed] [Google Scholar]
  17. Thomas S. P.; Pavan M. S.; Row T. N. G. Experimental evidence for ‘carbon bonding’ in the solid state from charge density analysis. Chem. Commun. 2014, 50, 49–51. 10.1039/c3cc47226d. [DOI] [PubMed] [Google Scholar]
  18. McDowell S. A. C.; Joseph J. A. The effect of atomic ions on model σ-hole bonded complexes of AH3Y (A = C, Si, Ge; Y = F, Cl, Br). Phys. Chem. Chem. Phys. 2014, 16, 10854–10860. 10.1039/c4cp01074d. [DOI] [PubMed] [Google Scholar]
  19. Mani D.; Arunan E. The X-C···π (X = F, Cl, Br, CN) Carbon Bond. J. Phys. Chem. A 2014, 118, 10081–10089. 10.1021/jp507849g. [DOI] [PubMed] [Google Scholar]
  20. Southern S. A.; Bryce D. L. NMR investigations of noncovalent carbon tetrel bonds. Computational assessment and initial experimental observation. J. Phys. Chem. A 2015, 119, 11891–11899. 10.1021/acs.jpca.5b10848. [DOI] [PubMed] [Google Scholar]
  21. Scheiner S. Comparison of CH···O, SH···O, Chalcogen, and Tetrel Bonds Formed by Neutral and Cationic Sulfur-Containing Compounds. J. Phys. Chem. A 2015, 119, 9189–9199. 10.1021/acs.jpca.5b06831. [DOI] [PubMed] [Google Scholar]
  22. Azofra L. M.; Scheiner S. Tetrel, chalcogen, and CH···O hydrogen bonds in complexes pairing carbonyl-containing molecules with 1, 2, and 3 molecules of CO2. J. Chem. Phys. 2015, 142, 034307. 10.1063/1.4905899. [DOI] [PubMed] [Google Scholar]
  23. Bauzá A.; Mooibroek T. J.; Frontera A. Tetrel bonding interactions. Chem. Rec. 2016, 16, 473–487. 10.1002/tcr.201500256. [DOI] [PubMed] [Google Scholar]
  24. Bauzá A.; Frontera A.; Mooibroek T. J. 1,1,2,2-Tetracyanocyclopropane (TCCP) as supramolecular synthon. Phys. Chem. Chem. Phys. 2016, 18, 1693–1698. 10.1039/c5cp06350g. [DOI] [PubMed] [Google Scholar]
  25. Liu M.; Li Q.; Li W.; Cheng J. Carbene tetrel-bonded complexes. Struct. Chem. 2017, 28, 823–831. 10.1007/s11224-016-0890-y. [DOI] [Google Scholar]
  26. Liu M.; Li Q.; Cheng J.; Li W.; Li H.-B. Tetrel bond of pseudohalide anions with XH3F (X = C, Si, Ge, and Sn) and its role in SN2 reaction. J. Chem. Phys. 2016, 145, 224310. 10.1063/1.4971855. [DOI] [PubMed] [Google Scholar]
  27. Bene J. E. D.; Alkorta I.; Elguero J. Carbon-Carbon Bonding between Nitrogen Heterocyclic Carbenes and CO2. J. Phys. Chem. A 2017, 121, 8136–8146. 10.1021/acs.jpca.7b08393. [DOI] [PubMed] [Google Scholar]
  28. Liu M.; Li Q.; Scheiner S. Comparison of tetrel bonds in neutral and protonated complexes of pyridineTF3 and furanTF3 (T = C, Si, and Ge) with NH3. Phys. Chem. Chem. Phys. 2017, 19, 5550–5559. 10.1039/c6cp07531b. [DOI] [PubMed] [Google Scholar]
  29. Legon A. C. Tetrel, pnictogen and chalcogen bonds identified in the gas phase before they had names: a systematic look at non-covalent interactions. Phys. Chem. Chem. Phys. 2017, 19, 14884–14896. 10.1039/c7cp02518a. [DOI] [PubMed] [Google Scholar]
  30. Scheiner S. Comparison of various means of evaluating molecular electrostatic potentials for noncovalent interactions. J. Comput. Chem. 2018, 39, 500–510. 10.1002/jcc.25085. [DOI] [PubMed] [Google Scholar]
  31. Zierkiewicz W.; Michalczyk M.; Scheiner S. Implications of monomer deformation for tetrel and pnicogen bonds. Phys. Chem. Chem. Phys. 2018, 20, 8832–8841. 10.1039/c8cp00430g. [DOI] [PubMed] [Google Scholar]
  32. Bauzá A.; Mooibroek T. J.; Frontera A. Tetrel-bonding interaction: rediscovered supramolecular force?. Angew. Chem., Int. Ed. 2013, 52, 12317–12321. 10.1002/anie.201306501. [DOI] [PubMed] [Google Scholar]
  33. Quiñonero D. Sigma-hole carbon-bonding interactions in carbon-carbon double bonds: an unnoticed contact. Phys. Chem. Chem. Phys. 2017, 19, 15530–15540. 10.1039/c7cp01780d. [DOI] [PubMed] [Google Scholar]
  34. Remya K.; Suresh C. H. Intermolecular carbon–carbon, nitrogen–nitrogen and oxygen–oxygen non-covalent bonding in dipolar molecules. Phys. Chem. Chem. Phys. 2015, 17, 18380–18392. 10.1039/c5cp01631b. [DOI] [PubMed] [Google Scholar]
  35. Varadwaj P. R.; Varadwaj A.; Jin B.-Y. Significant evidence of C···O and C···C long-range contacts in several heterodimeric complexes of CO with CH3-X, should one refer to them as carbon and dicarbon bonds!. Phys. Chem. Chem. Phys. 2014, 16, 17238–17252. 10.1039/c4cp01775g. [DOI] [PubMed] [Google Scholar]
  36. Scheiner S. The pnicogen bond: its relation to hydrogen, halogen, and other noncovalent bonds. Acc. Chem. Res. 2013, 46, 280–288. 10.1021/ar3001316. [DOI] [PubMed] [Google Scholar]
  37. Wang W.; Ji B.; Zhang Y. Chalcogen bond: a sister noncovalent bond to halogen bond. J. Phys. Chem. A 2009, 113, 8132–8135. 10.1021/jp904128b. [DOI] [PubMed] [Google Scholar]
  38. Politzer P.; Murray J. S.; Clark T. Halogen bonding: an electrostatically-driven highly directional noncovalent interaction. Phys. Chem. Chem. Phys. 2010, 12, 7748–7757. 10.1039/c004189k. [DOI] [PubMed] [Google Scholar]
  39. Davidson P. J.; Lappert M. F. Stabilisation of metals in a low co-ordinative environment using the bis(trimethylsilyl)methyl ligand; coloured SnII and PbII alkyls, M[CH(SiMe3)2]2. J. Chem. Soc., Chem. Commun. 1973, 317a. 10.1039/C3973000317A. [DOI] [Google Scholar]
  40. Lee V. Y.; Ichinohe M.; Sekiguchi A. The first metalladiene of group 14 elements with a silole-type structure with Si=Ge and C=C double Bonds. J. Am. Chem. Soc. 2000, 122, 12604–12605. 10.1021/ja0030921. [DOI] [Google Scholar]
  41. Ichinohe M.; Arai Y.; Sekiguchi A.; Takagi N.; Nagase S. A new approach to the synthesis of unsymmetrical disilenes and germasilene: unusual 29Si NMR chemical shifts and regiospecific methanol addition. Organometallics 2001, 20, 4141–4143. 10.1021/om010419d. [DOI] [Google Scholar]
  42. Sekiguchi A.; Izumi R.; Ihara S.; Ichinohe M.; Lee V. Y. The first isolable 1,1-dilithiogermane and Its unusual dimeric structure—an effective reagent for the preparation of double-bonded derivatives of group 14 elements. Angew. Chem., Int. Ed. 2002, 41, 1598–1600. . [DOI] [PubMed] [Google Scholar]
  43. Iwamoto T.; Masuda H.; Kabuto C.; Kira M. Trigermaallene and 1,3-digermasilaallene. Organometallics 2005, 24, 197–199. 10.1021/om049183e. [DOI] [Google Scholar]
  44. Igarashi M.; ıchinohe M.; Sekiguchi A. A stable silagermene (tBu3Si)2Si=Ge(mes)2 (mes = 2,4,6-trimethylphenyl): Synthesis, X-ray crystal structure, and thermal isomerization. Heteroat. Chem. 2008, 19, 649–653. 10.1002/hc.20503. [DOI] [Google Scholar]
  45. Iwamoto T.; Okita J.; Yoshida N.; Kira M. Structure and reactions of an isolable Ge=Si doubly bonded compound, tetra(t-butyldimethylsilyl)germasilene. Silicon 2010, 2, 209–216. 10.1007/s12633-011-9069-8. [DOI] [Google Scholar]
  46. Lee V. Y.; Sekiguchi A. Heteronuclear heavy alkenes E=E′ (E,E′ = Group 14 Elements): germasilenes, silastannenes, germastannenes... next stop?. Organometallics 2004, 23, 2822–2834. 10.1021/om040027h. [DOI] [Google Scholar]
  47. Power P. P. π-Bonding and the Lone Pair Effect in Multiple Bonds between Heavier Main Group Elements. Chem. Rev. 1999, 99, 3463–3504. 10.1021/cr9408989. [DOI] [PubMed] [Google Scholar]
  48. West R.; Fink M. J.; Michl J. Tetramesityldisilene, a stable compound containing a silicon-silicon double bond. Science 1981, 214, 1343–1344. 10.1126/science.214.4527.1343. [DOI] [PubMed] [Google Scholar]
  49. Baines K. M.; Cooke J. A. Thermolysis of a siladigermirane: evidence for the formation of a germasilene. Organometallics 1991, 10, 3419–3421. 10.1021/om00056a004. [DOI] [Google Scholar]
  50. Lee V. Y.; Ichinohe M.; Sekiguchi A.; Takagi N.; Nagase S. The first three-membered unsaturated rings consisting of different heavier group 14 elements:  1-disilagermirene with a Si=Si double bond and its isomerization to a 2-disilagermirene with a Si=Ge double bond. J. Am. Chem. Soc. 2000, 122, 9034–9035. 10.1021/ja001551s. [DOI] [Google Scholar]
  51. Apeloig Y.; Nakash M. Arrhenius Parameters for the Addition of Phenols to the Silicon–Silicon Double Bond of Tetramesityldisilene†. Organometallics 1998, 17, 2307–2312. 10.1021/om980016m. [DOI] [Google Scholar]
  52. Takahashi M.; Veszprémi T.; Hajgató B.; Kira M. Theoretical study on stereochemical diversity in the addition of water to disilene. Organometallics 2000, 19, 4660–4662. 10.1021/om000385u. [DOI] [Google Scholar]
  53. Veszprémi T.; Takahashi M.; Hajgató B.; Kira M. The mechanism of 1,2-addition of disilene and silene. 1. water and alcohol addition. J. Am. Chem. Soc. 2001, 123, 6629–6638. 10.1021/ja0040823. [DOI] [PubMed] [Google Scholar]
  54. Takahashi M.; Veszprémi T.; Kira M. 1,2-Addition Reaction of Monosubstituted Disilenes: An Ab Initio Study. Organometallics 2004, 23, 5768–5778. 10.1021/om049418m. [DOI] [Google Scholar]
  55. Yamabe S.; Mizukami N.; Tsuchida N.; Yamazaki S. A new mechanism for the addition of alcohols to disilenes revealed by DFT and ONIOM calculations. J. Organomet. Chem. 2008, 693, 1335–1345. 10.1016/j.jorganchem.2008.01.035. [DOI] [Google Scholar]
  56. Li B.-Y.; Su M.-D. Theoretical Investigation of the Mechanisms for the Reaction of Fused Tricyclic Dimetallenes Containing Highly Strained E=E (E = C, Si, Ge, Sn, and Pb) Double Bonds. J. Phys. Chem. A 2012, 116, 4222–4232. 10.1021/jp3018138. [DOI] [PubMed] [Google Scholar]
  57. Gilli G.; Gilli P.. The Nature of the Hydrogen Bond; Oxford University Press: Oxford, U.K., 2009. [Google Scholar]
  58. Raabe G.; Michl J. Multiple bonding to silicon. Chem. Rev. 1985, 85, 419–509. 10.1021/cr00069a005. [DOI] [Google Scholar]
  59. Yourdkhani S.; Korona T.; Hadipour N. L. Interplay between tetrel and triel bonds in RC6H4CN···MF3CN···BX3 complexes: A combined symmetry-adapted perturbation theory, Møller-Plesset, and quantum theory of atoms-in-molecules study. J. Comput. Chem. 2015, 36, 2412–2428. 10.1002/jcc.24226. [DOI] [PubMed] [Google Scholar]
  60. Marín-Luna M.; Alkorta I.; Elguero J. Cooperativity in tetrel bonds. J. Phys. Chem. A 2016, 120, 648–656. 10.1021/acs.jpca.5b11876. [DOI] [PubMed] [Google Scholar]
  61. Esrafili M. D.; Mohammadian-Sabet F. Cooperativity of tetrel bonds tuned by substituent effects. Mol. Phys. 2016, 114, 1528–1538. 10.1080/00268976.2016.1139207. [DOI] [Google Scholar]
  62. Rezaei Z.; Solimannejad M.; Esrafili M. D. Interplay between hydrogen bond and single-electron tetrel bond: H3C···COX2···HY and H3C···CSX2···HY (X = F, Cl; Y = CN, NC) complexes as a working model. Comput. Theor. Chem. 2015, 1074, 101–106. 10.1016/j.comptc.2015.10.015. [DOI] [Google Scholar]
  63. Xu H.; Cheng J.; Yang X.; Liu Z.; Bo X.; Li Q. Interplay between the σ-tetrel bond and σ-halogen bond in PhSiF3 ···4-iodopyridine···N-base. RSC Adv. 2017, 7, 21713–21720. 10.1039/c7ra02068f. [DOI] [Google Scholar]
  64. Li W.; Zeng Y.; Li X.; Sun Z.; Meng L. Insight into the pseudo π-hole interactions in the M3H6(NCF)n (M = C, Si, Ge, Sn, Pb; n = 1, 2, 3) complexes. Phys. Chem. Chem. Phys. 2016, 18, 24672–24680. 10.1039/c6cp03713e. [DOI] [PubMed] [Google Scholar]
  65. Chen Y.; Yao L.; Wang F. Synergistic and antagonistic interplay between tetrel bond and pnicogen bond in complexes involving ring compounds. J. Mol. Model. 2019, 25, 351. 10.1007/s00894-019-4206-1. [DOI] [PubMed] [Google Scholar]
  66. Liu M.; Yang L.; Li Q.; Li W.; Cheng J.; Xiao B.; Yu X. Modulating the strength of tetrel bonding through beryllium bonding. J. Mol. Model. 2016, 22, 192. 10.1007/s00894-016-3060-7. [DOI] [PubMed] [Google Scholar]
  67. McDowell S. A. C. Sigma-hole cooperativity in anionic [FX···CH3···YF]− (X, Y = Cl, Br) complexes. Chem. Phys. Lett. 2014, 598, 1–4. 10.1016/j.cplett.2014.02.054. [DOI] [Google Scholar]
  68. Esrafili M. D.; Mohammadirad N.; Solimannejad M. Tetrel bond cooperativity in open-chain (CH3CN)n and (CH3NC)n clusters (n = 2–7): An ab initio study. Chem. Phys. Lett. 2015, 628, 16–20. 10.1016/j.cplett.2015.04.001. [DOI] [Google Scholar]
  69. Solimannejad M.; Orojloo M.; Amani S. Effect of cooperativity in lithium bonding on the strength of halogen bonding and tetrel bonding: (LiCN)n···ClYF3 and (LiCN)n···YF3Cl (Y = C, Si and n = 1–5) complexes as a working model. J. Mol. Model. 2015, 21, 183. 10.1007/s00894-015-2722-1. [DOI] [PubMed] [Google Scholar]
  70. Frisch M. J.; Trucks G. W.; Schlegel H. B.; Scuseria G. E.; Robb M. A.; Cheeseman J. R.; Scalmani G.; Barone V.; Mennucci B.; Petersson G. A.; Nakatsuji H.; Caricato M.; Li X.; Hratchian H. P.; Izmaylov A. F.; Bloino J.; Zheng G.; Sonnenberg J. L.; Hada M.; Ehara M.; Toyota K.; Fukuda R.; Hasegawa J.; Ishida M.; Nakajima T.; Honda Y.; Kitao O.; Nakai H.; Vreven T.; Montgomery J. A.; Peralta J. E.; Ogliaro F.; Bearpark M.; Heyd J. J.; Brothers E.; Kudin K. N.; Staroverov V. N.; Kobayashi R.; Normand J.; Raghavachari K.; Rendell A.; Burant J. C.; Iyengar S. S.; Tomasi J.; Cossi M.; Rega N.; Millam J. M.; Klene M.; Knox J. E.; Cross J. B.; Bakken V.; Adamo C.; Jaramillo J.; Gomperts R.; Stratmann R. E.; Yazyev O.; Austin A. J.; Cammi R.; Pomelli C.; Ochterski J. W.; Martin R. L.; Morokuma K.; Zakrzewski V. G.; Voth G. A.; Salvador P.; Dannenberg J. J.; Dapprich S.; Daniels A. D.; Farkas O. ¨.; Foresman J. B.; Ortiz J. V.; Cioslowski J.; Fox D. J.. Gaussian 09, Revision D.01; Gaussian, Inc.: Wallingford CT, 2013.
  71. Feller D. The role of databases in support of computational chemistry calculations. J. Comput. Chem. 1996, 17, 1571–1586. . [DOI] [Google Scholar]
  72. Boys S. F.; Bernardi F. The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors. Mol. Phys. 1970, 19, 553–566. 10.1080/00268977000101561. [DOI] [Google Scholar]
  73. Reed A. E.; Curtiss L. A.; Weinhold F. Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint. Chem. Rev. 1988, 88, 899–926. 10.1021/cr00088a005. [DOI] [Google Scholar]
  74. Bader R. F. W.; Carroll M. T.; Cheeseman J. R.; Chang C. Properties of atoms in molecules: atomic volumes. J. Am. Chem. Soc. 1987, 109, 7968–7979. 10.1021/ja00260a006. [DOI] [Google Scholar]
  75. Lu T.; Chen F. Multiwfn: a multifunctional wavefunction analyzer. J. Comput. Chem. 2012, 33, 580–592. 10.1002/jcc.22885. [DOI] [PubMed] [Google Scholar]
  76. Li Q.-Z.; Zhuo H.-Y.; Li H.-B.; Liu Z.-B.; Li W.-Z.; Cheng J.-B. Tetrel-hydride interaction between XH3F (X = C, Si, Ge, Sn) and HM (M = Li, Na, BeH, MgH). J. Phys. Chem. A 2015, 119, 2217–2224. 10.1021/jp503735u. [DOI] [PubMed] [Google Scholar]
  77. Guo X.; An X.; Li Q. Se···N Chalcogen Bond and Se···X Halogen Bond Involving F2C=Se: Influence of Hybridization, Substitution, and Cooperativity. J. Phys. Chem. A 2015, 119, 3518–3527. 10.1021/acs.jpca.5b00783. [DOI] [PubMed] [Google Scholar]
  78. Scheiner S. Effects of Substituents upon the P···N Noncovalent Interaction: The Limits of Its Strength. J. Phys. Chem. A 2011, 115, 11202–11209. 10.1021/jp203964b. [DOI] [PubMed] [Google Scholar]
  79. Alkorta I.; Rozas I.; Elguero J. Molecular complexes between silicon derivatives and electron-rich groups. J. Phys. Chem. A 2001, 105, 743–749. 10.1021/jp002808b. [DOI] [Google Scholar]
  80. Tarakeshwar P.; Choi H. S.; Kim K. S. Olefinic vs Aromatic π–H Interaction: A Theoretical Investigation of the Nature of Interaction of First-row Hydrides with Ethene and Benzene. J. Am. Chem. Soc. 2001, 123, 3323–3331. 10.1021/ja0013531. [DOI] [PubMed] [Google Scholar]
  81. Cremer D.; Kraka E. A description of the chemical bond in terms of local properties of electron density and energy. Croat. Chem. Acta 1984, 57, 1259–1281. [Google Scholar]
  82. Kraka E.; Setiawan D.; Cremer D. Re-evaluation of the bond length-bond strength rule: The stronger bond is not always the shorter bond. J. Comput. Chem. 2016, 37, 130–142. 10.1002/jcc.24207. [DOI] [PubMed] [Google Scholar]
  83. Cremer D.; Kraka E. From molecular vibrations to bonding, chemical reactions, and reaction mechanism. Curr. Org. Chem. 2010, 14, 1524–1560. 10.2174/138527210793563233. [DOI] [Google Scholar]
  84. Setiawan D.; Kraka E.; Cremer D. Hidden bond anomalies: The peculiar case of the fluorinated amine chalcogenides. J. Phys. Chem. A 2015, 119, 9541–9556. 10.1021/acs.jpca.5b05157. [DOI] [PubMed] [Google Scholar]
  85. Setiawan D.; Sethio D.; Cremer D.; Kraka E. From strong to weak NF bonds: On the design of a new class of fluorinating agents. Phys. Chem. Chem. Phys. 2018, 20, 23913–23927. 10.1039/c8cp03843k. [DOI] [PubMed] [Google Scholar]
  86. Konkoli Z.; Cremer D. A new way of analyzing vibrational spectra. I. Derivation of adiabatic internal modes. Int. J. Quantum Chem. 1998, 67, 1–9. . [DOI] [Google Scholar]
  87. Konkoli Z.; Larsson J. A.; Cremer D. A new way of analyzing vibrational spectra. IV. Application and testing of adiabatic modes within the concept of the characterization of normal modes. Int. J. Quantum Chem. 1998, 67, 41–55. . [DOI] [Google Scholar]
  88. Grabowski S. J. Hydrogen bonds, and σ-hole and π-hole bonds - mechanisms protecting doublet and octet electron structures. Phys. Chem. Chem. Phys. 2017, 19, 29742–29759. 10.1039/c7cp06393h. [DOI] [PubMed] [Google Scholar]
  89. Ruedenberg K. The physical nature of the chemical bond. Rev. Mod. Phys. 1962, 34, 326–376. 10.1103/revmodphys.34.326. [DOI] [Google Scholar]
  90. Heredia J. J. D.; Ruedenberg K.; Gordon M. S. Quasi-atomic bonding analysis of Xe-containing compounds. J. Phys. Chem. A 2018, 122, 3442–3454. 10.1021/acs.jpca.8b00115. [DOI] [PubMed] [Google Scholar]
  91. Freindorf M.; Kraka E.; Cremer D. A comprehensive analysis of hydrogen bond interactions based on local vibrational modes. Int. J. Quantum Chem. 2012, 112, 3174–3187. 10.1002/qua.24118. [DOI] [Google Scholar]
  92. Sethio D.; Oliveira V.; Kraka E. Quantitative assessment of tetrel bonding utilizing vibrational spectroscopy. Molecules 2018, 23, 2763. 10.3390/molecules23112763. [DOI] [PMC free article] [PubMed] [Google Scholar]
  93. Angarov V.; Kozuch S. On the σ, π and δ hole interactions: a molecular orbital overview. New J. Chem. 2018, 42, 1413–1422. 10.1039/C7NJ03632A. [DOI] [Google Scholar]

Articles from ACS Omega are provided here courtesy of American Chemical Society

RESOURCES