2.1. Geometries and MEP Surfaces of Monomers
The optimized geometries of TH
2 with the percentage of s-character of the corresponding lone pairs based on the Natural bond orbital (NBO) analysis are displayed in
Figure 2. The values of H-T-H angles in metallylenes range from 90.2° to 92.1°, which are very close to 90° and are obviously smaller than that (101.6°) of H-C-H angle in singlet methylene. Additionally, the percentage of s-character of the lone pairs in metallylenes ranges from 74.2% to 85.1%, which is much larger than that in methylene (56.2%). These differences between metallylenes and methylene indicate that the heavier tetrel atoms, in contrast with the carbon atom, exhibit a weak ability to form hybrid orbitals and prefer to keep the ns
2np
2 valence electron configurations in metallylenes. It can also be observed that the s-character values increase with the increase of the T atomic number, suggesting that the lone pairs of metallylenes become more inert when the tetrel atoms become heavier. In other words, the electron-donating ability of TH
2 should go in the order SiH
2 > GeH
2 > SnH
2 > PbH
2.
The MEP surfaces of TH
2 are illustrated in
Figure 3, and the values of positive maxima (
VS,max) and negative minima (
VS,min) are also labeled. It can be observed that there exist two possible binding areas around T atoms, one of which is the π-hole area with a positive surface potential, and the other is the lone-pair (LP) area with a negative surface potential. The
VS,max values in different TH
2 molecules are very close to each other, ranging from 239.5 to 253.3 kJ/mol. Unlike
VS,max values, the
VS,min values exhibit obvious differences, ranging from −15.9 to −64.4 kJ/mol. It should be noted that the absolute values of
VS,max are much larger than those of
VS,min, which suggests that the electron-accepting ability of TH
2 are much stronger than their electron-donating ability. The
VS,min values of TH
2 go in the order SiH
2 > GeH
2 > SnH
2 > PbH
2, implying that the electron-donating ability of TH
2 goes in the same order, which is consistent with the previous conclusion based on the s-character values of lone pairs. A similar phenomenon was observed for the N-heterocyclic carbene and its heavy-atom analogues [
69].
Two types of TB complexes can be formed for metallylenes due to their ambiphilic character, which we refer to as type-A and type-B for convenience. Metallylenes act as Lewis bases in type-A complexes, and they act as Lewis acids in type-B ones. T’H
3F possess σ-holes and can act as Lewis acids in TB interactions, which can be expected to form the type-A TB complexes with TH
2.
Figure 3 gives the MEP surfaces of T’H
3F, and their
VS,max values go in the order PbH
3F ≈ SnH
3F > GeH
3F > SiH
3F. We select N
2, HCN, CO, and C
6H
6 as Lewis bases to form the type-B TB complexes with TH
2, and their MEP surfaces are illustrated in
Figure 4. N
2, HCN, and CO possess the lone pairs, and C
6H
6 possesses the π-system, which can be served as electron donors in TB interactions. It can be observed that the
VS,min value (−131.7 kJ/mol) of HCN is much larger than that (−34.3 kJ/mol) of N
2. Unlike N
2, CO is a heteronuclear diatomic molecule and possesses two negative areas, one of which is around the C atom with a
VS,min value of −57.3 kJ/mol, and the other is around the O atom with a
VS,min value of −18.0 kJ/mol. The negative area of C
6H
6 is parallel to the benzene ring with a
VS,min value of −68.1 kJ/mol.
2.2. Type-A (σ-Hole Tetrel Bond) Complexes: TH2 Act as Lewis Bases
The type-A complexes are formed between TH
2 and T’H
3F, and the corresponding intermolecular interactions exist between two tetrel atoms, which are the σ-hole tetrel bonds. The geometries of the type-A complexes (
A1–
A16) optimized at the MP2/aug-cc-pVDZ level with the binding distances are displayed in
Figure 5, and the corresponding Wiberg bond index (WBI) based on the NBO analysis are also labeled. Our previous studies indicate that the MP2/aug-cc-pVDZ level is more reasonable than MP2/aug-cc-pVTZ level for exploring the intermolecular interactions involving the heavy tetrel atoms. As a comparison, the geometries of these complexes were reoptimized at the MP2/aug-cc-pVTZ level, and the binding distances at the two levels are collected in
Table 1. Additionally, the interaction energies (
Eint) of these complexes at the four different computational levels are also collected in
Table 1. These four levels are referred to 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.
It can be observed from
Table 1 that the binding distances of all the sixteen type-A complexes at the L1 level are longer than those at the L3 level, which means that the complexes at the L3 level are overbound compared with the L1 level. It can also be found that the interaction energies at the L1 level are smaller than the corresponding values at the L2 level for all the type-A complexes, which indicates the L1 level underestimates the interaction energies compared with the L2 level. On the other hand, the L3 level overestimates the interaction energies compared with the L4 level. Furthermore, the interaction energies at the L2 level are larger than those at the L4 level in most cases, which suggests that the geometries optimized at the L1 level are more stable than those at the L3 level. The optimized geometries at the L1 level and the
Eint values at the L2 level are employed in the following discussion.
Our preceding discussion indicates that the lone pairs of TH
2 are relatively inert due to their high s-character, and the electron-donating ability of TH
2 is expected to be weak. As expected, the type-A complexes indeed exhibit relatively weak binding strength with
Eint values ranging from −7.11 to −15.55 kJ/mol. The type-A complexes possess relatively long T···T’ binding distances ranging from 3.618 to 3.910 Å and relatively small WBI values ranging from 0.050 to 0.104, suggesting that the tetrel bonds in TH
2···T’H
3F systems should be the noncovalent interactions, which is consistent with the Atoms in molecules (AIM) analysis as discussed below. The F-T’···T binding angles are linear for all the type-A complexes, ranging from 179° to 180°. For a given T’H
3F, the
Eint values of the type-A complexes go in the order SiH
2 > GeH
2 > SnH
2 > PbH
2. For example, the
Eint values of the complexes
A4,
A8,
A12, and
A16 are −15.42, −14.92, −13.25, and −9.86 kJ/mol, respectively. This order is in agreement with the LP
VS,min values of TH
2, as shown in
Figure 3. On the other hand, for a given TH
2, the
Eint values of the type-A complexes go in the order PbH
3F ≈ SnH
3F > GeH
3F > SiH
3F. For example, the
Eint values of the complexes
A5,
A6,
A7, and
A8 are −10.32, −11.08, −14.96, and −14.92 kJ/mol, respectively. This order is in agreement with the σ-hole
VS,max values of T’H
3F, as shown in
Figure 3.
The NBO and AIM analysis results of the type-A complexes are listed in
Table 2. NBO analysis shows that the dominant orbital interactions for the type-A complexes are LP (T)→σ* (T’-F), with the second-order perturbation stabilization energy
E(2) values ranging from 19.27 to 47.53 kJ/mol. In fact, there exists a linear relationship between the
Eint and
E(2) values, with
R2 = 0.974, as shown in
Figure 6. In this study, the value of charge transfer (
qCT) is the sum of the natural atomic charge over the TH
2 molecule in the complexes. A positive
qCT represents that the direction of charge transfer is from TH
2 to another molecule, and a negative
qCT represents the reverse direction. The
qCT values are positive for all the type-A complexes, indicating that TH
2 act as Lewis bases in type-A complexes. AIM analysis indicates that there exist the intermolecular T···T’ bond critical points (BCP) in all the type-A complexes, and the electron density (
ρ), Laplacian (∇
2ρ), and energy density (
H) at the BCP are listed in
Table 2. The
ρ values are smaller than 0.01 a.u. for all the type-A complexes. It can also be found that both ∇
2ρ and
H are positive for all the type-A complexes, suggesting that the tetrel bonds in type-A complexes are the purely closed-shell (noncovalent) interactions. The local kinetic energy density (
G) and the local potential energy density (
V) also might be used to analyze the electronic behavior at the intermolecular BCP. The values of
G and
V are listed in
Table 2. The previous study indicates that the
G and |
V| values are increased with an increase of the stabilization energy (the absolute value of interaction energy) for the halogen-bonded complexes, implying that
G and
V might be considered as a measure of the strength of the intermolecular interaction [
70]. Similar relations can also be found for most type-A complexes. For instance, there exist linear relationships between the |
Eint| and
G or |
V| values for the SiH
2···T’H
3F system, as shown in
Figure S1.
The symmetry-adapted perturbation theory (SAPT) is a perturbation theory aimed specifically at calculating the interaction energy between two molecules. The result is obtained as a sum of separate corrections accounting for the electrostatic, induction, dispersion, and exchange contributions to interaction energy, so the SAPT decomposition facilitates the understanding and physical interpretation of results. Electrostatic energy arises from the Coulomb interaction between charge densities of isolated molecules. Induction energy is the energetic effect of mutual polarization between the two molecules. Dispersion energy is a consequence of intermolecular electron correlation, usually explained in terms of correlated fluctuations of electron density on both molecules. Exchange energy is a short-range repulsive effect that is a consequence of the Pauli exclusion principle. The Energy decomposition analysis (EDA) results of the type-A complexes are listed in
Table 3, and the graphical changing trends of the contribution of the electrostatic, induction, and dispersion energy terms with the increase of the T atomic number are illustrated in
Figure 7. The total interaction energy (
Etot) values in
Table 3 are similar to the
Eint values at the L2 level in
Table 1 for most complexes, suggesting that the EDA results are reasonable for the systems in this study. It can be observed that the contribution values of the three energy terms go in the order of electrostatic > dispersion > induction for all the type-A complexes. The contribution of the electrostatic term exhibits a decreasing trend, and that of the dispersion term exhibits an increasing trend with the increase of the T atomic number. Additionally, the contribution of the induction term is basically unchanged with the increase of the T atomic number.
2.3. Type-B (π-Hole Tetrel Bond) Complexes: TH2 Act as Lewis Acids
The metallylenes are the highly reactive Lewis acids and can interact with various Lewis bases. In this section, we select N
2, HCN, CO, and C
6H
6 as Lewis bases to interact with TH
2 to form the type-B complexes, which are the π-hole TB complexes. The binding distances and interaction energies of all the twenty type-B complexes (
B1–
B20) at different levels are collected in
Table 4. Like type-A complexes, the binding distances of the type-B complexes at the L1 level are longer than those at the L3 level. It can also be found that the interaction energies of the type-B complexes at the L1 level are similar to those at the L2 level in most cases, but there exist relatively large differences between the L3 and L4 levels. The optimized geometries at the L1 level and the
Eint values at the L2 level are employed in the following discussion.
The optimized geometries of the type-B complexes (
B1–
B8) involving TH
2 with N
2 and HCN are shown in
Figure 8. The formation of the complex SiH
2···N
2 (
B1) was confirmed by the experimental study [
61]. It should be noted that N
2 is a rather weak Lewis base, and therefore the formation of
B1 reflects the high reactivity of SiH
2 as a Lewis acid. The T···N binding distances range from 2.175 to 2.736 Å for the TH
2···N
2 complexes (
B1–
B4), with the N-N···T binding angles ranging from 171.3° to 179.5°. The complexes
B1–
B4 possess larger
Eint values ranging from −14.59 to −26.08 kJ/mol, with larger WBI values ranging from 0.104 to 0.289, compared with the type-A complexes. Like N
2, HCN also uses the lone pair of the N atom as an electron-donor, but HCN is a stronger Lewis base compared with N
2. HCN can form the TB complexes with various molecules. The C-N···T binding angles of the TH
2···HCN complexes (
B5–
B8) range from 170.4° to 179.7°, which are similar to those of
B1–
B4, but
B5–
B8 possess shorter T···N binding distances ranging from 2.032 to 2.565 Å compared with
B1–
B4. The
Eint values of
B5–
B8 range from −40.13 to −71.77 kJ/mol, which are nearly three times as large as those of
B1–
B4, and this difference in
Eint values is in agreement with the
VS,min values of N
2 and HCN, as shown in
Figure 4. It can also be found that the WBI values of
B5–
B8 are larger than the corresponding values of
B1–
B4. The
Eint values of the complexes go in the order SiH
2 > GeH
2 > SnH
2 > PbH
2 for both the TH
2···N
2 and TH
2···HCN systems.
The optimized geometries of the type-B complexes (
B9–
B16) involving TH
2 with CO are shown in
Figure 9, and the formation of the complex between SiH
2 and CO was confirmed by the experimental study [
61]. Unlike N
2, CO is a heteronuclear diatomic molecule and exhibits two binding modes in the type-B complexes, one of which is TH
2···CO and the other is TH
2···OC. The fact that CO exhibits two binding modes and that complexes bound on the oxygen side are weaker has been previously reported [
71]. The O-C···T binding angles of the TH
2···CO complexes (
B9–
B12) range from 168.7° to 177.6°, which are similar to the C-O···T binding angles (174.8° to 179.4°) of the TH
2···OC complexes (
B13–
B16), but
B9–
B12 possess obviously shorter T···C binding distances ranging from 1.921 to 2.622 Å compared with the T···O binding distances (2.649 to 2.883 Å) of
B13–
B16. The WBI values of
B9–
B12 range from 0.294 to 0.928, which are also much larger than those (0.038 to 0.053) of
B13–
B16. As expected, the TH
2···CO complexes exhibit a stronger binding strength than the TH
2···OC complexes, which is in agreement with the
VS,min values around C and O atoms of CO, as shown in
Figure 4. The
Eint value (−98.44 kJ/mol) of the complex SiH
2···CO (
9) is ten times as large as that (−9.45 kJ/mol) of the complex SiH
2···OC (
13), and
9 also possesses a rather large WBI value of 0.928, suggesting that
9 has a partially covalent character, which is in agreement with the AIM analysis as discussed below. Considering that the
VS,min value (−57.3 kJ/mol) around the C atom of CO is not large, it is somewhat surprising that
9 possesses such a high
Eint value. The TH
2···CO complexes have a broad range of
Eint values ranging from −32.10 to −98.44 kJ/mol, and in contrast, the TH
2···OC complexes have a very narrow range of
Eint values ranging from −9.45 to −10.07 kJ/mol. The TH
2···OC complexes possess a weaker binding strength than the other type-B complexes and exhibit a different binding behavior, as discussed below. We refer to the TH
2···OC complexes as the type-B2 complexes and refer to the other type-B complexes as the type-B1 complexes in the following discussions. Like the TH
2···N
2 and TH
2···HCN systems, the
Eint values of the TH
2···CO system go in the order SiH
2 > GeH
2 > SnH
2 > PbH
2.
The optimized geometries of the type-B complexes (
B17–
B20) involving TH
2 with C
6H
6 are shown in
Figure 10. Unlike the other three Lewis bases for which the lone pairs are used as the electron-donors, C
6H
6 uses the π-system as an electron-donor to form the type-B complexes with TH
2. As expected, TH
2 molecules are parallel to the benzene ring in these π-hole TB complexes.
B17–
B20 possess the T···C binding distances ranging from 2.452 to 2.799 Å, with the WBI values ranging from 0.090 to 0.184. The
Eint values of
B17–
B20 range from −32.35 to −43.64 kJ/mol, which are larger than those of the TH
2···N
2 system but smaller than those of the TH
2···HCN system. Like the other type-B1 complexes, the
Eint values of the complexes go in the order SiH
2 > GeH
2 > SnH
2 > PbH
2 for the TH
2···C
6H
6 system.
As mentioned before, the relative binding strength of the type-A complexes can be clarified by the MEP maps of the corresponding monomers in a reasonable way, but this explanation is not applicable to the type-B1 complexes. Considering that TH2 have a narrow range of VS,max values ranging from 239.5 to 253.3 kJ/mol, one may expect that for a given Lewis base, the Eint values of the type-B complexes should be very close to each other. However, for a given Lewis base, the type-B1 complexes have a relatively broad range of Eint values, and the Eint values go in the order SiH2 > GeH2 > SnH2 > PbH2. Additionally, the Eint values of the type-B1 complexes go in the order CO > HCN > C6H6 > N2 for SiH2 and GeH2; HCN > CO > C6H6 > N2 for SnH2; and HCN > C6H6 ≈ CO > N2 for PbH2. Unlike the type-B1 complexes, the Eint values of the type-B2 complexes are very close to each other, which is consistent with the narrow range of VS,max values of TH2.
The NBO and AIM analysis results of the type-B complexes are listed in
Table 5. NBO analysis shows that the dominant orbital interactions for the type-B complexes are LP (B)→LP * (T) (B = N, C, and O) and π (C = C)→LP * (T) with a very broad range of
E(2) values ranging from 49.45 to 1488.16 kJ/mol. The
E(2) values of the type-B1 complexes are larger than those of the type-B2 and type-A complexes. The
qCT values are negative for all the type-B complexes, indicating that TH
2 act as Lewis acids in type-B complexes. AIM analysis indicates that there exist the intermolecular T···B (B = N, C, and O) bond critical points in the type-B complexes. Like
E(2) values, the
ρ values of the type-B1 complexes are larger than those of the type-B2 and type-A complexes. It can also be found that ∇
2ρ are positive and
H are negative for most type-B1 complexes, suggesting that these complexes have a partially covalent character. There exists a linear relationship between the |
Eint| and
G values and an approximately linear relationship between the |
Eint| and |
V| values for the TH
2···CO system, as shown in
Figure S2.
The EDA results of the type-B complexes are listed in
Table 6, and the graphical illustration is shown in
Figure 11. The contribution of the electrostatic term exhibits a fluctuating trend (first increase and then decrease) with the increase of the T atomic number. On the other hand, the contribution of the induction term exhibits a decreasing trend, and that of the dispersion term exhibits an increasing trend with the increase of the T atomic number. It can also be observed that the contribution values of the three energy terms go in the order electrostatic > induction > dispersion for the type-B1 complexes, and this order is electrostatic > dispersion > induction for the type-B2 complexes.