Tetrel-Bond Interactions Involving Metallylenes TH2 (T = Si, Ge, Sn, Pb): Dual Binding Behavior

The dual binding behavior of the metallylenes TH2 (T = Si, Ge, Sn, Pb) with some selected Lewis acids (T’H3F, T’ = Si, Ge, Sn, Pb) and bases (N2, HCN, CO, and C6H6) has been investigated by using the high-level quantum chemical method. Two types (type-A and type-B) of tetrel-bonded complexes can be formed for TH2 due to their ambiphilic character. TH2 act as Lewis bases in type-A complexes, and they act as Lewis acids in type-B ones. CO exhibits two binding modes in the type-B complexes, one of which is TH2···CO and the other is TH2···OC. The TH2···OC complexes possess a weaker binding strength than the other type-B complexes. The TH2···OC complexes are referred to as the type-B2 complexes, and the other type-B complexes are referred to as the type-B1 complexes. The type-A complexes exhibit a relatively weak binding strength with Eint (interaction energy) values ranging from –7.11 to –15.55 kJ/mol, and the type-B complexes have a broad range of Eint values ranging from −9.45 to −98.44 kJ/mol. The Eint values of the type-A and type-B1 complexes go in the order SiH2 > GeH2 > SnH2 > PbH2. The AIM (atoms in molecules) analysis suggests that the tetrel bonds in type-A complexes are purely closed-shell interactions, and those in most type-B1 complexes have a partially covalent character. The EDA (Energy decomposition analysis) results indicate that the contribution values of the three energy terms go in the order electrostatic > dispersion > induction for the type-A and type-B2 complexes, and this order is electrostatic > induction > dispersion for the type-B1 complexes.


Introduction
Intermolecular interactions are a key issue for supermolecular chemistry because of their central role in molecular recognition [1][2][3]. A hydrogen bond is the most important intermolecular interaction and has been extensively applied in supermolecular systems [4]. A tetrel bond (TB) is another important intermolecular interaction, and the tetrel atoms, such as C and Si, serve as electron acceptors in TB interactions . Its formation is ascribed to the areas of lower electronic density around tetrel atoms, and these areas are called σ-holes [29][30][31][32][33] or π-holes [34][35][36][37]. A σ-hole is an area of lower electronic density on the extension of a bond, and a π-hole is an area of a lower electronic density above and below a planar portion of a molecule. A number of investigations have been performed to understand the interplay between tetrel bonds and tetrel bonds or other types of noncovalent interactions [38][39][40][41][42][43][44][45][46][47][48]. The electron-rich species, such as lone pairs and π-systems, can be served as electron donors in TB interactions. The singlet carbenes can be expected to act as electron donors in TB interactions due to the existence of a lone-pair electron on the carbene C atom [49,50].
The simplest carbene is methylene (CH 2 ), and CH 2 is too reactive to be isolated. The heavy-atom analogues of methylene, i.e., silylene (SiH 2 ), germylene (GeH 2 ), stannylene (SnH 2 ), and plumbylene (PbH 2 ), are the so-called metallylenes [51]. Figure 1 gives the ground-state structures of CH 2 and TH 2 (T = Si, Ge, Sn, Pb), and CH 2 has a triplet ground state. Unlike CH 2 , the ground state is a singlet state for TH 2 . The singlet TH 2 possesses two binding sites, namely, the lone pair electrons and the vacant p-orbital on the T atom. The lone pair can act as an electron donor (Lewis base), and the vacant p-orbital can serve as an electron acceptor (Lewis acid). Like CH 2 , TH 2 is difficult to be isolated due to its especially high reactivity with other molecules [52][53][54][55][56][57][58][59][60][61][62][63][64]. This high reactivity is ascribed to the vacant p-orbital of TH 2 , and metallylenes serve as Lewis acids in these reactions. On the other hand, the lone pair of TH 2 is generally expected to be relatively inert because the lone pair of TH 2 exhibits higher s-character compared with CH 2 [51]. A theoretical study of the possible dual binding behavior of metallylenes in TB interactions is necessary. First, the theoretical studies of TB interactions in which metallylenes act as Lewis bases are absent. Second, the theoretical studies of TB interactions in which metallylenes act as Lewis acids are sparse [65][66][67][68], and systematic studies involving all four metallylenes are still absent. Finally, it is informative to explore how the binding strength of TB interactions changes when the tetrel atoms become heavier. A comprehensive study of TB interactions involving metallylenes should be interesting and can be expected to provide some new insights into TB interactions.
Molecules 2023, 28,  ground-state structures of CH2 and TH2 (T = Si, Ge, Sn, Pb), and CH2 has a triplet ground state. Unlike CH2, the ground state is a singlet state for TH2. The singlet TH2 possesses two binding sites, namely, the lone pair electrons and the vacant p-orbital on the T atom. The lone pair can act as an electron donor (Lewis base), and the vacant p-orbital can serve as an electron acceptor (Lewis acid). Like CH2, TH2 is difficult to be isolated due to its especially high reactivity with other molecules [52][53][54][55][56][57][58][59][60][61][62][63][64]. This high reactivity is ascribed to the vacant p-orbital of TH2, and metallylenes serve as Lewis acids in these reactions. On the other hand, the lone pair of TH2 is generally expected to be relatively inert because the lone pair of TH2 exhibits higher s-character compared with CH2 [51]. A theoretical study of the possible dual binding behavior of metallylenes in TB interactions is necessary. First, the theoretical studies of TB interactions in which metallylenes act as Lewis bases are absent. Second, the theoretical studies of TB interactions in which metallylenes act as Lewis acids are sparse [65][66][67][68], and systematic studies involving all four metallylenes are still absent. Finally, it is informative to explore how the binding strength of TB interactions changes when the tetrel atoms become heavier. A comprehensive study of TB interactions involving metallylenes should be interesting and can be expected to provide some new insights into TB interactions. methylene (CH2) metallylenes (TH2, T = Si, Ge, Sn, Pb) In this study, we investigate the possible dual-binding behavior of metallylenes in TB interactions. We select T'H3F (T' = Si, Ge, Sn, Pb) as electron acceptors to form the TB complexes with TH2 (T = Si, Ge, Sn, Pb). On the other hand, we select N2, HCN, CO, and C6H6 as electron donors to form the TB complexes with TH2. The molecular electrostatic potential (MEP) surface is useful for searching the approximate binding sites for intermolecular interactions. We first examine the MEP maps of the monomers to locate the possible binding sites for TB interactions, and then we discuss the geometries and binding strength of the TB complexes.

Geometries and MEP Surfaces of Monomers
The optimized geometries of TH2 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 2 np 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 TH2 should go in the order SiH2 > GeH2 > SnH2 > PbH2. In this study, we investigate the possible dual-binding behavior of metallylenes in TB interactions. We select T'H 3 F (T' = Si, Ge, Sn, Pb) as electron acceptors to form the TB complexes with TH 2 (T = Si, Ge, Sn, Pb). On the other hand, we select N 2 , HCN, CO, and C 6 H 6 as electron donors to form the TB complexes with TH 2 . The molecular electrostatic potential (MEP) surface is useful for searching the approximate binding sites for intermolecular interactions. We first examine the MEP maps of the monomers to locate the possible binding sites for TB interactions, and then we discuss the geometries and binding strength of the TB complexes.

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 2 np 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 .

SiH2 (silylene)
GeH2 (germylene) SnH2 (stannylene) PbH2 (plumbylene) The MEP surfaces of TH2 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 TH2 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 TH2 are much stronger than their electron-donating ability. The VS,min values of TH2 go in the order SiH2 > GeH2 > SnH2 > PbH2, implying that the electron-donating ability of TH2 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'H3F possess σ-holes and can act as Lewis acids in TB interactions, which can be expected to form the type-A TB complexes with TH2. Figure 3 gives the MEP surfaces of T'H3F, and their VS,max values go in the order PbH3F ≈ SnH3F > GeH3F > SiH3F. We select N2, HCN, CO, and C6H6 as Lewis bases to form the type-B TB complexes with TH2, and their MEP surfaces are illustrated in Figure 4. N2, HCN, and CO possess the lone pairs, and C6H6 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 N2. Unlike N2, 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 C6H6 is parallel to the benzene ring with a VS,min value of −68.1 kJ/mol. The MEP surfaces of TH 2 are illustrated in Figure 3, and the values of positive maxima (V S,max ) and negative minima (V S,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 V S,max values in different TH 2 molecules are very close to each other, ranging from 239.5 to 253.3 kJ/mol. Unlike V S,max values, the V S,min values exhibit obvious differences, ranging from −15.9 to −64.4 kJ/mol. It should be noted that the absolute values of V S,max are much larger than those of V S,min , which suggests that the electron-accepting ability of TH 2 are much stronger than their electron-donating ability. The V S,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 3 F 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 3 F, and their V S,max values go in the order PbH 3 F ≈ SnH 3 F > GeH 3 F > SiH 3 F. We select N 2 , HCN, CO, and C 6 H 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 6 H 6 possesses the π-system, which can be served as electron donors in TB interactions. It can be observed that the V S,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 V S,min value of −57.3 kJ/mol, and the other is around the O atom with a V S,min value of −18.0 kJ/mol. The negative area of C 6 H 6 is parallel to the benzene ring with a V S,min value of −68.1 kJ/mol.

Type-A (σ-Hole Tetrel Bond) Complexes: TH 2 Act as Lewis Bases
The type-A complexes are formed between TH 2 and T'H 3 F, 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 (E int ) 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.

Type-A (σ-Hole Tetrel Bond) Complexes: TH2 Act as Lewis Bases
The type-A complexes are formed between TH2 and T'H3F, 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. Table 1. Binding distance at MP2/aug-cc-pVDZ and MP2/aug-cc-pVTZ (in parentheses) levels (R in Å) and interaction energy at various levels (Eint, in kJ/mol) for type-A complexes.    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 TH2 are relatively inert due to their high s-character, and the electron-donating ability of TH2 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 TH2···T'H3F 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'H3F, the Eint values of the type-A com-  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 E int values at the L2 level are employed in the following discussion.

Complex
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 E int 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 3 F 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 3 F, the E int values of the type-A complexes go in the order SiH 2 > GeH 2 > SnH 2 > PbH 2 . For example, the E int 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 V S,min values of TH 2 , as shown in Figure 3. On the other hand, for a given TH 2 , the E int values of the type-A complexes go in the order PbH 3 F ≈ SnH 3 F > GeH 3 F > SiH 3 F. For example, the E int 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 V S,max values of T'H 3 F, 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 E int and E(2) values, with R 2 = 0.974, as shown in Figure 6. In this study, the value of charge transfer (q CT ) is the sum of the natural atomic charge over the TH 2 molecule in the complexes. A positive q CT represents that the direction of charge transfer is from TH 2 to another molecule, and a negative q CT represents the reverse direction. The q CT 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 (∇ 2 ρ), 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 ∇ 2 ρ 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 |E int | and G or |V| values for the SiH 2 ···T'H 3 F 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 (E tot ) values in Table 3 are similar to the E int 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.

Type-B (π-Hole Tetrel Bond) Complexes: TH 2 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 6 H 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 E int values at the L2 level are employed in the following discussion. Table 2. Second-order perturbation stabilization energy (E(2), in kJ/mol), charge transfer (qCT, in e), electron density (ρ, in a.u.), Laplacian (∇2ρ, in a.u.), energy density (H, in a.u.), local kinetic energy density (G, in a.u.) and potential energy density (V, in a.u.) at the BCP for type-A complexes.

Complex
Orbital Interaction analysis shows that the dominant orbital interactions for the type-A complexes are (T)→σ* (T'-F), with the second-order perturbation stabilization energy E(2) values rang from 19.27 to 47.53 kJ/mol. In fact, there exists a linear relationship between the Eint E(2) values, with R 2 = 0.974, as shown in Figure 6. In this study, the value of charge tran (qCT) is the sum of the natural atomic charge over the TH2 molecule in the complexes positive qCT represents that the direction of charge transfer is from TH2 to another m cule, and a negative qCT represents the reverse direction. The qCT values are positive for the type-A complexes, indicating that TH2 act as Lewis bases in type-A complexes. A analysis indicates that there exist the intermolecular T···T' bond critical points (BCP) in the type-A complexes, and the electron density (ρ), Laplacian (∇ 2 ρ), and energy den (H) at the BCP are listed in Table 2. The ρ values are smaller than 0.01 a.u. for all the ty A complexes. It can also be found that both ∇ 2 ρ and H are positive for all the type-A co plexes, suggesting that the tetrel bonds in type-A complexes are the purely closed-s (noncovalent) interactions. The local kinetic energy density (G) and the local potential ergy density (V) also might be used to analyze the electronic behavior at the intermole lar BCP. The values of G and V are listed in Table 2. The previous study indicates that G and |V| values are increased with an increase of the stabilization energy (the absol value of interaction energy) for the halogen-bonded complexes, implying that G an might be considered as a measure of the strength of the intermolecular interaction [ Similar relations can also be found for most type-A complexes. For instance, there e linear relationships between the |Eint| and G or |V| values for the SiH2···T'H3F system shown in Figure S1.  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 E int 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 E int 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 E int values is in agreement with the V S,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 E int 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. Table 3. Decomposition of the total interaction energy (Etot) for type-A complexes into electrostatic (Eele), induction (Eind), dispersion (Edisp), and exchange (Eex) energy terms. All energies in kJ/mol. The relative values in percent represent the contribution of electrostatic, induction, and dispersion energy terms to the sum of all the three energy terms.     The optimized geometries of the type-B complexes (B9-B16) involving TH2 with CO are shown in Figure 9, and the formation of the complex between SiH2 and CO was confirmed by the experimental study [61]. Unlike N2, CO is a heteronuclear diatomic molecule and exhibits two binding modes in the type-B complexes, one of which is TH2···CO and the other is TH2···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 bind- 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 V S,min values around C and O atoms of CO, as shown in Figure 4. The E int 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 V S,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 E int value. The TH 2 ···CO complexes have a broad range of E int values ranging from −32.10 to −98.44 kJ/mol, and in contrast, the TH 2 ···OC complexes have a very narrow range of E int 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 E int values of the TH 2 ···CO system go in the order SiH 2 > GeH 2 > SnH 2 > PbH 2 .

Complex
Molecules 2023, 28, 2577 12 of 19 the type-B1 complexes in the following discussions. Like the TH2···N2 and TH2···HCN systems, the Eint values of the TH2···CO system go in the order SiH2 > GeH2 > SnH2 > PbH2. The optimized geometries of the type-B complexes (B17-B20) involving TH2 with C6H6 are shown in Figure 10. Unlike the other three Lewis bases for which the lone pairs are used as the electron-donors, C6H6 uses the π-system as an electron-donor to form the type-B complexes with TH2. As expected, TH2 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 TH2···N2 system but smaller than those of the TH2···HCN system. Like the other type-B1 complexes, the Eint values of the complexes go in the order SiH2 > GeH2 > SnH2 > PbH2 for the TH2···C6H6 Figure 9. Optimized geometries of the type-B complexes involving CO at the MP2/aug-cc-pVDZ level, distances in Å, angles in • , and WBI values (in parenthesis).
The optimized geometries of the type-B complexes (B17-B20) involving TH 2 with C 6 H 6 are shown in Figure 10. Unlike the other three Lewis bases for which the lone pairs are used as the electron-donors, C 6 H 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 E int 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 E int values of the complexes go in the order SiH 2 > GeH 2 > SnH 2 > PbH 2 for the TH 2 ···C 6 H 6 system. 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.  (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 ∇ 2 ρ 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 TH2···CO system, as shown in Figure S2. Table 5. Second-order perturbation stabilization energy (E(2), in kJ/mol), charge transfer (qCT, in e), electron density (ρ, in a.u.), Laplacian (∇ 2 ρ, in a.u.), energy density (H, in a.u.), local kinetic energy density (G, in a.u.) and potential energy density (V, in a.u.) at the BCP for type-B complexes.

Complex
Orbital Interaction 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 TH 2 have a narrow range of V S,max values ranging from 239.5 to 253.3 kJ/mol, one may expect that for a given Lewis base, the E int 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 E int values, and the E int values go in the order SiH 2 > GeH 2 > SnH 2 > PbH 2 . Additionally, the E int values of the type-B1 complexes go in the order CO > HCN > C 6 H 6 > N 2 for SiH 2 and GeH 2 ; HCN > CO > C 6 H 6 > N 2 for SnH 2 ; and HCN > C 6 H 6 ≈ CO > N 2 for PbH 2 . Unlike the type-B1 complexes, the E int values of the type-B2 complexes are very close to each other, which is consistent with the narrow range of V S,max values of TH 2 .
The NBO and AIM analysis results of the type-B complexes are listed in Table 5.  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 ∇ 2 ρ 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 |E int | and G values and an approximately linear relationship between the |E int | and |V| values for the TH 2 ···CO system, as shown in Figure S2. Table 5. Second-order perturbation stabilization energy (E(2), in kJ/mol), charge transfer (q CT , in e), electron density (ρ, in a.u.), Laplacian (∇ 2 ρ, in a.u.), energy density (H, in a.u.), local kinetic energy density (G, in a.u.) and potential energy density (V, in a.u.) at the BCP for type-B complexes.

Complex
Orbital Interaction 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. Table 6. Decomposition of the total interaction energy (E tot ) for type-B complexes into electrostatic (E ele ), induction (E ind ), dispersion (E disp ), and exchange (E ex ) energy terms. All energies in kJ/mol. The relative values in percent represent the contribution of electrostatic, induction, and dispersion energy terms to the sum of all the three energy terms.  TH2···CO system TH2···OC system TH2···C6H6 system Figure 11. The changing trends of the contribution of the electrostatic, induction, and dispersion energy terms with the increase of the T atomic number for the type-B complexes.

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 [72]. The augcc-pVDZ-PP basis set, which uses pseudopotentials to describe the inner core orbitals [73], 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 all the complexes were reoptimized at the MP2/augcc-pVTZ (aug-cc-pVTZ-PP for Sn and Pb atoms) level. Single-point energy calculations Figure 11. The changing trends of the contribution of the electrostatic, induction, and dispersion energy terms with the increase of the T atomic number for the type-B complexes.

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 [72]. The aug-cc-pVDZ-PP basis set, which uses pseudopotentials to describe the inner core orbitals [73], 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 all the complexes were reoptimized at the MP2/aug-cc-pVTZ (aug-cc-pVTZ-PP for Sn and Pb atoms) level. Single-point energy calculations were performed at the CCSD (T)/aug-cc-pVTZ level to obtain more accurate energies. 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 (BSSE) correction was carried out following the counterpoise (CP) method [74]. AIM analysis [75] and MEP calculation were carried out using the Multiwfn program [76], and the MEP maps were generated on a 0.001 a.u. isodensity surface and plotted using GaussView software [77]. NBO analysis [78] was performed via the procedures contained within Gaussian 09. Energy decomposition analysis (EDA) based on symmetry-adapted perturbation theory (SAPT) [79] was performed at the sapt2+dmp2/aug-cc-pVDZ level using the Psi4 package [80].

Conclusions
In this study, the dual binding behavior of the metallylenes TH 2 with some selected Lewis acids and bases has been investigated. Two types (type-A and type-B) of TB complexes can be formed for TH 2 due to their ambiphilic character. TH 2 act as Lewis bases in type-A complexes, and they act as Lewis acids in type-B ones. T'H 3 F possess σ-holes and can act as Lewis acids to form the type-A complexes with TH 2 , which are the σ-hole TB complexes. N 2 , HCN, CO, and C 6 H 6 possess the lone pair or π-system and can act as Lewis bases to form the type-B complexes with TH 2 , which are the π-hole TB complexes. CO exhibits two binding modes in the type-B complexes, one of which is TH 2 ···CO and the other is TH 2 ···OC. The TH 2 ···OC complexes possess a weaker binding strength than the other type-B complexes. The TH 2 ···OC complexes are referred to as the type-B2 complexes, and the other type-B complexes are referred to as the type-B1 complexes. The type-A complexes exhibit a relatively weak binding strength with E int values ranging from −7.11 to −15.55 kJ/mol. The type-B complexes have a broad range of E int values ranging from −9.45 to −98.44 kJ/mol, and the E int values of the type-B1 complexes are larger than those of the type-B2 and type-A complexes. For a given T'H 3 F, the E int values of the type-A complexes go in the order SiH 2 > GeH 2 > SnH 2 > PbH 2 , and for a given TH 2 , the E int values of the type-A complexes go in the order PbH 3 F ≈ SnH 3 F > GeH 3 F > SiH 3 F, which can be clarified by the MEP maps of TH 2 and T'H 3 F in a reasonable way. For a given Lewis base, the type-B1 complexes have a relatively broad range of E int values, and the E int values go in the order SiH 2 > GeH 2 > SnH 2 > PbH 2 . Additionally, the E int values of the type-B1 complexes go in the order CO > HCN > C 6 H 6 > N 2 for SiH 2 and GeH 2 ; HCN > CO > C 6 H 6 > N 2 for SnH 2 ; and HCN > C 6 H 6 ≈ CO > N 2 for PbH 2 . Unlike the type-B1 complexes, the E int values of the type-B2 complexes are very close to each other, which is consistent with the narrow range of V S,max values of TH 2 . The AIM analysis suggests that the tetrel bonds in type-A complexes are the purely closed-shell interactions, and those in most type-B1 complexes have a partially covalent character. The EDA results indicate that the contribution values of the three energy terms go in the order of electrostatic > dispersion > induction for the type-A and type-B2 complexes, and this order is electrostatic > induction > dispersion for the type-B1 complexes.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/molecules28062577/s1. Figure S1. Correlation between the |E int | and G or |V| values for the SiH 2 ···T'H 3 F system, and Figure S2. Correlation between the |E int | and G or |V| values for the TH 2 ···CO system.