Identification of the Tetrel Bonds between Halide Anions and Carbon Atom of Methyl Groups Using Electronic Criterion

The consideration of the disposition of minima of electron density and electrostatic potential along the line between non-covalently bound atoms in systems with Hal−···CH3–Y (Hal− = Cl, Br; Y = N, O) fragments allowed to prove that the carbon atom in methyl group serves as an electrophilic site provider. These interactions between halide anion and carbon in methyl group can be categorized as the typical tetrel bonds. Statistics of geometrical parameters for such tetrel bonds in CSD is analyzed. It is established that the binding energy in molecular complexes with tetrel bonds correlate with the potential acting on an electron in molecule (PAEM). The PAEM barriers for tetrel bonds show a similar behavior for both sets of complexes with Br− and Cl− electron donors.


Introduction
The problem of categorizing non-covalent interactions in molecular crystals and complexes is now a focus of attention [1,2]. Nowadays, the systematization of the halogen, chalcogen, pnictogen, and tetrel bonds already exists [3]; however, in most cases, only the simplistic geometrical approach underlies the analysis of such types of interactions. In this context, the types of non-covalent interactions are traditionally discussed in terms of interatomic distances and angles, which specify the mutual orientation of pivotal chemical bonds [4,5]. However, due to the pronounced and specific electrostatic component of such non-covalent bonds [6,7], more careful analysis of the electronic features of the halogen, chalcogen, pnictogen, and tetrel bonds is required. Such analysis needs to focus on the features of valence electron shells and related anisotropy of the electrostatic potential of interacting atoms.
The estimation of the binding energy for molecules in the Y 4 T···Hal − complexes, where a tetrel atom T = C, Si, Ge, Sn, as well as the description of electron density characteristics for tetrel bonds, were presented in References [8][9][10][11][12][13]. The carbon atom in the CH 3 -group is fairly often noted as the owner of σ-hole, and the fact that the oxygen atom can act as an electron-rich center in the CH 3 ···O tetrel bonding has been confirmed in studies [14,15]. Note that in these early works such non-covalent interaction has been referred as a "carbon bond". Pal et al. [16] described the CH 3 ···N tetrel bonding in a Co(II) coordination polymeric system using the analysis of calculated electron density. The typical tetrel bonds formed by CH 3 -group in crystals have been also been observed by high-precision X-ray diffraction method using the analysis of the experimental electron density [17,18]. the minimum of electron density on the interatomic line is always closer to the atom that has delivered its own electrophilic site for bonding.
We have recently proposed the potential acting on an electron in molecule (PAEM [36]) [37] as a function that not only characterizes the properties of non-covalent bonding with a significant electrostatic component, but also allows us to observe the quantitative relationship with the interaction energy in complexes. Unlike ESP, the PAEM contains both Coulomb and exchange components. The first of them has a classic nature and the second one is the two-electron contribution of the quantum exchange-correlation potential. PAEM was examined [38] for the halogen and chalcogen bonding characterization and its usefulness was confirmed.
The aim of the present study is to demonstrate the efficiency and productivity of the above-mentioned electronic criterion and the PAEM for analysis of tetrel bonds between the carbon atom of methyl groups and halide anions, which sometimes occur in molecular crystals. We also try to understand to what extent the characteristics of the gas-phase complexes are suitable for describing Hal − ···CH 3 Y (Hal − = Cl, Br; Y = N, O) tetrel bonds in crystals.

Population of Hal − ···CH 3 Y Tetrel Bonds in Crystals
The search of short contacts between a halide anion and the methyl carbon, Hal − ···CH 3 -Y, in Cambridge Structural Database (CSD) v.5.39 (The Cambridge Crystallographic Data Centre, Cambridge, UK) [39] was performed with the following restrictions: organic derivatives without disordered, polymeric, powder, organometallic and repeating structures have been considered. The main condition was to choose interactions in which the halide anion, Hal − = Cl, Br, I, was placed on the extension of the C-Y covalent bond, where Y = C, N, O. We set that condition using the angle θ (Hal − -C-Y), the value of which was in the range from 160 • to 180 • . At the same time, we selected the structures with interatomic distances, d(Hal, C), falling into the range (r vdw (C) + r vdw (Hal) ± 0.2 Å), where r vdw is the Bondi atomic radius [40]. The total number of selected structures that satisfied those conditions was 164. The analysis of the obtained sample has shown that the Y atom covalently bound with the CH 3 group is nitrogen in most cases. We have found 43 cases of Cl − ···CH 3 -N interactions, 36 cases of Br − ···CH 3 -N interactions and 53 cases of I − ···CH 3 -N interactions. Oxygen and carbon are involved in such covalent bonds much less frequently and approximately equally. In these cases, the methyl group forms more interactions with the Cl − anion than with the Br − and I − anions taken together. It can be concluded that the polarity of the covalent bond CH 3 -Y affects the probability and strength of the tetrel bond formation. It should be noted that the distances d(Hal, C) for the cases of Hal − ···CH 3 -C interactions everywhere exceed the sum of van der Waals radii ( Figure 1). If the CH 3 -group is bound with oxygen (Hal − ···CH 3 -O), the distances d(Hal, C) can be less than the sum of van der Waals radii, though all of these distances are more than this sum for I − cases.
Therefore, we conclude that the studied type of interactions, Hal − ···CH 3 -Y, are not widely spread within crystals listed in CSD, but they are not exceptional.

Evidence of Electrophilic Sites for the CH 3 -Groups Bound in Tetrel Bonds
Let us now look at the same examples of halide crystal structures containing tetrel bonds ( Figure 2). All the results considered in this chapter were obtained for crystal structures by the calculations with the periodic boundary conditions. In the crystalline N,N,N ,N -tetramethylchloroformamide chloride, LONGEB [41], the Cl − anion forms non-covalent interactions with the Cl, H, C atoms, which are characterized by interatomic distances smaller than the sums of van der Waals radii. The Cl − ···Cl-C non-covalent interaction with a distance of 3.122 Å refers to a typical charge-assisted halogen bond; the next five hydrogen bonds, Cl − ···H-C, are characterized by interatomic distances ranging from 2.924 to 2.664 Å. Finally, the Cl − ···CH 3 interaction of 3.425 Å can be called a tetrel bond. In the crystalline dimethylmethyleneammonium chloride VAPREJ [42], the chloride anion forms eight Cl − ···H-C interactions, which are shorter than the sum of van der Waals radii and two Cl − ···CH 3 tetrel bonds. In the dimethylmethylenimine bromide crystal, LILLOH [43], in addition to multiple Br − ···H-C interactions, there are two tetrel bonds: Br − ···CH 3 (3.533 Å) and Br − ···CH 2 (3.503 Å). Quantum-topological analysis of the electron density in all considered crystals have confirmed the presence of the Hal − ···C bond path and bcp of electron density (Table 1). Our series of tetrel bonds in the considered crystals does not vary much, and we have observed the small changes in electron density at the bond critical points, (r bcp ), which are in the range 0.0042-0.0070 a.u. for Cl − ···CH 3 -Y and 0.0060-0.0068 a.u. for Br − ···CH 3 -Y.

Evidence of Electrophilic Sites for the CH3-Groups Bound in Tetrel Bonds
Let us now look at the same examples of halide crystal structures containing tetrel bonds ( Figure  2). All the results considered in this chapter were obtained for crystal structures by the calculations with the periodic boundary conditions. In the crystalline N,N,N′,N′-tetramethylchloroformamide chloride, LONGEB [41], the Cl − anion forms non-covalent interactions with the Cl, H, C atoms, which are characterized by interatomic distances smaller than the sums of van der Waals radii. The Cl − ···Cl-C non-covalent interaction with a distance of 3.122 Å refers to a typical charge-assisted halogen bond; the next five hydrogen bonds, Сl − ···H-C, are characterized by interatomic distances ranging from 2.924 to 2.664 Å. Finally, the Cl − ···CH3 interaction of 3.425 Å can be called a tetrel bond. In the crystalline dimethylmethyleneammonium chloride VAPREJ [42], the chloride anion forms eight Сl − ···H-C interactions, which are shorter than the sum of van der Waals radii and two Cl -···CH3 tetrel bonds. In the dimethylmethylenimine bromide crystal, LILLOH [43], in addition to multiple Br − ···H-C interactions, there are two tetrel bonds: Br − ···CH3 (3.533 Å) and Br − ···CH2 (3.503 Å). Quantumtopological analysis of the electron density in all considered crystals have confirmed the presence of the Hal − ···C bond path and bcp of electron density (Table 1). Our series of tetrel bonds in the considered crystals does not vary much, and we have observed the small changes in electron density at the bond critical points, ρ(rbcp), which are in the range 0.0042-0.0070 a.u. for Cl − ···CH3-Y and 0.0060-0.0068 a.u. for Br − ···CH3-Y.    It is possible to demonstrate the electrophilic site on a carbon atom using the electrostatic potential (ESP) mapped on the isosurface of electron density or the distribution of Electron Localization Function (ELF) [44] for CH 3 -group, which participate in a tetrel bond. For example, relatively higher positive values of ESP on the isosurface of electron density (0.003 a.u.) we can see in the region of the σ-hole, which belongs to the C atomic basin in trimethylammonium cation (Figure 3a,b). It is possible to demonstrate the electrophilic site on a carbon atom using the electrostatic potential (ESP) mapped on the isosurface of electron density or the distribution of Electron Localization Function (ELF) [44] for CH3-group, which participate in a tetrel bond. For example, relatively higher positive values of ESP on the isosurface of electron density (0.003 a.u.) we can see in the region of the σ-hole, which belongs to the C atomic basin in trimethylammonium cation ( Figure  3a    Now let us consider and evaluate how the electronic criterion works for the cases of non-covalent interactions formed by the carbon atoms of methyl groups in halide crystals. In Figure 5a it can be seen that in the LONGEB crystal, the Cl − anion forms two non-covalent interactions at least, as follows from the presence of corresponding bcp. In both cases, Cl(2)···Cl(1) − ···C(4), the one-dimensional ESP minimum is closer to electron donating anion, Cl(1) − in a crystal. The electron density minima along the Cl(2)···Cl(1) − and Cl(1) − ···C(4) lines are located on the side of the Cl(2) and C(4) atoms. They indicate the electrophilic site providers and dictate the name of the non-covalent bonding. Now let us consider and evaluate how the electronic criterion works for the cases of non-covalent interactions formed by the carbon atoms of methyl groups in halide crystals. In Figure 5a it can be seen that in the LONGEB crystal, the Cl − anion forms two non-covalent interactions at least, as follows from the presence of corresponding bcp. In both cases, Cl(2)···Cl(1) − ···C(4), the one-dimensional ESP minimum is closer to electron donating anion, Cl(1) -in a crystal. The electron density minima along the Cl(2)···Cl(1) − and Cl(1) − ···C(4) lines are located on the side of the Cl(2) and C(4) atoms. They indicate the electrophilic site providers and dictate the name of the non-covalent bonding.
According to the proposed electronic criterion, the first interaction, Cl(2)···Cl(1) − , can be categorized as a charge-assisted halogen bond, and the second one, Cl(1) − ···C (4), is a tetrel bond enhanced by charges. In Figure 5b, the minimum of electron density along the Br(1) − ···C(2) line is located on the side of the C(4) atom, while the minimum of ESP is closer to Br(1) − . Such disposition of minima shows that the carbon atom accepts electrons along the Br(1) − ···C(2) line and that interaction can be called a tetrel bond.

Binding Energy in Molecular Complexes with the Hal-···CH3 Tetrel Bonds
The determination of the equilibrium geometry for ion pairs "halide anion-cation" extracted from the crystal environment is not a straightforward procedure. In general, the retention of the halide anion position strictly on the extension of a covalent bond of CH3-group is rather difficult in the gas phase state. This task requires us to dwell on the level of gas phase calculations, different from those used for crystal structures. Nevertheless, this step allows us to obtain the stationary state for the maximal number of complexes, for which the tetrel bonds in crystalline state have attracted our attention. Some relative estimations and the features of electronic properties can be quite useful for According to the proposed electronic criterion, the first interaction, Cl(2)···Cl(1) − , can be categorized as a charge-assisted halogen bond, and the second one, Cl(1) − ···C (4), is a tetrel bond enhanced by charges. In Figure 5b, the minimum of electron density along the Br(1) − ···C(2) line is located on the side of the C(4) atom, while the minimum of ESP is closer to Br(1) − . Such disposition of minima shows that the carbon atom accepts electrons along the Br(1) − ···C(2) line and that interaction can be called a tetrel bond.

Binding Energy in Molecular Complexes with the Hal − ···CH3 Tetrel Bonds
The determination of the equilibrium geometry for ion pairs "halide anion-cation" extracted from the crystal environment is not a straightforward procedure. In general, the retention of the halide anion position strictly on the extension of a covalent bond of CH 3 -group is rather difficult in the gas phase state. This task requires us to dwell on the level of gas phase calculations, different from those used for crystal structures. Nevertheless, this step allows us to obtain the stationary state for the maximal number of complexes, for which the tetrel bonds in crystalline state have attracted our attention. Some relative estimations and the features of electronic properties can be quite useful for understanding the nature of charge-assisted tetrel bonds.
The binding energy, E b , between the halide anion and cation in the considered complexes varies from −52.28 to −82.67 kcal/mol ( Table 2). These values do not fall out of the range that is determined in similar studies [8][9][10][11]. The BSSE correction, ∆E BSSE , is negligible and influences the energy values of the third decimal place of kcal/mol units. The considered tetrel bonds exhibit significantly shorter lengths in the models of complexes extracted from the crystalline environment. On average, the observed Hal − ···C bond lengths in such complexes differ by~17% from those in crystal structures. As a result, the different approaches for complexes and crystals calculations lead to the values of (r bcp ) that are almost twice higher in crystals. Obviously, the direct transfer of tetrel bond properties in isolated complexes to the crystals, neglecting the rest of interactions between a halide anion and crystalline environment, is not entirely correct. Comparing the properties of the CH 3 -Y (Y=N, O) covalent bonds in complexes and isolated cations, we see that the participation of CH 3 -group in tetrel bond with Hal − weakens the CH 3 -Y covalent bond. Therefore, the tetrel bonding elongates the covalent bond of a methyl group by 0.01-0.04 Å, and the values of (r bcp ) for the CH 3 -Y bonds decrease by~8%.
It is useful to understand how the electronic properties of Hal − ···CH 3 Y tetrel bonds in complexes are related to the strength of complexes. In our opinion, the tetrel bonds belong to electrostatically driven interactions. In addition, the binding energy between two oppositely charged ions is much higher in comparison with neutral molecules. For this reason, the electrostatic properties of tetrel bonds have been analyzed first of all.
We found that the properties of both ESP and PAEM for the Hal − ···CH 3 Y tetrel bonds are linearly correlated with the binding energy, E b , in complexes, as shown in Figure 6. The correlation coefficient for the minima of the electrostatic potential, ESP min , on the line between Hal − and C atoms is 0.917. For the maximum of PAEM along this line, PAEM max , or PAEM barrier, the correlation coefficient is 0.985. It is important to note that in the relationship "PAEM max vs E b ", PAEM max for the tetrel bonds formed by Br − and Cl − fits strictly on the common line. This is a rare case among the established relationships between local properties of non-covalent bonds and the binding energy for bound fragments. For example, the electronic potential and kinetic energy densities at bcp do not allow constructing a good common relationship for Br − and Cl − rows ( Figure S1). This finding has been discussed by us earlier for the halogen bonds formed by different atoms or fragments that play the role of halogen acceptors [45]. This fact has recently been illustrated in detail in Reference [46], where the large series of non-covalent interactions with different halide anions have been studied. Note that the extreme values of ESP min and PAEM max slightly differ from their local values at the bond critical points of tetrel bonds (Table S4). Nevertheless, the PAEM(r bcp ) values correlate with the binding energy better than ESP(r bcp ) ( Figure S2). This is probably due to the fact that in our series the maximum of PAEM is closer to the tetrel bond critical point than the minimum of ESP (Figure 7). The relative location of ESP min and PAEM max in the common projection is demonstrated by examples of the weakest Cl − ···CH 3 (ZENJAD) and the strongest Br − ···CH 3 (FADXIR) tetrel bonds in our set. Though the gap between the PAEM max and the minimum of electron density is larger for the Cl − ···CH 3 tetrel bond, and ESP has a lower negative minimum, it can be seen that the PAEM barrier is higher in absolute value. It means that the Cl − ···CH 3 tetrel bond is weaker, and this is confirmed by the linear correlation between PAEM max and E b . Moreover, the relative positions of ESP min and PAEM max along the tetrel bond line allow us to distinguish, which atom is the acceptor of electrons. As it has been noted earlier [45], and as can be seen from the above, PAEM max position is located closer to the electrophilic site, while the position of ESP min is closer to the electron donor. Note that the extreme values of ESPmin and PAEMmax slightly differ from their local values at the bond critical points of tetrel bonds (Table S4). Nevertheless, the PAEM(rbcp) values correlate with the binding energy better than ESP(rbcp) ( Figure S2). This is probably due to the fact that in our series the maximum of PAEM is closer to the tetrel bond critical point than the minimum of ESP (Figure 7). The relative location of ESPmin and PAEMmax in the common projection is demonstrated by examples of the weakest Cl − ···CH3 (ZENJAD) and the strongest Br − ···CH3 (FADXIR) tetrel bonds in our set. Though the gap between the PAEMmax and the minimum of electron density is larger for the Cl -···CH3 tetrel bond, and ESP has a lower negative minimum, it can be seen that the PAEM barrier is higher in absolute value. It means that the Cl − ···CH3 tetrel bond is weaker, and this is confirmed by the linear correlation between PAEMmax and Eb. Moreover, the relative positions of ESPmin and PAEMmax along the tetrel bond line allow us to distinguish, which atom is the acceptor of electrons. As it has been noted earlier [45], and as can be seen from the above, PAEMmax position is located closer to the electrophilic site, while the position of ESPmin is closer to the electron donor.

Materials and Methods
The structure optimization of molecular complexes consisting of organic cations and halide anions was carried out at M06-2X/aug-cc-pVDZ level [47][48][49] in GAMESS (v. 2017 R2, Mark Gordon's Quantum Theory Group, Ames Laboratory, Iowa State University, Ames, IA, USA [50]) with gradient convergence that equaled 0.00001. The optimized structures were tested for the absence of imaginary

Materials and Methods
The structure optimization of molecular complexes consisting of organic cations and halide anions was carried out at M06-2X/aug-cc-pVDZ level [47][48][49] in GAMESS (v. 2017 R2, Mark Gordon's Quantum Theory Group, Ames Laboratory, Iowa State University, Ames, IA, USA [50]) with gradient convergence that equaled 0.00001. The optimized structures were tested for the absence of imaginary frequencies. The binding energy between cations and halide anions in electrically neutral complexes was estimated as E b = E com − (E Hal + E cat ) − ∆E BSSE , where E com , E cat , E Hal were the total energies of the optimized complex, relaxed isolated organic cation and halide anion. BSSE correction, ∆E BSSE , was carried out taking into account the phantom orbitals in complexes calculated for compounds without energy relaxation, see Table S1 in Supporting Information.
All calculations with periodic boundary conditions were performed using CRYSTAL14 (v. 1.0.4, CRYSTAL Theoretical Chemistry Group, Chemistry Department, University of Turin, Turin, Italy [51]) at the B3LYP/6-31G** level for C, N, O, H atoms and DZVP basis set for halogen atoms [52,53] with Grimme dispersion correction D2 [54]. The structure relaxation was carried out with the atomic coordinate optimization only, with the fixed unit cell parameters for the purpose of maximum conformity to experimental data. The following convergence parameters have been used for all calculation: TOLDEG (root-mean-square on gradient) is less than 0.0001 a.u., TOLDEX (root-mean-square on estimated displacements) is less than 0.0003 a.u., TOLDEE (energy change between optimization steps threshold) is less than 10 −10 a.u., TOLINTEG (truncation criteria for bielectronic integrals: overlap threshold for Coulomb integrals; penetration threshold for Coulomb integrals; overlap threshold for HF exchange integrals; pseudo-overlap for g and n HF exchange series) are 10, 10, 10, 10 and 16, respectively. The number of k-points in the Pack-Monkhorst net (in the irreducible part of Brillouin zone) was 125 or 170 depending on crystals; the number of k-points in the Gilat net was 729 or 1170, that corresponded to the set SHRINK 8 16 values. All calculations for isolated cations were performed using CRYSTAL17 (v. 1.0.2, CRYSTAL Theoretical Chemistry Group, Chemistry Department, University of Turin, Turin, Italy [55]) at the B3LYP/6-31G** level with the Grimme dispersion correction D2 and DOPING option to account for the cation positive charge.
The QTAIM analyses of electron density and electrostatic potential were carried out in TOPOND [56] in crystals and in AIMAll software package [57] for the complexes. PAEM and ESP distributions were computed using Multiwfn [58] program (Beijing Kein Research Center for Natural Sciences, Beijing, China).
The reported calculations were performed using the supercomputer resources of the South Ural State University [59].

Conclusions
In this computational study, the charge-assisted tetrel bonds in the crystals formed between halide anions and the methyl groups of organic cations such as Hal − ···CH 3 Y (Hal − = Cl, Br; Y = N, O) have been considered. The bond paths between the Hal − and C atoms confirm the existence of these uncommon bonds in both the crystal structures and gas phase complexes. To define the type of Hal − ···CH 3 Y bonding in crystals more precisely, we have suggested using the order of one-dimensional minima of electron density and electrostatic potential along the interatomic lines between the carbon atom of CH 3 -group and the halide anion. This allowed us to apply a simple criterion which reveals that the carbon atom provides its electrophilic site for a typical tetrel bond formation.
The strong correlation between the binding energy in complexes and the extreme values of potential acting on an electron in a molecule calculated along the lines between the Hal − and C atoms has been obtained. Therefore, PAEM extends and enforces the electronic criterion for revealing electrophilic sites and sheds some light on the nature of tetrel bonds. We may speculate that its application will be useful for the other electrostatically driven non-covalent interactions as well.