*2.3. 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 understanding the nature of charge-assisted tetrel bonds.

The binding energy, Eb, 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 [8–11]. The BSSE correction, ΔEBSSE, is negligible and influences the energy values of the third decimal place of kcal/mol units.

**Table 2.** Calculated binding energy Eb (kcal/mol), bond lengths Dcalc (Å), electron density (rbcp) at bcp (a.u.) for Hal−···CH3 minimum of electrostatic potential ESPmin (a.u.) and maximum of potential acting on an electron in molecule PAEMmax (a.u.) along the line of tetrel bonds in complexes.


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 (rbcp) 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 CH3–Y (Y=N, O) covalent bonds in complexes and isolated cations, we see that the participation of CH3-group in tetrel bond with Hal− weakens the CH3–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 (rbcp) for the CH3–Y bonds decrease by ~8%.

It is useful to understand how the electronic properties of Hal−···CH3Y 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−···CH3Y tetrel bonds are linearly correlated with the binding energy, Eb, in complexes, as shown in Figure 6. The correlation coefficient for the minima of the electrostatic potential, ESPmin, on the line between Hal− and C atoms is 0.917. For the maximum of PAEM along this line, PAEMmax, or PAEM barrier, the correlation coefficient is

0.985. It is important to note that in the relationship "PAEMmax vs Eb", PAEMmax 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.

**Figure 6.** Binding energy in complexes vs minimum of electrostatic potential (**a**) and maximum of potential acting on an electron in a molecule, (**b**) along the line of tetrel bonds.

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.

**Figure 7.** Potential acting on an electron in a molecule, a.u., (blue), electrostatic potential, a.u., (red) and electron density, a.u., (black) along the tetrel bond in (**a**) ZENJAD and (**b**) FADXIR complexes.

#### **3. 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 [47–49] 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 Eb = Ecom − (EHal + Ecat) − ΔEBSSE, where Ecom, Ecat, EHal were the total energies of the optimized complex, relaxed isolated organic cation and halide anion. BSSE correction, ΔEBSSE, 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−<sup>10</sup> 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].

#### **4. 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−···CH3Y (Hal<sup>−</sup> = 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−···CH3Y 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 CH3-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.

**Supplementary Materials:** The following are available online, Figure S1: Binding energy (kcal/mol) in complexes vs the potential (a) and kinetic (b) energy density (a.u.) at the bond critical point of tetrel bonds, Figure S2: Binding *Molecules* **2019**, *24*, 1083

energy (kcal/mol) in complexes vs the electrostatic potential (a.u.) (a) and (b), potential acting on an electron in molecule (a.u.) at the bond critical point of tetrel bonds, Figure S3: ESP in the trimethylammonium chloride on the isosurface of electron density of 0.02 a.u, Table S1: The energy characteristics of Hal−···CH3–YR (Hal<sup>−</sup> = Cl, Br) complexes taken from crystal structures with listed refcodes, Table S2. Experimental and calculated tetrel and C–Y bond lengths D (Å), angles Hal−···C–Y and electron density (a.u.) at bond critical points for considered crystal and cation structures calculated in CRYSTAL code. Table S3, Bond lengths D(Å), the characteristics of electron density, potential and kinetic energy densities (a.u.), electrostatic potential (a.u.), potential acting on an electron in molecule PAEM at bcp (a.u.) for Hal−···CH3 and Y–C bonds in complexes and cations calculated in GAMESS code.

**Author Contributions:** Conceptualization, V.T. and E.B.; investigation, Y.M.; formal analysis and project administration E.B.

**Funding:** This research was funded by the Russian Foundation for Basic Research, grant No. 17-03-00406, Ministry of Science and Higher Education of the Russian Federation (grant No. 4.1157.2017/4.6) and by the Government of the Russian Federation, Act 211, contract No. 02.A03.21.0011.

**Conflicts of Interest:** The authors declare no conflicts of interest.
