**Ekaterina Bartashevich 1,\*, Yury Matveychuk <sup>1</sup> and Vladimir Tsirelson 1,2**


Received: 26 February 2019; Accepted: 16 March 2019; Published: 19 March 2019

**Abstract:** 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<sup>−</sup> = 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.

**Keywords:** tetrel bond; electron density; electrostatic potential; potential acting on an electron in molecule

## **1. 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 Y4T···Hal<sup>−</sup> 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 [8–13]. The carbon atom in the CH3-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 CH3···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 CH3···N tetrel bonding in a Co(II) coordination polymeric system using the analysis of calculated electron density. The typical tetrel bonds formed by CH3-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 rows of binding energy were calculated for the series of complexes in which the compounds NH3 [19–22], PH3 and AsH3 [23], benzene and unsaturated hydrocarbons [24], HCN and pyrazine [25] acted as the tetrel bond acceptors. According to these results, the tetrel bond strength depends on the tetrel atom, the Lewis base that acts as a tetrel bond acceptor, and the fragments covalently bound with this atom. Therefore, in the complexes with ammonia at transition from CF4 to SnF4, the binding energy increases from −0.82 to −25.53 kcal/mol (MP2/aug-cc-pVDZ) [21], that is, the tetrels of higher periods form stronger interactions in complexes. Decrease of the Lewis base strength in series from X = NH3 to AsH3 reduces the binding energy from −3.23 to −1.28 kcal/mol (MP2/aug-cc-pVDZ) in complexes X···CH3Cl [23]. Therefore, the values of binding energy estimated in neutral complexes with tetrel bonds formed by the carbon in a methyl group are commonly very small. The binding energy grows more sharply if the hydrogen atoms are replaced by halogens, which leads to enhancement of electron acceptor properties of the tetrel atom providing the σ-hole for bonding. This fact is illustrated by complexes H4Sn···NH3 (−2.44 kcal/mol) and F4Sn···NH3 (−25.53 kcal/mol) with the tetrel bond lengths of 3.17 and 2.28 Å (MP2/aug-cc-pVDZ), respectively [21]. If the anion acts as the tetrel bond acceptor, the estimated binding energy can be greater by an order of magnitude as compared to the neutral complexes [9–11]. The highest value of binding energy, −93.58 kcal/mol, has been recorded for the SnF4···F<sup>−</sup> complex (MP2/aug-ccpVTZ) [11]; replacing the F<sup>−</sup> ion with Cl<sup>−</sup> and Br<sup>−</sup> reduces this energy by 2–3 times.

Therefore, a variety of functional groups can act as the tetrel bond donors in molecular complexes and a methyl group as an electrophilic site deliverer is quite often in the focus of attention for the study of tetrel bond properties. The tetrel bonds formed by the methyl carbon atom occur in crystalline systems as well. There are at least two studies [17,26] based on high-precision X-ray diffraction data, which established the participation of the carbon atom of a methyl group in non-covalent interactions. These facts motivate us to focus on the search for evidential electronic criterion for recognizing the type of non-covalent bonding and for systematization of the electrophilic site features for the carbon atom of a methyl group in molecular complexes and crystals.

Quantum Theory of Atoms in Molecules (QTAIM) [27] suggests zero-flux conditions for electron-density gradient [28] and electrostatic-potential gradient [29] to determine the boundaries of chemically bonded atoms and electrically neutral atomic fragments, respectively. For non-covalent interactions with a significant electrostatic component, the boundaries of the electron density basins (-basins) do not coincide with the boundaries of the electrostatic potential (ESP) basins (ϕ-basins). It means that electrons formally belonging to the electron donor atom can be electrostatically attracted to the nucleus of an electron acceptor atom along a specific direction. The superposition of the and ϕ-basins has been discussed in the literature [30–32], and the features of zero-flux surface in electrostatic potential in solids have been studied using the experimental charge density [29,33].

Previously we have proposed the following electronic criterion for recognizing the atom that prescribes the name of non-covalent bonding [34,35]. The minimum of electrostatic potential along the interaction line is located at the side of the atom that donates electrons; the minimum of electron density is closer to the atom that delivers its electrophilic site for bonding. More explicitly, the latter atom prescribes the name of bonding. This observation opens up the broad possibilities for identifying the role of atoms involved in non-covalent interactions. For example, atoms of the Group 14 of the Periodic Table are able to deliver their electrophilic sites for non-covalent interactions with electron donors for the tetrel bond formation, and the suggested electronic criterion can specify the electron acceptor role of these atoms. Along the Hal−···C interatomic line, the 1D minimum of ESP should be located closer to the electron donor atom, while the minimum of the electron density will be found closer to the atom that is an electron acceptor. Such disposition of minima indicates that the fraction of electron density from the atomic -basin of an electron donor is electrostatically attracted to the nucleus of an electron acceptor atom. In this case, the disposition of the 1D minima of both functions can unambiguously indicate that only one of the pair of atoms provides its electrophilic site. Namely, 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−···CH3Y (Hal<sup>−</sup> = Cl, Br; Y = N, O) tetrel bonds in crystals.

#### **2. Results and Discussion**
