The Influence of Halogenated Hypercarbon on Crystal Packing in the Series of 1-Ph-2-X-1,2-dicarba-closo-dodecaboranes (X = F, Cl, Br, I) †

Although 1-Ph-2-X-closo-1,2-C2B10H10 (X = F, Cl, Br, I) derivatives had been computed to have positive values of the heat of formation, it was possible to prepare them. The corresponding solid-state structures were computationally analyzed. Electrostatic potential computations indicated the presence of highly positive σ-holes in the case of heavy halogens. Surprisingly, the halogen•••π interaction formed by the Br atom was found to be more favorable than that of I.


Introduction
Icosahedral closo-1,2-C 2 B 10 H 12 , known as o-carborane, was found to have the positive part of its relatively large value of the experimental dipole moment, 4.50 D [1], in the midpoint of the C-C vector. When one of the hypercarbon atoms is substituted with phenyl (Ph), the dipole moment is even increased to 4.93 D. The difference between these two values was interpreted as a mesomeric contribution to the overall dipole moment as a consequence of the electron transfer from the benzene ring towards the icosahedral cage. This 1-Ph-closo-1,2-C 2 B 10 H 11 was structurally studied by the techniques of gas-phase electron diffraction and X-ray diffraction in the gas phase and solid state [2]. When the second hypercarbon of the cage is substituted with halogens, the overall dipole moments in the series of 1-Ph-2-X-closo-1,2-C 2 B 10 H 10 (X = F, Cl, Br, and I, denoted here as 1, 2, 3, and 4, respectively) decrease, in the case of F and Cl by more than 1 D due to the electron-withdrawing effect of these two halogen atoms [3]. The fact that the dipole moment of Br-and I-derivatives only decreased by 0.8 and even 0.2 D, respectively, was ascribed to the close position of halogen and Ph, and also to the partially positively charged outer part of the heavy halogen atoms, known as σ-holes [4]. A σ-hole can be characterized by its magnitude, V S,max , defined as the value of the most positive electrostatic potential (ESP) of an electron density surface. The higher the V S,max value, the more favorable the forming σ-hole interactions [5]. The halogen•••π interactions have been extensively studied in the solid state   The unit cell of 4 contains two independent molecules. The molecular structures of all complexes 1-4 are similar ( Figure 1). The distances С1-С2 and С1-С3(Ph) lie within the intervals (1.620(13)-1.706(2) Å) and (1.476(16)-1.505(9) Å), respectively. The largest geometric differences are observed when the relative position of phenyl rings is analyzed. The torsion angle C2-C1-C3-C8 is 70.5(6)° and 72.0(2)° in the case of 1 and 2, respectively, 87.3(13)° for 3, and 84.9(11)° and 82.9(11)° for 4. Such differences can be explained by the features of crystal packing and the presence of   The unit cell of 4 contains two independent molecules. The molecular structures of all complexes 1-4 are similar ( Figure 1). The distances С1-С2 and С1-С3(Ph) lie within the intervals (1.620(13)-1.706(2) Å) and (1.476(16)-1.505(9) Å), respectively. The largest geometric differences are observed when the relative position of phenyl rings is analyzed. The torsion angle C2-C1-C3-C8 is 70.5(6)° and 72.0(2)° in the case of 1 and 2, respectively, 87.3(13)° for 3, and 84.9(11)° and 82.9(11)° for 4. Such differences can be explained by the features of crystal packing and the presence of  The computed ∆H f 298 values of the studied compounds and their 10-vertex analogues are summarized in Table 2. Since all the considered compounds have a high energy level (positive ∆H f 298 values), their thermodynamic stability should be low as they can lose a great deal of energy by reacting to lower-energy products. The thermodynamic stability has decreased with the increasing atomic number of the halogen atom and with the reduced size of the carborane cage. Note that the positive values of the heat of formation do not necessarily mean experimental unavailability, as exemplified by e.g., closo-SB 9 H 9 with the computed ∆H f 298 value of 11.3 kcal mol −1 [14,15]. Moreover, we have computed the ∆H f 298 of 26.5 kcal mol −1 for closo-1,2-C 2 B 8 H 10 , which was previously prepared as well [16]. As the studied compounds are neutral and the halogen atoms are bound to a C-vertex, one can expect the heavier halogen atoms with highly positive σ-holes. The molecular ESP surfaces of the studied molecules were computed in order to validate this assumption (see Figure 3). Indeed, the top of the I and Br atoms with the V S,max values of 36.2 and 25.8 kcal mol −1 , respectively, is the most positive part of the 3 and 4 molecules. In the case of 2, the σ-hole of the Cl atom has the V S,max value of 19.5 kcal mol −1 . The H atoms of the Ph ring are thus more positive (V S,max value of 23.9 kcal mol −1 ). The F atom of 1 does not have a positive σ-hole (the V S,max value of −5.7 kcal mol −1 ) due to its large electronegativity. The most negative values (V S,min ) of the molecular surfaces of the studied molecules are on BH(9) vertices, which are antipodal to CX(2) vertices. The V S,min values range from −14.0 to −12.9 kcal mol −1 (for 4 and 1 compounds, respectively). Besides hydridic BH vertices, the σ-holes on the heavier halogen can also interact with the π electrons of Ph rings, which have a negative ESP surface as well (the V S,min values range between −6.8 and −6.4 kcal mol −1 for 4 and 2 compounds, respectively).

Heat of Formation (ΔHf 298 )
The computed ΔHf 298 values of the studied compounds and their 10-vertex analogues are summarized in Table 2. Since all the considered compounds have a high energy level (positive ΔHf 298 values), their thermodynamic stability should be low as they can lose a great deal of energy by reacting to lower-energy products. The thermodynamic stability has decreased with the increasing atomic number of the halogen atom and with the reduced size of the carborane cage. Note that the positive values of the heat of formation do not necessarily mean experimental unavailability, as exemplified by e.g., closo-SB9H9 with the computed ΔHf 298 value of 11.3 kcal mol −1 [14,15]. Moreover, we have computed the ΔHf 298 of 26.5 kcal mol −1 for closo-1,2-C2B8H10, which was previously prepared as well [16].

Compound
ΔHf As the studied compounds are neutral and the halogen atoms are bound to a C-vertex, one can expect the heavier halogen atoms with highly positive σ-holes. The molecular ESP surfaces of the studied molecules were computed in order to validate this assumption (see Figure 3). Indeed, the top of the I and Br atoms with the VS,max values of 36.2 and 25.8 kcal mol −1 , respectively, is the most positive part of the 3 and 4 molecules. In the case of 2, the σ-hole of the Cl atom has the VS,max value of 19.5 kcal mol −1 . The H atoms of the Ph ring are thus more positive (VS,max value of 23.9 kcal mol −1 ). The F atom of 1 does not have a positive σ-hole (the VS,max value of −5.7 kcal mol −1 ) due to its large electronegativity. The most negative values (VS,min) of the molecular surfaces of the studied molecules are on BH(9) vertices, which are antipodal to CX(2) vertices. The VS,min values range from −14.0 to −12.9 kcal mol −1 (for 4 and 1 compounds, respectively). Besides hydridic BH vertices, the σ-holes on the heavier halogen can also interact with the π electrons of Ph rings, which have a negative ESP surface as well (the VS,min values range between −6.8 and −6.4 kcal mol −1 for 4 and 2 compounds, respectively).

Interactions in the Single Crystals of 1-4
Interactions in the reported single-crystal structures were studied by computing two-body and many-body interaction energy (∆E 2 and ∆E MB ) values between the central molecules and two layers of surroundings molecules. The first layer consisted of molecules within 5 Å of the central molecule, and the second layer was formed by molecules within 5 Å of the first layer. The obtained sums of the ∆E values are summarized in Table 3. The computed total binding became more favorable with the increasing atomic number of the halogen atom (i.e. −48.4, −51.4, −53.3, and −55.2 kcal mol −1 for F-, Cl-, Br-, and I-containing compounds, respectively). The total binding thus correlated more with the molecular masses of these molecules (R 2 of 0.91) than with their experimental dipole moments (R 2 of 0.76). The interaction motifs with the most favorable ∆E 2 values are shown in Figure 4 and the corresponding values in Table 4. This analysis confirmed the strength of the halogen•••π interaction of 3-the motif with the C-Br•••Ph interaction had the ∆E 2 of −6.91 kcal mol −1 at the DFT-D3 level. Considering that each molecule of 3 formed two such C-Br•••Ph interactions, it thus accounted for about 26% of the total computed binding of 3. According to the SAPT0 decomposition, this motif was mainly stabilized by dispersion, which formed approximately 65 of the attractive terms. The second most important term was electrostatic. It formed about 28% of the attractive terms, which was the largest contribution to the electrostatic term among all the motifs studied (see Table 4). The second most favorable motif of 3 had two diH-bonds and contributed considerably less to the overall binding. With the ∆E 2 of −5.67 kcal mol −1 , it only formed about 11% of the total binding of 3.
In the case of 4, the motif with the halogen•••π interaction had the ∆E 2 of −5.79 kcal mol −1 and thus formed about 21% of the overall binding of 4. Therefore, it was less favorable than the motif with the halogen•••π interaction of 3. It was surprising considering the large V S,max value of 4 (see part 2.3.2.). However, examples of a reverse hierarchy in strength of halogen interactions have already been reported in literature [17,18]. In our case, the lack of strength of the I•••π interaction corresponded to the bent C-I•••Ph center angle. An optimal arrangement for a σ-hole hole interaction is linear, whereas the C-I The most favorable motif of 2 had the highly negative ∆E 2 of −7.10 kcal mol −1 (the most negative ∆E 2 of this study). This motif formed about 14% of the total binding of 2 and did not have any close contact below the sum of van der Waals radii. The motif can be characterized by a large dispersion term, which formed about 73% of the attractive terms of the SAPT (Symmetry Adapted Perturbation Theory) decomposition. The second most favorable motif of 2 had multiple diH-bonds, the ∆E 2 of −7.10 kcal mol −1 and a large dispersion term (i.e., about 75% of the attractive terms).
The analogous motif of the crystal structure by A. Welch et al. [13] was computed to have the interaction energy of −6.73 kcal mol −1 at the MP2/CBS level [12]. 2 The analogous motif of the crystal structure by Welch [13] was computed to have the interaction energy of −5.09 kcal mol −1 at the MP2/CBS level [12].
Molecules 2020, 25, x FOR PEER REVIEW 5 of 13 Interactions in the reported single-crystal structures were studied by computing two-body and many-body interaction energy (ΔE 2 and ΔE MB ) values between the central molecules and two layers of surroundings molecules. The first layer consisted of molecules within 5 Å of the central molecule, and the second layer was formed by molecules within 5 Å of the first layer. The obtained sums of the ΔE values are summarized in Table 3. The computed total binding became more favorable with the increasing atomic number of the halogen atom (i.e. −48.4, −51.4, −53.3, and −55.2 kcal mol −1 for F-, Cl-, Br-, and I-containing compounds, respectively). The total binding thus correlated more with the molecular masses of these molecules (R 2 of 0.91) than with their experimental dipole moments (R 2 of 0.76).
The interaction motifs with the most favorable ΔE 2 values are shown in Figure 4 and the corresponding values in Table 4. This analysis confirmed the strength of the halogen•••π interaction of 3-the motif with the C-Br•••Ph interaction had the ΔE 2 of −6.91 kcal mol −1 at the DFT-D3 level. Considering that each molecule of 3 formed two such C-Br•••Ph interactions, it thus accounted for about 26% of the total computed binding of 3. According to the SAPT0 decomposition, this motif was mainly stabilized by dispersion, which formed approximately 65 of the attractive terms. The second most important term was electrostatic. It formed about 28% of the attractive terms, which was the largest contribution to the electrostatic term among all the motifs studied (see Table 4). The second most favorable motif of 3 had two diH-bonds and contributed considerably less to the overall binding. With the ΔE 2 of −5.67 kcal mol −1 , it only formed about 11% of the total binding of 3. In the case of 4, the motif with the halogen•••π interaction had the ΔE 2 of −5.79 kcal mol −1 and thus formed about 21% of the overall binding of 4. Therefore, it was less favorable than the motif with the halogen•••π interaction of 3. It was surprising considering the large VS,max value of 4 (see The two most favorable motifs of 1 had comparable ∆E 2 of −6.93 and −6.58 kcal mol −1 . Together, they formed about 28% of the total binding of 1. Neither of them formed close contact below the sum of van der Waals radii, and both had a large dispersion term in the SAPT decomposition, i.e., the dispersion term ranged from 75 to 80% of the attractive terms.

Cambridge Structural Database (CSD) search
We have searched the Cambridge structural database (CSD) [19] for X-ray structures containing halogenated carboranes that exhibit interactions between a halogen and a Ph ring. The analysis of CSD [19], however, did not show any analogous halogen•••Ph interactions in similar ortho-carborane derivatives. Additionally, we analyzed short B-X•••Ph-ring contacts in various halogenated boron compounds (for the definition of the criteria, see Figure 5). We fixed d 1 and d 2 to be less than sum of van der Waals radii of the appropriate elements [20], as well as angles B1-X•••C1,2 (90 • < α1, α2 < 180 • ). A minor number of hits was excluded as clearly not suitable for the criteria of this type of interaction. The data are presented in Table 5; the found contacts may be potential candidates for studies of unusual B-X•••π interactions.
Molecules 2020, 25, x FOR PEER REVIEW 8 of 13 considered products of Cl•••π interactions [23][24][25]. A different situation occurs for brominated compounds, where the Br•••π interaction has been found to be dominant in most compounds in a set selected based on defined parameters, except for a couple of examples of type C and B ( Figure 5) and boarder-line cases [26]. Surprisingly enough, only three relevant compounds have been found in the set of iodo compounds [27][28][29][30][31][32][33]. To conclude here, the most probable is an interaction of the desired type in brominated and iodinated compounds, where the aromatic ring is not a part of the same moiety as the halogen. The desired criteria are also accomplished for chlorinated ionic compounds, where the weak nucleophiles, such as CHB11X11 − , are compensated for by aromatic ring-containing cations. If all the restrictions were removed, leaving only the Ph ring, halogen, and three boron atoms, then 418 hits would be obtained. One can hence assume that the probability of the formation of such a motif in crystals containing both halogenated boranes and aromatic systems is 8.9%.

X-ray Crystallography.
The X-ray data for the compounds 1-4 (colorless crystals obtained by slow evaporation of a hexane solution) were collected at 150(2)K with a Bruker D8-Venture diffractometer equipped with a Mo (Mo/Kα radiation; λ = 0.71073 Å) microfocus X-ray (IµS) source, by a Photon CMOS detector and an Oxford Cryosystems cooling device. The frames were integrated with the Bruker SAINT software package [34] using a narrow-frame algorithm. The data were corrected for absorption effects using the Multi-Scan method (SADABS) [35]. The obtained data were treated by XT-version 2014/5 [36] and SHELXL-2017/1 [37] software implemented in the APEX3 v2018.1-0 (Bruker AXS  Specifically, the set of four fluorine-substituted compounds mostly contain the side-on intermolecularly interacting compounds with the B-Hal bond lying in the plane of the aromatic ring ( Figure 5C). This could be attributed more or less to the non-classical C-H•••X hydrogen bond [21,22]. Nineteen relevant chlorine-substituted compounds exhibit mainly contacts contrived by C-H•••Cl or B-H•••H-C interactions, and only four structures of ionic compounds (halogenated carbadodecaborate anions are compensated by tritylium, silylium, and borinium cations), which are considered products of Cl•••π interactions [23][24][25]. A different situation occurs for brominated compounds, where the Br•••π interaction has been found to be dominant in most compounds in a set selected based on defined parameters, except for a couple of examples of type C and B ( Figure 5) and boarder-line cases [26]. Surprisingly enough, only three relevant compounds have been found in the set of iodo compounds [27][28][29][30][31][32][33]. To conclude here, the most probable is an interaction of the desired type in brominated and iodinated compounds, where the aromatic ring is not a part of the same moiety as the halogen. The desired criteria are also accomplished for chlorinated ionic compounds, where the weak nucleophiles, such as CHB 11 X 11 − , are compensated for by aromatic ring-containing cations. If all the restrictions were removed, leaving only the Ph ring, halogen, and three boron atoms, then 418 hits would be obtained. One can hence assume that the probability of the formation of such a motif in crystals containing both halogenated boranes and aromatic systems is 8.9%.

Interaction Energy
The interactions of the crystal structures were studied by using a cluster model. Hydrogen atoms of the central molecule and the surrounding molecules of the first layer were optimized by the DFT-D3/BLYP/DZVP method [43]. The resolution-of-identity (RI) approximation to the DFT method was used. Hydrogen atoms of the surrounding molecules of the second layer were optimized by the semiempirical quantum mechanical PM6-D3H4X method [44]. Heavy atoms were kept in crystallographic positions. Interaction energies were computed at the DFT-D3/TPSS/TZVPP level. Two-body interaction energy (∆E 2 ) was computed as the energy difference between the energy of the dimer and the sum of monomer energies. For the first layer, the interaction energy between the central molecule and the whole first layer (∆E(AQ)) was computed as well. The many-body interaction energy (∆E MB ) was computed as the difference between ∆E(AQ) and the sum of ∆E 2 values. ∆E values of selected motifs were decomposed using symmetry-adapted perturbation-theory (SAPT) methodology. The simplest truncation of SAPT (SAPT0) decomposition [45] was performed with the recommended jun-cc-pVDZ basis set [46]. Turbomole (7.0) [42], MOPAC2016 [47], PSI4 [48], and Cuby4 [41] programs were used.

Conclusions
A series of 1−4 derivatives was prepared, crystallized, and computationally analyzed. Even though their heat of formation had been computed to be positive, it was possible to prepare them. The obtained solid-state structures were computationally analyzed and the presence of σ-holes in the case of heavy halogens was computationally established. Interestingly, the halogen•••π interaction coming from the Br atom was found to be more favorable than that of I.