The Interplay between Various σ-and π-Hole Interactions of Trigonal Boron and Trigonal Pyramidal Arsenic Triiodides

Boron and arsenic triiodides (BI3 and AsI3, respectively) are similar molecules that differ mainly in their geometries. BI3 is a planar trigonal molecule with D3h symmetry, while AsI3 exhibits a trigonal pyramidal shape with C3v symmetry. Consequently, the As atom of the AsI3 molecule has three σ-holes, whereas the B atom of the BI3 molecule has two symmetrical π-holes. Additionally, there are σ-holes on the iodine atoms in the molecules studied. In the first step, we have studied σ-hole and π-hole interactions in the known monocrystals of BI3 and AsI3. Quantum mechanical calculations have revealed that the crystal packing of BI3 is dominated by π-hole interactions. In the case of AsI3, the overall contribution of dihalogen bonding is comparable to that of pnictogen bonding. Additionally, we have prepared the [Na(THF)6][I(AsI3)6](AsI3)2 complex, which can be described as the inverse coordination compound where the iodine anion is the center of the aggregate surrounded by six AsI3 molecules in the close octahedral environment and adjacent two molecules in remote distances. This complex is, besides expected dihalogen and pnictogen bonds, also stabilized by systematically attractive dispersion interactions.


Introduction
The σ-hole and π-hole are regions with a positive electrostatic potential (ESP) surface along the extension of a covalent σ-bond and in the direction perpendicular to the σ-bond framework, respectively.These areas with a positive ESP surface enable a counterintuitive noncovalent interaction, at which a partially negatively charged atom interacts with an electron-rich region [1,2].The best known and most extensively studied is the σ-hole on halogen (X) atoms, where the respective interactions are called X-bonds [3].This concept has been extended to chalcogens, pnictogens (Pn), and tetrels [4].The respective interactions are then called chalcogen-, Pn-, and tetrel-bonds.The σ-hole can be characterized by its size and magnitude (V max ).V max is defined as the value of the most positive ESP of an electron density surface.The more positive the V max , the stronger the respective interaction [5].
The properties of σ-holes can be modulated by changing the chemical environment in order to tune the interactions, e.g., by introducing electron-withdrawing groups in the vicinity of the atom possessing a σ-hole or a π-hole.This has already been demonstrated in model systems [6] as well as in protein-ligand complexes [7,8].In contrast to our previous studies, we have compared two very similar molecules here.Specifically, we have opted for BI 3 and AsI 3 .Boron and arsenic have nearly the same value of Pauling electronegativity (2.04 and 2.05, respectively).The major difference between these two molecules thus consists in their geometries.While BI 3 is a planar trigonal molecule with D 3h symmetry (π-back donation is possible here but not in AsI 3 ), AsI 3 exhibits a trigonal pyramidal shape with C 3v symmetry with the lone electron pair being pointed to the fourth vertex of virtual Ψ-tetrahedron.Firstly, we analyzed single crystalline material, which had already been described in the literature [9,10].Secondly, we reported and analyzed much larger system containing [I(AsI 3 ) 6 ] − units within [Na(THF) 6 ] + [I(AsI 3 ) 6 ] − (AsI 3 ) 2 complex.In interactions of such large molecular entities, other types of noncovalent interactions like the dispersion ones also play an important role besides the already mentioned σ-hole interactions.Benchmark interaction energy (∆E) values of the binding motifs within the studied crystals were obtained using highly accurate coupled cluster with single, double and perturbative triple excitations CCSD(T) calculations.

Experimental
The preparation and isolation of [Na(THF) 6 ] + [I(AsI 3 ) 6 ] − (AsI 3 ) 2 : Perylene (207 mg, 0.82 mmol) and AsI 3 (748 mg, 1.64 mmol) were mixed in a THF/CH 2 Cl 2 mixture of solvents (10 mL, 1:1 v/v).The deep orange turbid reaction mixture was stirred overnight and filtered.The clear orange filtrate was stored in a common Schlenk tube in a freezing box for several months.A deep orange precipitate formed very slowly during that period of time.The reaction mixture was filtered one more time to provide a clear orange filtrate, which was stored for several more months at −40 • C to provide orange single crystals of the title compound in low yield.Melting point: 140-141 • C.
A clear intense orange block-like specimen of C 24 H 48 As 8 I 25 NaO 6 , approximate dimensions 0.251 mm × 0.260 mm × 0.311 mm, was used for the X-ray crystallographic analysis.The X-ray intensity data were measured.A total of 592 frames were collected.The total exposure time was 0.62 h.The frames were integrated with the Bruker SAINT software package using a narrow-frame algorithm.The integration of the data using a trigonal unit cell yielded a total of 27971 reflections to a maximum θ angle of 28.32 • (0.75 Å resolution), of which 3416 were independent (average redundancy 8.188, completeness = 99.8%,R int = 5.13%, R sig = 2.85%) and 3165 (92.65%) were greater than 2σ(F 2 ).The final cell constants of a = 16.5457(7) Å, b = 16.5457(7)Å, c = 26.0339(11)Å, volume = 6172.2(6)Å 3 , are based upon the refinement of the XYZ-centroids of 9856 reflections above 20 σ(I) with 4.923 • < 2θ < 56.58 • .Data were corrected for absorption effects using the Numerical Mu Calculated method (SADABS).The ratio of minimum to maximum apparent transmission was 0.118.The calculated minimum and maximum transmission coefficients (based on crystal size) are 0.1110 and 0.1440.
The structure was solved and refined using the Bruker SHELXTL Software Package (Bruker AXS Inc., Madison, WI, USA), using the space group R-3, with Z = 3 for the formula unit, C 24 H 48 As 8 I 25 NaO 6 .The final anisotropic full-matrix least-squares refinement on F 2 with 99 variables converged at R 1 = 2.14%, for the observed data and wR 2 = 6.19% for all data.The goodness-of-fit was 1.024.The largest peak in the final difference electron density synthesis was 1.010 e − /Å 3 and the largest hole was −0.866 e − /Å 3 with an RMS deviation of 0.188 e − /Å 3 .On the basis of the final model, the calculated density was 3.412 g/cm 3 and F(000), 5520 e − .
Hydrogen atoms were mostly localized on a difference Fourier map, however to ensure uniformity of treatment of crystal, all hydrogen was recalculated into idealized positions (riding model) and assigned temperature factors H iso (H) = 1.2 U eq (pivot atom).H atoms in methylene groups was 0.97.
Crystallographic data for structural analysis have been deposited with the Cambridge Crystallographic Data Centre, CCDC no.1555393.Copies of this information may be obtained free of charge from The Director, CCDC, 12 Union Road, Cambridge CB2 1EY, UK (fax: +44-1223-336033; e-mail: deposit@ccdc.cam.ac.uk or www: http://www.ccdc.cam.ac.uk).

Computations
Electrostatic potentials were computed by Hartree-Fock (HF) method with the correlation consistent-polarized valence double zeta (cc-pVDZ) basis set (for I, the double zeta polarized (DZP) basis set and a pseudopotential were used) [12] using the Gaussian09 [13] and Molekel4.3[14,15] programs.It has recently been shown that such a basis set size is sufficient for these purposes [16].
∆E values were calculated at the CCSD(T) level of theory using the Turbomole 6.6 [17] and Cuby4 [18] programs.CCSD(T) with complete basis set (CBS) was calculated as the sum of the Møller-Plesset perturbation theory to second order (MP2) CBS energy and CCSD(T) correction.MP2 energy was extrapolated to the CBS from correlation consistent-polarized triple zeta (cc-pVTZ) to correlation consistent-polarized valence quadruple zeta cc-pVQZ (for I atoms, cc-pVTZ-PP and cc-pVQZ-PP with pseudopotentials (PP) were used) [19].The CCSD(T) correction term was calculated using the aug-cc-pVDZ basis set (aug-cc-pVDZ-PP for I).Counterpoise corrections for the basis set superposition error (BSSE) and the resolution of identity (RI) approximation were used.

Results and Discussion
In the first step, the computed properties of isolated BI 3 and AsI 3 molecules were compared (see Table 1 and Figure 1).The iodine atoms of both BI 3 and AsI 3 have σ-holes with comparable V s,max values of about 22.3 and 23.2 kcal•mol −1 , respectively, which make them good X-bond donors.Due to the partially negative belt around the center of the X atoms, they can also act as electron donors.The belt of iodine atoms is slightly more negative in the case of the AsI 3 molecule (the V min values of BI 3 and AsI 3 are −6.0 and −7.5 kcal•mol −1 , respectively; see also Figure 1).Bigger differences can be found when comparing the ESP on central B and As atoms.Whereas the As atom of the AsI 3 molecule has three σ-holes, the B atom of the BI 3 molecule has two symmetrical π-holes.Both the B and As atoms have high V max values, slightly higher than the σ-holes on the iodine atoms.Additionally, the V max values of the π-holes of BI 3 with those of B(CH 3 ) 3 and B(CH=CH 2 ) 3 have been compared.While B(CH 3 ) 3 has a π-hole with a similar V max value of 25.4 kcal•mol −1 , B(CH=CH 2 ) 3 has a considerably lower V max value of 10.4 kcal•mol −1 (ESP surfaces not shown).This difference in V max values might be explained through π-back donation from the C=C double bond to the vacant p z orbital on the B atom.Such a hypothesis has already been used to explain the elongation of the C=C bond in the electron-diffraction structure of B(CH=CH 2 ) 3 [20].In the case of B(NHCH 3 ) 3 [21], the π-hole vanishes completely and V max has a negative value.In the next step, the strength of pairwise interactions in the single crystals of BI3 and AsI3 molecules was analyzed by means of quantum chemistry (Table 2).The structure in single crystalline BI3 is mainly stabilized by interactions between the positive π-holes on the B atom and the negative belt on iodine atoms, i.e., a parallel displaced motif (see Figure 2a).

Crystal Motif Interaction CCSD(T)/CBS
In the case of AsI3, the most negative ΔE has also been found for the binding motif where the electron acceptor is the central atom (see Figure 2b  Finally, we report the [Na(THF)6] + [I(AsI3)6] − (AsI3)2 complex.Crystalline material was prepared accidentally during the attempts to synthesize a complex analogous to the previously published adducts of arenes and SbCl3 [22 -24].The exchange of the sodium cation from the borosilicate Simax ® glassware (Kavalierglass, a.s., Sázava, Czech Republic) and the arsenic atom obviously took place (see Figure 3).This is easily acceptable as the arsenic impurities or additives can be found in various types of glasses [25,26].A high tendency of the sodium atom to migrate from the glass surface and to In the next step, the strength of pairwise interactions in the single crystals of BI 3 and AsI 3 molecules was analyzed by means of quantum chemistry (Table 2).The structure in single crystalline BI 3 is mainly stabilized by interactions between the positive π-holes on the B atom and the negative belt on iodine atoms, i.e., a parallel displaced motif (see Figure 2a).Table 2. Interaction energies in kcal•mol −1 .

Crystal Motif Interaction CCSD(T)/CBS
In the case of AsI 3 , the most negative ∆E has also been found for the binding motif where the electron acceptor is the central atom (see Figure 2b and Table 2 Finally, we report the [Na(THF) 6 ] + [I(AsI 3 ) 6 ] − (AsI 3 ) 2 complex.Crystalline material was prepared accidentally during the attempts to synthesize a complex analogous to the previously published adducts of arenes and SbCl 3 [22][23][24].The exchange of the sodium cation from the borosilicate Simax ® glassware (Kavalierglass, a.s., Sázava, Czech Republic) and the arsenic atom obviously took place (see Figure 3).This is easily acceptable as the arsenic impurities or additives can be found in various types of glasses [25,26].A high tendency of the sodium atom to migrate from the glass surface and to form ionic compounds and complexes in solution is documented, for instance, by the existence of this phenomenon in glass electrodes and almost eighty examples of the sodium cation coordinated by six THF molecules found in the Cambridge Crystallographic Database.The [Na(THF) 6 ] + [I(AsI 3 ) 6 ] − (AsI 3 ) 2 complex is formed of a sodium cation surrounded by six THF molecules with octahedral geometry and iodide which has six molecules of the arsenic triiodide localized in the 'primary coordination sphere' (d As1-I5 3.294(3)Å) and adjacent two molecules of arsenic triiodide in the 'second coordination sphere' (d As2-I5 5.738(3)Å).From the point of view of the closer analysis, the topology of the underlying net is bcu-x in molecular ion-packing representation [27].The geometry of the described object based on the locations of the arsenic atoms and the central iodine ion is thus the dual pair of the Platonic solids-the cube and the octahedron, where only two vertexes of the cube are present bi-capping the opposite vertexes of the octahedra (Figure 4).According to the novel inverse coordination concept [28], the title complex could be also described as the inverse coordination compound where the iodine anion is the center of the aggregate.Such a concept is valid for oxygen and other halogens as the coordination centers bridging various metals, but is still undisclosed for halogen atoms.Only a limited number of coordination compounds with a halogen central atom were described, falling mainly to the groups of periodo tungstates or molybdates [29][30][31].To the best of our knowledge, there are only three examples of coordination compounds where a low valent halogen atom is present in an aggregate bridging, thus more metal centers with minimum number of 'ligands' being six-(Bi 10 I 20 ) 10+ , (Pb 10 I 20 ) [32], and (Pb 10 I 24 ) 4− [33]-mostly on the basis of the topological analysis being considered as Archimedean polyhedra not Platonian solids.These facts and the unusual bonding behavior of the low valent arsenic fragments to the negatively charged iodine atom led us to the idea of a broader inspection of the nature of these interactions.
Crystals 2017, 7, 225 5 of 9 sphere' (dAs1-I5 3.294(3)Å) and adjacent two molecules of arsenic triiodide in the 'second coordination sphere' (dAs2-I5 5.738(3)Å).From the point of view of the closer analysis, the topology of the underlying net is bcu-x in molecular ion-packing representation [27].The geometry of the described object based on the locations of the arsenic atoms and the central iodine ion is thus the dual pair of the Platonic solids-the cube and the octahedron, where only two vertexes of the cube are present bi-capping the opposite vertexes of the octahedra (Figure 4).According to the novel inverse coordination concept [28], the title complex could be also described as the inverse coordination compound where the iodine anion is the center of the aggregate.Such a concept is valid for oxygen and other halogens as the coordination centers bridging various metals, but is still undisclosed for halogen atoms.Only a limited number of coordination compounds with a halogen central atom were described, falling mainly to the groups of periodo tungstates or molybdates [29][30][31].To the best of our knowledge, there are only three examples of coordination compounds where a low valent halogen atom is present in an aggregate bridging, thus more metal centers with minimum number of 'ligands' being six-(Bi10I20) 10+ , (Pb10I20) [32], and (Pb10I24) 4− [33]-mostly on the basis of the topological analysis being considered as Archimedean polyhedra not Platonian solids.These facts and the unusual bonding behavior of the low valent arsenic fragments to the negatively charged iodine atom led us to the idea of a broader inspection of the nature of these interactions.this interaction might seem weak and not very important.Evidently, the σ-hole interactions of AsI3 units contribute significantly to the stability of the crystal but interactions of higher units could be important as well.Therefore, we also investigated interactions between the larger (AsI3)6I − units.The resulting ΔE is repulsive due to the electrostatic repulsion between I − ions.In the real crystal, this electrostatic repulsion is screened by counter ions and, therefore, we computed the interaction energy for the neutral (AsI3)6 dimer not containing the I anions.Since the (AsI3)6 dimer would be an excessively large molecule for the demanding CCSD(T) calculations, we have tested various DFT-D3 methods on the small AsI3 dimer.The best agreement between CCSD(T)/CBS and DFT-D3 values was found for the DFT-D3/BLYP/def2-QZVP level [34] (the ΔE of −2.24 and −2.27 kcal•mol −1 , respectively).The DFT-D3/BLYP/def2-QZVP method was then applied for the (AsI3)6 dimer.The resulting stabilization energy of 8.46 kcal•mol −1 is very large and clearly exceeds the energy of the Pn-bonding Evidently, the σ-hole interactions of AsI 3 units contribute significantly to the stability of the crystal but interactions of higher units could be important as well.Therefore, we also investigated interactions between the larger (AsI 3 ) 6 I − units.The resulting ∆E is repulsive due to the electrostatic repulsion between I − ions.In the real crystal, this electrostatic repulsion is screened by counter ions and, therefore, we computed the interaction energy for the neutral (AsI 3 ) 6 dimer not containing the I anions.Since the (AsI 3 ) 6 dimer would be an excessively large molecule for the demanding CCSD(T) calculations, we have tested various DFT-D3 methods on the small AsI 3 dimer.The best agreement between CCSD(T)/CBS and DFT-D3 values was found for the DFT-D3/BLYP/def2-QZVP level [34] (the ∆E of −2.24 and −2.27 kcal•mol −1 , respectively).The DFT-D3/BLYP/def2-QZVP method was then applied for the (AsI

Conclusions
We have studied the interplay between σ-and π-hole interactions in the known solid state structures of BI3 and AsI3 as well as in the newly reported [Na(THF)6] + [I(AsI3)6] − (AsI3)2 complex.The last one can be described as the inverse coordination compound where the iodine anion is the center of the aggregate.The quantum chemical calculations have revealed that the crystal packing of BI3 is dominated by π-hole interactions.In the case of the AsI3 molecule, a more important role is played by diX-bonding, whose overall contribution is comparable to the Pn-bonding for the monocrystal packing of AsI3.Finally, we found a strong stabilization between two [I(AsI3)6] − units where besides expected σ-hole interactions, systematically attractive dispersion interactions play a surprisingly important role.

Conclusions
We have studied the interplay between σand π-hole interactions in the known solid state structures of BI 3 and AsI 3 as well as in the newly reported [Na(THF) 6 ] + [I(AsI 3 ) 6 ] − (AsI 3 ) 2 complex.The last one can be described as the inverse coordination compound where the iodine anion is the center of the aggregate.The quantum chemical calculations have revealed that the crystal packing of BI 3 is dominated by π-hole interactions.In the case of the AsI 3 molecule, a more important role is played by diX-bonding, whose overall contribution is comparable to the Pn-bonding for the monocrystal packing of AsI 3 .Finally, we found a strong stabilization between two [I(AsI 3 ) 6 ] − units where besides expected σ-hole interactions, systematically attractive dispersion interactions play a surprisingly important role.

Figure 1 .
Figure 1.The computed electrostatic potential (ESP) on a 0.001 a.u.molecular surface and molecular diagrams.The color range of the ESP in kcal•mol −1 .
The A•••B binding motif has two symmetrical interactions of the π-holes with the negative belt of I atoms (the B•••I distance of 4.4 Å, the I-B•••I angle of 71.1°, the B•••I-B angle of 108.8° and the ΔE of −6.13 kcal•mol −1 ).BI3 also forms a bifurcated diX-bonds, found in the A•••C motif (the I•••I distances of 4.2 and 4.3 Å, the B-I•••I angles of 156.3° and 153.1°, and the I•••I-B angles of 96.4 and 93.1°), which are, however, weaker in this case, with the ΔE of −2.78 kcal•mol −1 .
and Table 2).It is the A-B motif with two symmetrical Pn-bonds (the As•••I distance of 3.5 Å, the I-As•••I angle of 160.7°, the As•••I-As angle of 91.3° and the ΔE of −7.52 kcal•mol −1 ).Interestingly, diX-bonds are more numerous in the case of AsI3 (the diX-bonds with the I•••I distances of 4.2-4.3Å, the As-I•••I angles of 142°-151° and the I•••I-B angles of 92°-99°) and also stronger (the ΔE of −4.43 and −3.26 kcal•mol−1for the A•••C and A•••D motifs, respectively).Consequently, Pn-bonding and diX-bonding have a comparable overall contribution for the crystal packing of AsI3.

Figure 1 .
Figure 1.The computed electrostatic potential (ESP) on a 0.001 a.u.molecular surface and molecular diagrams.The color range of the ESP in kcal•mol −1 .
The A•••B binding motif has two symmetrical interactions of the π-holes with the negative belt of I atoms (the B•••I distance of 4.4 Å, the I-B•••I angle of 71.1 • , the B•••I-B angle of 108.8 • and the ∆E of −6.13 kcal•mol −1 ).BI 3 also forms a bifurcated diX-bonds, found in the A•••C motif (the I•••I distances of 4.2 and 4.3 Å, the B-I•••I angles of 156.3 • and 153.1 • , and the I•••I-B angles of 96.4 and 93.1 • ), which are, however, weaker in this case, with the ∆E of −2.78 kcal•mol −1 .
).It is the A-B motif with two symmetrical Pn-bonds (the As•••I distance of 3.5 Å, the I-As•••I angle of 160.7 • , the As•••I-As angle of 91.3 • and the ∆E of −7.52 kcal•mol −1 ).Interestingly, diX-bonds are more numerous in the case of AsI 3 (the diX-bonds with the I•••I distances of 4.2-4.3Å, the As-I•••I angles of 142 • -151 • and the I•••I-B angles of 92 • -99 • ) and also stronger (the ∆E of −4.43 and −3.26 kcal•mol −1 for the A•••C and A•••D motifs, respectively).Consequently, Pn-bonding and diX-bonding have a comparable overall contribution for the crystal packing of AsI 3 .