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

Abstract

Boron and arsenic triiodides (BI₃ and AsI₃, respectively) are similar molecules that differ mainly in their geometries. BI₃ is a planar trigonal molecule with D_3h symmetry, while AsI₃ exhibits a trigonal pyramidal shape with C_3v 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.

1. 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 BI₃ and AsI₃. 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 BI₃ is a planar trigonal molecule with D_3h symmetry (π-back donation is possible here but not in AsI₃), AsI₃ 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(AsI₃)₆]⁻ units within [Na(THF)₆]⁺[I(AsI₃)₆]⁻(AsI₃)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 (ΔE) 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.

2. Methods

2.1. Experimental

The preparation and isolation of [Na(THF)₆]⁺[I(AsI₃)₆]⁻(AsI₃)₂: Perylene (207 mg, 0.82 mmol) and AsI₃ (748 mg, 1.64 mmol) were mixed in a THF/CH₂Cl₂ 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 C₂₄H₄₈As₈I₂₅NaO₆, 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(F²). The final cell constants of a = 16.5457(7) Å, b = 16.5457(7) Å, c = 26.0339(11) Å, volume = 6172.2(6) ų, 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, C₂₄H₄₈As₈I₂₅NaO₆. The final anisotropic full-matrix least-squares refinement on F² with 99 variables converged at R₁ = 2.14%, for the observed data and wR₂ = 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⁻/ų and the largest hole was −0.866 e⁻/ų with an RMS deviation of 0.188 e⁻/ų. On the basis of the final model, the calculated density was 3.412 g/cm³ and F(000), 5520 e⁻.

Full-sets of diffraction data for [Na(THF)₆]⁺[I(AsI₃)₆]⁻(AsI₃)₂ were collected at 150(2)K with a Bruker D8-Venture diffractometer equipped with Mo (Mo/K_λ radiation; λ = 0.71073 Å) microfocus X-ray (IµS) source, Photon CMOS detector (Bruker AXS Inc., Madison, WI, USA) and Oxford Cryostream 800 Series cooling device (Oxford Cryosystems Ltd., Oxford, UK) was used for data collection.

The frames were integrated with the Bruker SAINT software package (Bruker AXS Inc., Madison, WI, USA) using a narrow-frame algorithm. Data were corrected for absorption effects using the Multi-Scan method (SADABS). Obtained data were treated by XT-version 2014/5 (Bruker AXS Inc., Madison, WI, USA) and SHELXL-2014/7 software implemented in APEX3 v2016.5-0 (Bruker AXS) system [11].

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).

2.2. 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].

ΔE 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.

3. Results and Discussion

In the first step, the computed properties of isolated BI₃ and AsI₃ molecules were compared (see

Table 1. The electrostatic potential surface maxima (V_max) in kcal·mol⁻¹. Dipole moments (μ) in D.

Molecule	Atom	Vmax	μ
BI3	B	2 × 23.5	0.00
	I	22.3
AsI3	As	3 × 25.7	0.74
	I	23.2

and Figure 1). The iodine atoms of both BI₃ and AsI₃ 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 AsI₃ molecule (the V_min values of BI₃ and AsI₃ 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 AsI₃ molecule has three σ-holes, the B atom of the BI₃ 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 BI₃ with those of B(CH₃)₃ and B(CH=CH₂)₃ have been compared. While B(CH₃)₃ has a π-hole with a similar V_max value of 25.4 kcal·mol⁻¹, B(CH=CH₂)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=CH₂)₃ [20]. In the case of B(NHCH₃)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. Interaction energies in kcal·mol⁻¹.

Crystal	Motif	Interaction	CCSD(T)/CBS
BI3	A···B	2 × π-hole bonding	−6.13
	A···C	Bifurcated diX-bond	−2.78
AsI3	A···B	2 × Pn-bonding	−7.52
	A···C	2 × Bifurcated diX-bonding	−4.43
	A···D	Bifurcated diX-bonding	−3.26
[Na(THF)6]+[I(AsI3)6]−(AsI3)2	A···I−	Pn-bonding	−23.59
	A···B	Pn-bonding	−4.64
	B···C	diX-bonding	−2.24

). 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). 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.

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 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 4.2–4.3 Å, 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⁻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 AsI₃.

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 [22,23,24]. 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(AsI₃)₆]⁻(AsI₃)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—(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.

When analyzing Pn- and diX-bonding in the [Na(THF)₆]⁺[I(AsI₃)₆]^-(AsI₃)₂ complex (see Figure 5), we found very strong Pn-bonding to an iodine ion (the As···I⁻ distance of about 3.3 Å, the I-As···I⁻ angle of 162.6°, the ΔE of −23.59 kcal·mol⁻¹). Another Pn-bond can be found between two AsI₃ molecules (the As···I distance of about 3.5 Å, the I-As···I angle of 168.9°, the As···I-As angle of 98.0°, the ΔE of −4.64 kcal·mol⁻¹). There is also interesting diX-bonding in the crystal structure with the I···I distance of about 3.7 Å, the As-I···I angle of 167.9°, the I···I-As angle of 154.7° and the ΔE −2.24 kcal·mol⁻¹. Based on the values of the I···I-As angle and the ΔE of this diX-bonding in the B···C motif, 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 in the single A···B crystal motif. Interestingly, the dominant part (−11.5 kcal·mol⁻¹) of the overall stabilization originates in the dispersion energy which again stresses the important stabilization role of this systematically attractive contribution.

4. 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.