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. 2024 Feb 23;9(9):10391–10399. doi: 10.1021/acsomega.3c08178

σ-Hole Site-Based Interactions within Hypervalent Pnicogen, Halogen, and Aerogen-Bearing Molecules with Lewis Bases: A Comparative Study

Mahmoud AA Ibrahim †,‡,*, Asmaa MM Mahmoud †, Mohammed NI Shehata †, Rehab RA Saeed †, Nayra AM Moussa †, Shaban RM Sayed §, Mohamed Khaled Abd El-Rahman ∥, Tamer Shoeib ⊥,*
PMCID: PMC10918780  PMID: 38463322

Abstract

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σ-Hole site-based interactions in the trigonal bipyramidal geometrical structure of hypervalent pnicogen, halogen, and aerogen-bearing molecules with pyridine and NCH Lewis bases (LBs) were comparatively examined. In this respect, the ZF5···, XF3O2···, and AeF2O3···LB complexes (where Z = As, Sb; X = Br, I; Ae = Kr, Xe; and LB = pyridine and NCH) were investigated. The electrostatic potential (EP) analysis affirmations outlined the occurrence of σ-holes on the systems under consideration with disparate magnitudes that increased according to the following order: AeF2O3 < XF3O2 < ZF5. In line with EP outcomes, the proficiency of σ-hole site-based interactions increased as the atomic size of the central atom increased with a higher favorability for the pyridine-based complexes over NCH-based ones. The interaction energy showed the most favorable negative values of −35.97, −44.53, and −56.06 kcal/mol for the XeF2O3···, IF3O2···, and SbF5···pyridine complexes, respectively. The preferentiality pattern of the studied interactions could be explained as a consequence of (i) the dramatic rearrangement of ZF5 molecules from the trigonal bipyramid geometry to the square pyramidal one, (ii) the significant and tiny deformation energy in the case of the interaction of XF3O2 molecules with pyridine and NCH, respectively, and (iii) the absence of geometrical deformation within the AeF2O3···pyridine and ···NCH complexes other than the XeF2O3···pyridine one. Quantum theory of atoms in molecules and noncovalent interaction index findings reveal the partially covalent nature of most of the investigated interactions. Symmetry–adapted perturbation theory affirmations declared that the electrostatic component was the driving force beyond the occurrence of the considered interactions. The obtained findings will help in improving our understanding of the effect of geometrical deformation on intermolecular interactions.

Introduction

Noncovalent interactions have been stated to play a substantial role in various chemical and biochemical processes.1−9 In particular, σ-hole interactions have received considerable attention over the past decade because of their unique contributions to crystal materials,10−14 biological systems,15−18 and catalysis.19 The first σ-hole conceptualization was described as a region suffering from a lack of electron density along the σ-bond of the group VII element-containing molecules.20 The σ-hole term was then extended until it encompassed the group IV–VIII elements. The interactions of the so-called σ-hole of the abovementioned groups with a Lewis base led to form tetrel,21−24 pnicogen,25−30 chalcogen,31−37 halogen,38−42 and aerogen43−45 bonds, respectively.

In the literature, the favorability of the σ-hole interaction was denoted to be affected by various factors, comprising the atomic size of the σ-hole donor atom and the electron-withdrawing power of its attached atom.46,47 It is worth mentioning that geometrical deformation plays a significant role in magnifying these interactions. As a point of departure, the effect of geometrical deformation was adequately assessed within the interactions of the tetrel-bearing molecules in the fashion of the tetrahedral geometry.48−50 Subsequently, the hypervalent pnicogen-, chalcogen-, and halogen-bearing molecules were addressed with an outstanding geometrical deformation effect on their interactions with LBs.51 It is worth mentioning that the trigonal bipyramidal geometry of the pnicogen-bearing molecules in their complexed form was recorded with the highest interaction energy in comparison to the seesaw/octahedral and square pyramidal of the chalcogen- and halogen-bearing ones, respectively. Such preferentiality could be attributed to the geometrical deformation of the ZF5 molecule (where Z = P, As, and Sb) from a trigonal bipyramidal geometry to a square pyramidal counterpart, which is accompanied by a larger σ-hole size.52,53 However, the deformation effect on the trigonal bipyramidal geometry of the halogen and aerogen-bearing molecules through their interactions with LBs has not yet been studied yet.

In this regard, the ability of halogen- and aerogen-bearing molecules within a trigonal bipyramidal geometry to engage in σ-hole site-based interactions with LBs was thoroughly studied and then compared with the previously reported pnicogen-bearing analogues. For this aim, ZF5···, XF3O2···, and AeF2O3···pyridine/NCH complexes were investigated (Figure 1). The presented work will open up a wide range of research on hypervalent noncovalent interactions, leading to a more significant improvement in their applications in anion recognition, biological systems, and crystal engineering.

Figure 1.

Figure 1

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Illustrative representation of the investigated pnicogen(ZF5)/halogen(XF3O2)/aerogen(AeF2O3)···Lewis base (LB) complexes (where Z = As and Sb; X = Br and I; Ae = Kr and Xe; and LB = pyridine and NCH).

Computational Methods

Various ab initio calculations were conducted to comparatively study the σ-hole site-based interactions of hypervalent pnicogen, halogen, and aerogen-bearing molecules with LBs using Gaussian 09 software.54 In this regard, the ZF5, XF3O2, and AeF2O3 molecules (where Z = As and Sb; X = Br and I; and Ae = Kr and Xe) within the trigonal bipyramidal geometry were devoted to directly interacting with pyridine and NCH molecules. All the systems under study were optimized at the MP2/aug-cc-pVTZ level of theory except for the Z, X, and Ae atoms.55−57 The pseudopotentials (PPs) were treated for the aforementioned excluded atoms for the relativistic effect considerations.58

The electrostatic potential (EP) analysis was performed for the optimized ZF5, XF3O2, and AeF2O3 molecules using a 0.002 a.u. electron density envelope upon previous recommendations, owing to its deserving representation for the surfaces of chemical systems.59 Molecular electrostatic potential (MEP) maps were accordingly visualized to illustrate the nucleophilic and electrophilic regions accompanied by evaluation of the maximum positive electrostatic potential (Vs,max) values.

Upon the optimized ZF5/XF3O2/AeF2O3···pyridine/NCH complexes, the interaction energy (Eint) was assessed as the variation between the complex’s energy and the sum of its monomer within their complexation geometry (eq 1), while binding energies (Ebind) were computed as the energy produced by subtracting the sum of the optimized monomers’ energies from the complex’s energy, as demonstrated in eq 2.60 The basis set superposition error (BSSE) was eliminated by considering the counterpoise correction method.61 The deformation energy (Edef) was also enumerated as the variation between the Ebind and Eint, as given in eq 3.62

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Moreover, the nature of the studied interactions was unveiled using the quantum theory of atoms in molecules (QTAIM)63 along with the noncovalent interaction (NCI) index analyses.64 The EP, QTAIM, and NCI analyses were executed through the Multiwfn 3.7 package.65 The QTAIM schemes and NCI plots were built using Visual Molecular Dynamics software.66 Symmetry–adapted perturbation theory (SAPT) analysis was accomplished to illustrate the physical nature of the inspected interactions.67 SAPT calculations were proceeded at the SAPT2+(3)dMP2 level of truncation via a PSI4 code68 to assess the fundamental energetic terms into dispersion (Edisp), exchange (Eexch), electrostatic (Eelst), and induction (Eind) energies. The total SAPT2+(3)dMP2 energy (ESAPT2+(3)dMP2) was given via eq 4.69

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Results and Discussion

EP Analyses

EP analyses were employed to visualize and evaluate the electron-deficient/rich regions over the molecular systems by generating MEP maps and Vs,max values for the ZF5, XF3O2, and AeF2O3 molecules (Figure 2).

Figure 2.

Figure 2

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Distributions of charge over the entities of the hypervalent pnicogen (ZF5), halogen (XF3O2), and aerogen (AeF2O3)-bearing molecules (where Z= As and Sb; X = Br and I; and Ae = Kr and Xe). EP varies from −6.28 (red) to 6.28 (blue) kcal/mol. Values of Vs,max are given in kcal/mol.

Inspecting the displayed MEP maps, the occurrence of the blue-coded region (i.e., σ-hole) was denoted with variable sizes (Figure 2) along the extension of the F-Z, F-X, and O-Ae covalent bonds for ZF5, XF3O2, and AeF2O3, respectively. These findings confirmed the noticeable versatility of the examined molecules to engage in σ-hole interactions. Notably, the σ-hole size was detected to increase by going from the AeF2O3 molecules to XF3O2 and ZF5 ones, which could be interpreted as a consequence of the higher polarizability of the heavier atoms.

Turning to Vs,max affirmations, the σ-hole magnitude was denoted with observable increase according to the following order AeF2O3 < XF3O2 < ZF5 molecules. For instance, the Vs,max values of the XeF2O3, IF3O2, and SbF5 molecules were 45.2, 57.6, and 79.1 kcal/mol, respectively. In line with MEP outcomes, an increase in Vs,max values were observed for the heavier atoms with values up to 33.6 and 45.2 kcal/mol for KrF2O3 and XeF2O3 molecules, respectively.

Interaction Energy

σ-Hole site-based interactions among the hypervalent ZF5, XF3O2, and AeF2O3 molecules in the trigonal bipyramidal geometry and the utilized LBs were intensively studied. Geometry optimization calculations were carried out for ZF5/XF3O2/AeF2O3···pyridine/NCH, and the obtained structures are given in Figure 3. Upon the optimized geometries, the Eint, Ebind, and Edef values were computed and are gathered in Table 1. The correlation between the Eint of the studied complexes and Vs,max values of their deformed monomers was graphed (Figure 4).

Figure 3.

Figure 3

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Optimized structures of the pnicogen(ZF5)/halogen(XF3O2)/aerogen(AeF2O3)···Lewis base (LB) complexes (where Z = As and Sb; X = Br and I; Ae = Kr and Xe; and LB = pyridine and NCH).

Table 1. Computed Values of Eint, Ebind, and Edef (in kcal/mol) for the Optimized Pnicogen (ZF5)/Halogen (XF3O2)/Aerogen (AeF2O3)···Lewis Base (LB) Complexes (where Z = As and Sb; X = Br and I; Ae = Kr and Xe; and LB = Pyridine and NCH).

  complex distance (Å) %of ∑rcovalenta θ1b (deg) θ2c (deg) Eint Ebind Edefd Vs,max
pnicogen AsF5···pyridine 2.04 108 179.99 89.82 –52.39 –30.89 21.50 131.5
SbF5···pyridine 2.17 105 179.99 89.71 –56.06 –40.20 12.86 153.0
AsF5···NCH 2.15 114 179.99 89.15 –19.22 –9.52 19.22 122.2
SbF5···NCH 2.24 108 179.99 89.11 –26.55 –19.68 6.87 147.1
halogen BrF3O2···pyridine 2.18 115 179.99 89.90 –32.61 –6.39 26.22 76.6
IF3O2···pyridine 2.23 107 180.00 89.89 –44.53 –26.04 18.49 92.2
BrF3O2···NCH 3.33 176 180.00 92.97 –2.55 –2.36 0.19 44.5
IF3O2···NCH 2.82 136 180.00 91.46 – 7.04 –3.98 3.06 74.4
aerogen KrF2O3···pyridine 3.29 151 179.99 89.72 –3.85 –3.37 0.48 39.7
XeF2O3···pyridine 2.29 105 179.99 88.39 –35.97 –13.33 22.64 93.1
KrF2O3···NCH 3.53 162 179.99 89.94 –2.04 –1.93 0.11 36.6
XeF2O3···NCH 3.36 154 179.99 89.65 –2.84 –2.28 0.56 52.6
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a

% of ∑rcovalent represents the percentage of the sum of the corresponding covalent radii (∑rcovalent).

b

θ1 represents ∠F1–Z/X···N and ∠O2–Ae···N within the optimized ZF5/XF3O2··· and AeF2O3···LB complexes, respectively (see Figure 3).

c

θ2 represents ∠F2–Z–F3 and ∠O1–X/Ae–F3 within the ZF5 and XF3O2/AeF2O3 molecules, respectively (see Figure 3).

d

Vs,max of the deformed structures of the ZF5, XF3O2, and AeF2O3 monomers are given in kcal/mol.

Figure 4.

Figure 4

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Correlation between the interaction energy (Eint) of the optimized pnicogen(ZF5)/halogen(XF3O2)/aerogen(AeF2O3)···Lewis base (LB) complexes (where Z = As and Sb; X = Br and I; Ae = Kr and Xe; and LB = pyridine and NCH) and Vs,max values of their deformed monomers. (a, b) Pyridine-based and NCH-based complexes, respectively.

As illustrated in Figure 3, the optimized structures demonstrated the significant effect of the deformation process that was noticed in the investigated σ-hole site-based interactions within almost all of the studied complexes. Moreover, the optimum distances were denoted to be less than the sum of the corresponding van der Waals radii, affirming the evident ability of the ZF5/XF3O2/AeF2O3 molecules to engage in the investigated interactions. Meanwhile, the percentage (%) of the sum of the corresponding covalent radii (∑rcovalent) values emphasized that the obtained complexes would not have covalent bonding features, only a partially covalent or noncovalent nature.

Inspecting the change in the θ2 angles of the ZF5/XF3O2/AeF2O3 molecules after complexation with Lewis bases, noticeable deformation in the trigonal bipyramidal structures was obtained with disparate degrees relying on the central atom in the investigated interactions (Figure 3). Detailedly, a drastic deformation of the ZF5 geometries from the trigonal bipyramid structure to the square pyramidal one was denoted upon complexation of the pnicogen-bearing molecules with the pyridine and NCH LBs, enabling the ZF5 molecules to efficiently engage in opulent σ-hole site-based interactions. As evident in Table 1, considerable Edef values were obtained within an energetic range of 6.87–21.50 kcal/mol.

Regarding the halogen-bearing complexes, significant Edef was observed in the case of XF3O2···pyridine complexes only with Edef values up to 26.22 and 18.49 kcal/mol, where X = Br and I, respectively. Subsequently, the geometrical structure of the XF3O2 molecules within the aforementioned complexes mimicked the rearrangement relevant to the pnicogen-bearing counterparts. In comparison, small Edef values of 0.19 and 3.06 kcal/mol were found in the case of the BrF3O2··· and IF3O2···NCH complexes with a slight change in the XF3O2 trigonal bipyramid geometry.

Turning to aerogen-bearing complexes, tiny Edef values were observed for the studied complexes except for the XeF2O3···pyridine complex. Such an observation outlined an inconspicuous change of the geometrical structure of the AeF2O3 molecules upon complexation with either the pyridine or NCH LBs regardless of the XeF2O3···pyridine complex.

As a consequence of the preceding observations, the strength of σ-hole site-based interactions was detected to increase with significant Eint and Ebind values in the posterior pattern: AeF2O3 < XF3O2 < ZF5···pyridine/NCH complexes (Table 1). The Eint energies of the investigated complexes were generally consistent with Vs,max values of the deformed monomers, giving correlation coefficient (R2) values of 0.85 and 0.97 in the case of the pyridine and NCH-based complexes, respectively (Figure 4). Evidently, the Eint energies were −2.84, −7.04, and −26.55 kcal/mol for XeF2O3···, IF3O2···, and SbF5···NCH complexes along with Vs,max values of 52.6, 74.4, and 147.1 kcal/mol for their deformed XeF2O3, IF3O2, and SbF5 monomers, respectively (Table 1).

Additionally, negative values of Eint and Ebind increased with increasing the atomic size of the inspected pnicogen, halogen, and aerogen atoms. For instance, the Eint/Ebind values of the BrF3O2··· and IF3O2···pyridine complexes were −32.61/–6.39 and −44.53/–26.04 kcal/mol, respectively. Conspicuously, higher Eint/Ebind values were observed for the pyridine-based complexes compared to the NCH analogues. Impressively, optimum intermolecular distances were disclosed to be directly correlated with energetic trends, where the studied interactions were enhanced by decreasing the intermolecular distances. Illustratively, the XeF2O3···, IF3O2···, and SbF5···NCH complexes were characterized by Eint/Ebind values of −2.84/–2.28, – 7.04/–3.98, and −26.55/–19.68 kcal/mol at optimum intermolecular distances of 3.36, 2.82, and 2.24 Å, respectively.

QTAIM Analysis

Toward more validation for the occurrence of noncovalent interactions, QTAIM analysis was implemented.70,71 Diagrams of QTAIM relevant to the optimized ZF5/XF3O2/AeF2O3···pyridine/NCH complexes are graphed in Figure 5. The corresponding topological parameters, encompassing the ∇2ρb, Hb, and ρb, were computed and are enrolled in Table 2.

Figure 5.

Figure 5

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Diagrams of QTAIM relevant to the optimized pnicogen(ZF5)/halogen(XF3O2)/aerogen(AeF2O3)···Lewis base (LB) complexes (where Z = As and Sb; X = Br and I; Ae = Kr and Xe; and LB = pyridine and NCH). Red dots indicate the locations of the BPs and BCPs. The small red and yellow dots represent bond critical points (BCPs) and ring critical points (RCPs), respectively.

Table 2. Topological Parameters (in a.u.), Including ρb, ∇2ρb, and Hb, at BCPs of the Optimized Pnicogen(ZF5)/Halogen(XF3O2)/Aerogen(AeF2O3)···Lewis Base (LB) Complexes (where Z = As and Sb; X = Br and I; Ae = Kr and Xe; and LB = Pyridine and NCH).

complex ρb ∇2ρb Hb
pnicogen AsF5···pyridine 0.0718 0.0718 –0.0612
SbF5···pyridine 0.0918 0.1895 –0.0373
AsF5···NCH 0.0678 0.1236 –0.0251
SbF5···NCH 0.0679 0.1991 –0.0184
halogen BrF3O2···pyridine 0.0981 0.0337 –0.0397
IF3O2···pyridine 0.2164 0.4931 –0.1687
BrF3O2···NCH 0.0082 0.0316 0.0015
IF3O2···NCH 0.0245 0.0691 0.0001
aerogen KrF2O3···pyridine 0.0115 0.0436 0.0018
XeF2O3···pyridine 0.0936 0.0271 –0.0409
KrF2O3···NCH 0.0069 0.0273 0.0015
XeF2O3···NCH 0.0095 0.0360 0.0017
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According to Figure 5, the existence of σ-hole site-based interactions was confirmed within the pnicogen-bearing complexes via the appearance of a single BCP and BP between the Z atom and the Lewis base. Additionally, two BCPs and BPs were disclosed in the case of ZF5···pyridine complexes, indicating the occurrence of hydrogen bonds. The same findings were found within the halogen-bearing complexes other than that of the BrF3O2···NCH complex. The interactions within the latter complex were characterized by the existence of secondary interactions between the oxygen atoms and the Lewis base.

Turning to aerogen-bearing complexes, two BPs and BCPs were observed between the oxygen atoms and the N atom of the Lewis base with an exception for the XeF2O3···pyridine complex. For the latter exceptional complex, three BCPs and BPs were observed: one for the σ-hole site-based interactions and two for hydrogen bonds. Accordingly, the strong contribution of the σ-hole···N interaction to the overall strength of the XeF2O3···pyridine complex was outlined. While no evidence for the contribution of the latter interaction was observed within the XeF2O3···NCH and KrF2O3···pyridine/NCH complexes. This observation was consistent with the previously documented emphasis on the BPs’ minimal significance in determining the origin of the interactions under consideration.72,73

From Table 2, high positive ρb values along with negative Hb values were denoted for the pnicogen-bearing complexes, parading their partially covalent character. In parallel, the same findings were observed for the XF3O2··· and XeF2O3···pyridine complexes. This finding demonstrated the significant effect of the deformation process on enhancing the investigated interactions. Unlike the prior findings, positive signs of ρb and Hb with low values were detected for the other complexes, illustrating their closed-shell nature. Generally, the topological parameter trends were in sync with the energetic pattern. Evidently, noticeable ρb, ∇2ρb, and Hb values were detected for the ZF5/XF3O2/AeF2O3···pyridine complexes over the ZF5/XF3O2/AeF2O3···NCH complexes. For instance, ρb values of SbF5···pyridine and ···NCH complexes were 0.0918 and 0.0679 a.u. along with Eint/Ebind values of −56.06/–40.20 and −26.55/–19.68 kcal/mol, respectively.

NCI Analysis

The NCI index has previously been described as a powerful tool for detecting the presence of closed- and open-shell interactions.74 NCI plots were built for the ZF5/XF3O2/AeF2O3···pyridine/NCH complexes by using a reduced density gradient value of 0.50 a.u. (Figure 6).

Figure 6.

Figure 6

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3D NCI diagrams of the optimized pnicogen(ZF5)/halogen(XF3O2)/aerogen(AeF2O3)···Lewis base (LB) complexes (where Z = As and Sb; X = Br and I; Ae = Kr and Xe; LB = pyridine and NCH).

As evident in Figure 6, empty areas surrounded by blue/red circles were observed within the ZF5···pyridine/NCH, XF3O2···pyridine, and XeF2O3···pyridine complexes, reflecting their partially covalent bonding nature. Regarding XF3O2···NCH complexes, NCI findings showed the existence of blue-colored surfaces, addressing the occurrence of a strong intermolecular attractive interaction. Apparently, greenish-red and brownish-red areas within the AeF2O3···pyridine/NCH complexes were observed, revealing the existence of van der Waals attraction and repulsive forces, respectively. These results were in line with the QTAIM outlines.

SAPT Calculations

SAPT analysis has been developed as a reliable tool for elucidating the driving force that plays a significant role in intermolecular interactions.75 For the optimized ZF5/XF3O2/AeF2O3···LB complexes, the attractive and repulsive energetic components are graphed in Figure 7 and Table 3.

Figure 7.

Figure 7

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Bar chart of the four physical energetic components for the optimized pnicogen(ZF5)/halogen(XF3O2)/aerogen(AeF2O3)···Lewis base (LB) complexes (where Z = As and Sb; X = Br and I; Ae = Kr and Xe; and LB = pyridine and NCH).

Table 3. Eelst, Eind, Edisp, Eexch, and ESAPT2+(3)dMP2 (in kcal/mol) along the Energy Difference (ΔΔE) between the MP2 and SAPT2+(3)dMP2 Energies of the Optimized Pnicogen(ZF5)/Halogen(XF3O2)/Aerogen(AeF2O3)···Lewis Base (LB) Complexes (where Z = As and Sb; X = Br and I; Ae = Kr and Xe; and LB = Pyridine and NCH).

complex Eelst Eind Edisp Eexch ESAPT2+(3)dMP2a ΔΔEb
pnicogen AsF5···pyridine –84.13 –65.18 –25.03 119.62 –54.71 –2.32
SbF5···pyridine –77.30 –55.48 –21.80 95.44 –59.14 –3.08
AsF5···NCH –41.71 –29.75 –14.27 66.44 –19.28 –0.06
SbF5···NCH –42.50 –30.52 –13.20 59.11 –27.11 –0.56
halogen BrF3O2···pyridine –71.89 –52.53 –25.38 117.43 –32.37 0.24
IF3O2···pyridine –82.58 –60.77 –26.56 125.24 –44.68 –0.15
BrF3O2···NCH –3.45 –0.37 –3.04 4.37 –2.48 0.07
IF3O2···NCH –14.71 –5.07 –6.89 19.63 –7.04 0.00
aerogen KrF2O3···pyridine –6.77 –0.42 –6.38 9.51 –4.06 –0.21
XeF2O3···pyridine –74.15 –51.49 –25.83 116.58 –34.90 1.07
KrF2O3···NCH –2.39 –0.19 –2.69 3.27 –2.00 0.04
XeF2O3···NCH –4.72 –0.49 –3.74 6.05 –2.90 –0.06
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a

Inline graphic

b

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Manifestly, in Figure 7, the Eelst component was detected with predominant contributions in the investigated interactions within the ZF5/XF3O2/AeF2O3···pyridine/NCH complexes except for the KrF2O3···NCH complex that was dominated by the Edisp. Additionally, significant contributions to the Eind and Edisp were also denoted. The obtained negative values of the abovementioned energetic components manifested the role of their attractive nature in stabilizing all ZF5/XF3O2/AeF2O3···pyridine/NCH complexes. Unlike the prior components, Eexch was announced as a repulsive one with high positive values. For instance, the Eelst, Eind, Edisp, and Eexch of the SbF5···pyridine complex were −77.30, – 55.48, – 21.80, and 95.44 kcal/mol, respectively (Table 3).

As listed in Table 3, growing contributions of the attractive forces to the studied interactions within the ZF5···pyridine/NCH, XF3O2···pyridine, and XeF2O3···pyridine complexes were noticed to follow the Edisp < Eind < Eelst sequence. For the other complexes, the attractive energetic components of the interactions were generally aligned following the Eind < Edisp < Eelst order. For instance, Eelst, Eind, and Edisp of the SbF5···pyridine complex were −77.30, −55.48, and −21.80 kcal/mol, respectively.

Further, a notable agreement was observed between the ESAPT2+(3)dMP2, Eint, and Vs,max values of all of the investigated systems. For instance, ESAPT2+(3)dMP2 were −59.14, – 44.68, and −34.90 kcal/mol for the SbF5···, IF3O2···, and XeF2O3···pyridine complexes that exhibited Eint values of −56.06, – 44.53, and −35.97 kcal/mol, accompanied by Vs,max values of 79.1, 57.6, and 45.2 kcal/mol for the SbF5, IF3O2, and XeF2O3 molecules, respectively.

The reliability of the incorporated SAPT level was confirmed via the tiny ΔΔE values between the EMP2 and the total ESAPT2+(3)dMP2 energies (Table 3). The desirable SAPT components exhibited the same pattern of the energetic results of the considered complexes. For example, Eelst values of the SbF5···, IF3O2···, and XeF2O3···NCH complexes were −42.50, −14.71, and −4.72 kcal/mol in a company with Eint values of −26.55, −7.04, and −2.84 kcal/mol, respectively.

Conclusions

σ-Hole site-based interactions between the hypervalent pnicogen, halogen, and aerogen-bearing molecules within the trigonal bipyramidal structure and pyridine/NCH LBs were minutely studied. For this purpose, ZF5···, XF3O2···, and AeF2O3···LB complexes (where Z = As and Sb; X = Br and I; Ae = Kr and Xe; and LB = pyridine and NCH) were investigated. EP affirmations elucidated the ability of the inspected systems to form σ-hole with different magnitudes that increased according to the following order AeF2O3 < XF3O2 < ZF5. Consistent with EP findings, the proficiency of σ-hole site-based interactions increased based on the atomic size of the central atom in the succeeding order: AeF2O3··· < XF3O2··· < ZF5···pyridine/NCH complexes along with more favorability for the pyridine-based complexes over the NCH ones. Such preferentiality was attributed to the drastic deformation energies (i.e., geometrical deformation) that could be concluded as follows: (i) the drastic geometrical deformation of ZF5 molecules from the trigonal bipyramidal geometry to the square pyramidal one upon complexation with the pyridine and NCH LBs; (ii) the notable Edef in the case of XF3O2···pyridine complexes rather than ···NCH counterparts; and (iii) the absence of geometrical deformation within most of the AeF2O3···pyridine and ···NCH complexes. QTAIM and NCI index affirmations admitted the partially covalent nature of most of the investigated complexes. Generally, SAPT indications outlined Eelst as the driving force beyond the occurrence of the considered interactions. Such outcomes will help in understanding the intermolecular interactions and will subsequently blaze a trail for the forthcoming applications in crystal engineering and biological systems.

Acknowledgments

The authors extend their appreciation to the Researchers Supporting Project No. (RSPD2024R743), King Saud University, Riyadh, Saudi Arabia, for funding this work. The computational work was performed with resources provided by the Science and Technology Development Fund (STDF-Egypt, grants nos. 5480 and 7972), Bibliotheca Alexandrina (http://hpc.bibalex.org), and The American University in Cairo. M.A.A.I. thanks the Center for High-Performance Computing (CHPC, www.chpc.ac.za), Cape Town, South Africa, for providing computational resources. M.A.A.I. extends his appreciation to the Academy of Scientific Research and Technology (ASRT, Egypt) for funding the Graduation Projects conducted at CompChem Lab, Egypt.

Author Contributions

M.A.A.I. contributed in the conceptualization, methodology, software, resources, project administration, supervision, and writing—review and editing. A.M.M.M. contributed in data curation, formal analysis, investigation, visualization, and writing—original draft. M.N.I.S. participated in methodology, investigation, project administration, and writing—review and editing. R.R.A.S. contributed in the methodology, investigation, project administration, and writing—review and editing. N.A.M.M. participated in the methodology, investigation, project administration, and writing—review and editing. S.R.M.S. is responsible for the resources and writing—review and editing. M.K.A.E.-R. participated in the writing—review and editing. T.S. contributed in the conceptualization, methodology, and writing—review and editing.

The authors declare no competing financial interest.

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