Interactions of hypervalent IF₅ and XeF₄O molecules via σ-hole site with Lewis bases and anions: a comparative ab initio study

Abstract

Interactions of hypervalent IF₅ and XeF₄O molecules within the square pyramidal geometry via σ-hole site with Lewis bases (LB = NH₃ and NCH) and anions (X⁻ = F⁻, Cl⁻, Br⁻, and I⁻) were comparatively investigated using ab initio methods. The energetic features outlined remarkable interaction (E_int) and binding (E_bind) energies for all complexes aligned from −5.65 to −91.02 kcal mol⁻¹ and from −5.53 to −65.89 kcal mol⁻¹, respectively. More negative E_int and E_bind values were demonstrated for XeF₄O⋯LB complexes, compared to IF₅⋯LB complexes, along with nominal deformation energies for all complexes. Turning to IF₅⋯ and XeF₄O⋯X⁻ complexes, E_bind demonstrated the proficiency of the latter complexes, which was in synchronic with the V_s,max claims. On the contrary, IF₅⋯X⁻ complexes demonstrated higher negative E_int values in comparison to XeF₄O⋯X⁻ complexes, which may be attributed to the considerable favorable deformation energies relevant to the former complexes rather than the latter candidates. Moreover, the E_int and E_bind were disclosed to ameliorate in coincidence with the Lewis basicity strength as follows: IF₅/XeF₄O⋯NCH < ⋯NH₃ < ⋯I⁻ < ⋯Br⁻ < ⋯Cl⁻ < ⋯F⁻. Quantum theory of atoms in molecules/noncovalent interactions index observations affirmed that the interactions of IF₅/XeF₄O molecules via σ-hole site with NH₃ and NCH were characterized with open- and closed-shell nature, respectively, while the IF₅/XeF₄O⋯X⁻ complexes were characterized with the coordinative covalent nature. Symmetry-adapted perturbation theory results pinpointed the predominance of the inspected interactions with the electrostatic forces. The acquired results will be advantageous for the ubiquitous investigation of understanding the impact of geometrical deformation on the interactions of hypervalent molecules and their applications in diverse fields such as materials science and crystal engineering.

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Introduction

σ-Hole interaction is one of the most common noncovalent interactions within the scientific community, due to its vital role in drug discovery,^1,2 crystal material,^3–7 supramolecular chemistry,^8,9 anion recognition,¹⁰ biochemistry,^11,12 and catalysis.¹³ σ-Hole interaction is characterized as an attractive interaction between an electron-deficient region that exists along the extension of a covalent σ-bond of group VI–VIII element-containing molecules (i.e., σ-hole) and a nucleophile.^14,15 Accordingly, σ-hole interactions of group VI–VIII element-containing molecules were termed tetrel,^16,17 pnicogen,^18–21 chalcogen,^22–24 halogen,^25–28 and aerogen^29–31 bonds, respectively.

In the literature, σ-hole interactions were discerned to be greatly affected by diverse factors. Basically, several studies pinpointed that σ-hole interactions are affected by the atomic size of the σ-hole donor atom and the electron-withdrawing power of its attached atom/group within electrophilic molecules.^32,33 Furthermore, a significant impact of the Lewis basicity of the utilized nucleophilic molecules on the strength of σ-hole interactions was unveiled. Illustratively, pnicogen-containing molecules were addressed to interact with various types of nucleophiles, forming different-in-strength pnicogen bonding interactions with favorable ones when nucleophiles were anions (X⁻) compared to the neutral Lewis bases (LB).^34,35 These outcomes could be explained owing to the noncovalent nature of σ-hole site-based interactions within pnicogen-containing molecules⋯LB complexes, while the investigated interactions were characterized with a coordinative covalent nature within pnicogen-containing molecules⋯X⁻ complexes.

The effect of geometrical deformation on the σ-hole size of hypervalent molecules upon the complexation process with an LB was also investigated.^36–38 Such a deformation effect was extensively studied in molecules within the trigonal bipyramidal geometry. In this context, the pnicogen-(ZF₅) and halogen-(XF₃O₂) containing molecules demonstrated a drastic geometrical deformation after their interaction with LBs.^37,38 On the other hand, a tiny response for the aerogen-(XF₂O₃) containing molecules within the trigonal bipyramidal geometry to the geometrical deformation was denoted; hence, lower interaction energies were perceived. These annotations indicated the effective role of geometrical deformation in enhancing the emerging interactions. In the same avenue, a paucity of studies concerned with investigating the deformation effect on the characteristics of molecules in square pyramidal geometry upon the complexation process was uncovered. A recent study declared that the complexation process of the halogen-containing molecule in square pyramidal geometry, such as IF₅, with LBs resulted in significant deformation energies;³⁷ however, the impact of deformation on the interactions of the aerogen-containing molecule, such as XeF₄O, with LBs has not been inspected yet.

In this respect, the propensity of hypervalent IF₅ and XeF₄O molecules in the square pyramidal geometry to interact via σ-hole site with LBs and X⁻ was minutely inspected. In that vein, the IF₅⋯ and XeF₄O⋯LB/X⁻ complexes (where LB = NH₃ and NCH; X⁻ = F⁻, Cl⁻, Br⁻, and I⁻) were investigated. Moreover, the nucleophilicity effect on the strength of the investigated interactions was detailedly considered. The obtained observations would serve as a valuable milestone for elucidating the comprehensive role of geometrical deformation on the interactions of hypervalent molecules and their applications in anion recognition and crystal engineering.

Computational method

Ab initio calculations were implemented to investigate the interactions of the hypervalent IF₅ and XeF₄O molecules in square pyramidal geometry via σ-hole site with LB and X⁻ using Gaussian 09 program³⁹ (Fig. 1). In this context, NH₃ and NCH were designated as LBs, and F⁻, Cl⁻, Br⁻, and I⁻ were picked as X⁻. Accordingly, the MP2/aug-cc-pVTZ level of theory was utilized to geometrically optimize the inspected monomers and complexes.^40–44 The aug-cc-pVTZ-PP basis set was used for the I and Xe atoms to take the relativistic effects into account. The frequency computations were carried out for all optimized complexes, elucidating the true minima nature of all complexes except for the IF₅⋯NCH and XeF₄O⋯NH₃ ones. EP analysis was conducted to identify the regions with electron-poor and electron-rich nature over the surface of chemical systems.^45–47 Based on the previous recommendations, an electron density contour of 0.002 a.u. was utilized owing to its worthy representation for the surfaces of chemical systems.^48,49 Consequently, the descriptive and numerical results of the electron density distributions over the entity of the chemical systems were performed by molecular electrostatic potential (MEP) maps and surface electrostatic potential extrema (V_s,max/V_s,min), respectively. Moreover, the electron localization function (ELF) analysis was executed to indicate the Lewis basicity affinity of the studied LB and X⁻. In this context, ELF maps were generated to indicate the localized electron density region through visualizing the bonding pattern and lone pairs within the studied systems.

Fig. 1 Depictive representation for (a) PoC approach and (b) the modeled IF₅⋯ and XeF₄O⋯LB/X⁻ complexes.

To evaluate the Lewis basicity effect from the electrostatic viewpoint, molecular stabilization of halogen- and aerogen-containing molecules in the presence of PoCs = −0.25, −0.50, −0.75, and −1.00 a.u. was inspected.⁵⁰ In this vein, molecular stabilization energy (E_{stabilization}) was calculated at I/Xe⋯PoC distance in the range from 2.5 to 5.0 with a step size of 0.1 Å according to eqn (1).⁵¹

E_{stabilization} = E_molecule⋯_PoC − E_molecule (1)

Within the complexation process, interaction energy (E_int) for optimized IF₅⋯ and XeF₄O⋯LB/X⁻ complexes was formulated as the difference between the total energy of the complex and the sum of its monomers correlated to their coordinates in the optimized complex. The binding energy (E_bind) was calculated as the difference between the total energy of the optimized complexes and the sum of the energies of isolated monomers.⁵² Consequently, the deformation energy (E_def) was brought about by the complexation of the two interacting monomers and was yielded by subtracting the E_int from the E_bind.⁵³ Using the Boys-Bernard counterpoise correction method, the inherent basis set superposition error (BSSE) was eradicated from the aforementioned calculations.⁵⁴ The E_int, E_bind, and E_def of the studied complexes were explained in the following equations.

E_int = E_{IF5/XeF4O⋯LB/X⁻} − (E_{IF5/XeF4O in complex} + E_{LB/X⁻in complex}) + E_BSSE (2)

E_bind = E_{IF5/XeF4O⋯LB/X⁻} − (E_IF5/XeF4O + E_LB/X⁻) + E_BSSE (3)

E_def = E_bind − E_int (4)

The computed interaction energy at E_{MP2/aug-cc-pVTZ(PP)} was benchmarked through the CCSD(T)/CBS computational level, depending on the subsequent equations.⁵⁵

E_CCSD(T)/CBS = ΔE_MP2/CBS + ΔE_CCSD(T) (5)

where

ΔE_MP2/CBS = (64E_{MP2/aug-cc-pVQZ} − 27E_{MP2/aug-cc-pVTZ})/37 (6)

ΔE_CCSD(T) = E_{CCSD(T)/aug-cc-pVDZ} − E_{MP2/aug-cc-pVDZ} (7)

In eqn (6), the 64 and 27 factors were driven from the well-established two-point X⁻³ extrapolation method, where the cardinal number (X) equals 4 and 3 for the aug-cc-pVQZ and aug-cc-pVTZ basis sets, respectively.⁵⁶ At the same time, the 37 factor represents the difference between the cube of the above-mentioned cardinal numbers. To qualitatively illustrate the nature of interactions within the IF₅⋯ and XeF₄O⋯LB/X⁻ complexes, QTAIM and NCI index analyses were invoked.^57,58 By employing QTAIM, bond paths (BPs) and bond critical points (BCPs) were generated. Various topological properties such as potential energy density (V_b), electron density (ρ_b), Laplacian (∇²ρ_b), lagrangian kinetic energy (G_b), total energy density (H_b), and the negative ratio of kinetic and potential electron energy density (−G_b/V_b) were assessed. The 2D reduced density gradient (RDG) and 3D colored NCI plots were also mapped. The V_s,max, V_s,min, ELF, QTAIM, and NCI analyses were carried out using the Multiwfn 3.7 package.⁵⁹ The schemes of QTAIM and NCI were portrayed using Visual Molecular Dynamics software.⁶⁰ SAPT calculations were executed as a vigorous method to dissect the essential physical components of the E_{SAPT2+(3)dMP2} into electrostatic (E_elst), induction (E_ind), dispersion (E_disp), and exchange energies (E_exch) through eqn (8)–(12).^61,62 In this vein, SAPT upshots were computed at the SAPT2+(3)dMP2 truncation level using PSI4 code⁶³ for all the inspected complexes.

E^{SAPT2+(3)dMP2}_int = E_elst + E_ind + E_disp + E_exch (8)

where

E_elst = E⁽¹⁰⁾_elst + E⁽¹²⁾_elst + E⁽¹³⁾_elst (9)

E_ind = E⁽²⁰⁾_ind,resp + E⁽²⁰⁾_{exch-ind,resp} + E⁽²²⁾_ind,resp + E⁽²²⁾_{exch-ind,resp} + δE⁽²⁾_HF + δE⁽²⁾_MP2 (10)

E_disp = E⁽²⁰⁾_disp + E⁽²⁰⁾_exch-disp + E⁽²¹⁾_disp + E⁽²²⁾_disp(SDQ) + E⁽²²⁾_dispT + E⁽³⁰⁾_disp (11)

E_exch = E⁽¹⁰⁾_exch + E⁽¹¹⁾_exch + E⁽¹²⁾_exch (12)

Results

EP analysis

EP analysis was established to systematically outline the electron density distribution over the surface of the inspected IF₅ and XeF₄O molecules, along with LBs and X⁻. Fig. 2 portrays the MEP maps along with V_s,max and V_s,min values of the optimized IF₅, XeF₄O, LBs, and X⁻ molecules.

Fig. 2 Molecular electrostatic potential maps of the investigated IF₅ and XeF₄O molecules as Lewis acids, along with the utilized LB and X⁻ using 0.002 a.u. electron density isosurface. MEP scale varies from −6.28 (red) to 6.28 (blue) kcal mol⁻¹.

As displayed in Fig. 2, for the Lewis acid centers, σ-hole was found at the outer surface of I and Xe atoms of the IF₅ and XeF₄O molecules, respectively. In this context, a larger σ-hole was denoted for the XeF₄O molecule rather than the IF₅ candidate, outlining an elevated potency for the former molecule to engage in favorable interactions via σ-hole site compared to the latter one. In coincidence with the MEP claims, the paramount V_s,max values were evaluated, showing values up to 63.7 and 71.5 kcal mol⁻¹ for IF₅ and XeF₄O molecules, respectively.

Regarding the studied LBs, the surface of the N atom within the NH₃ and NCH molecules was decorated with red negative sites with V_s,min values of −44.1 and −36.0 kcal mol⁻¹, respectively. Moreover, the entity of X⁻ was entirely covered with red color as a result of its full negative charge. It was also noted that the extent of anions' charge was discerned to diminish by increasing their atomic size, giving V_s,min values amounting to −183.1, −151.0, −142.1, and −130.1 kcal mol⁻¹ for F⁻, Cl⁻, Br⁻, and I⁻, respectively. Comparatively, the X⁻ anions were detected with a higher discriminatory nucleophilic nature over the inspected LBs.

ELF analysis

ELF analysis provides a topological framework illustrating the localized electron density regions in atoms and molecules, with the objective of elucidating the chemical reactivity of chemical systems.^64,65 Accordingly, the ELF maps were generated for the studied LB and X⁻ and are displayed in Fig. 3.

Fig. 3 ELF maps of the studied LBs and X⁻. The red (ELF = 1) and blue (ELF = 0) show the localized and delocalized electron density regions, respectively. The coordinates are expressed in bohr.

From Fig. 3, a red lobe (i.e., free lone pair basin) was observed over the NH₃ and NCH molecules. The tight and compact nature of this basin indicated the confinement of the lone pair electrons owing to the elevated electronegativity character of the N atom. Turning to the studied X⁻, the ELF map of F⁻ demonstrated a small and dense red region near the nucleus surrounded by tightly packed rings, pinpointing the highly localized core electrons and compact free electron pair basins. These findings outlined the high Lewis basicity character of the F⁻. Notably, the red regions were found to expand radially outward, and the ELF basins became broader on going from Cl⁻ to Br⁻ and I⁻, indicating the retreating of Lewis basicity character.

PoC calculations

Towards more illustration of the propensity of the studied chemical systems (i.e., IF₅ and XeF₄O) to electrostatically form noncovalent interactions, the PoC approach was implemented.⁶⁶ In PoC context, negatively-charged PoC with values of −0.25, −0.50, −0.75, and −1.00 a.u. were used to imitate the Lewis basicity effect on the studied interactions.⁵¹ The molecular stabilization energy curves of the IF₅⋯ and XeF₄O⋯PoC systems were created and are portrayed in Fig. 4, and their E_{stabilization} at I/Xe⋯PoC distance of 2.5 Å are gathered in Table 1.

Fig. 4 Molecular stabilization energy curves of the IF₅⋯ and XeF₄O⋯PoC systems.

Table 1 E_{stabilization} of IF₅⋯ and XeF₄O⋯PoC systems at I/Xe⋯PoC distance of 2.5 Å

Systems	Molecular stabilization energy (kcal mol^−1)
	PoC = −0.25 a.u.	PoC = −0.50 a.u.	PoC = −0.75 a.u.	PoC = −1.00 a.u.
IF5⋯PoC	−11.31	−25.13	−41.17	−59.22
XeF4O⋯PoC	−12.30	−26.82	−43.33	−61.70

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As evident in Fig. 4, a significant potency for the IF₅ and XeF₄O molecules to engage in favorable interactions via σ-hole site was detected by obtaining negative E_{stabilization} values for all IF₅ and XeF₄O molecules in the presence of negative PoC. Further, E_{stabilization} curves were noted to augment simultaneously with the negativity of PoC, showing the proficient role of the nucleophilicity in the favorability of the noncovalent interactions. Further, the E_{stabilization} was detected to decrease by increasing the I/Xe⋯PoC distance.

The collected data in Table 1 demonstrated that a considerable increment of E_{stabilization} was harmonically in line with elevating the negative PoC values. For example, E_{stabilization} values for IF₅⋯PoC systems were −11.31, −25.13, −41.17, and −59.22 kcal mol⁻¹ with PoCs of −0.25, −0.50, −0.75, and −1.00 a.u., respectively. Obviously, a direct correlation was observed between EP claims and PoC ones. Evidently, more preferential E_{stabilization} outcomes were disclosed for the IF₅⋯PoC systems compared to the XeF₄O⋯PoC candidates. For instance, in the being of PoC = −0.25 a.u., E_{stabilization} was disclosed to be −11.31 and −12.30 kcal mol⁻¹ for IF₅⋯ and XeF₄O⋯PoC systems along with V_s,max of 63.7 and 71.5 kcal mol⁻¹ for IF₅ and XeF₄O molecules, respectively.

Geometrical structure and stability

Interactions of IF₅ and XeF₄O molecules via σ-hole site with LBs and X⁻ were investigated. The optimized structures of IF₅⋯ and XeF₄O⋯LB/X⁻ complexes are portrayed in Fig. 5, and their related E_bind, E_int, E_def, and E_CCSD(T)/CBS are included in Table 2.

Fig. 5 Structures of the optimized IF₅⋯ and XeF₄O⋯LB/X⁻ complexes accompanied by their F–I and O–Xe intra (d₁)- and I/Xe⋯LB/X⁻ inter (d₂)-molecular distances in Å.

Table 2 Complexation parameters of the optimized IF₅⋯ and XeF₄O⋯LB/X⁻ complexes. Energies, distances, and angles are in kcal mol⁻¹, Å, and °, respectively

Complexes	Distances		∑rvdW^c	∑rcovalent^c	Angle	Energies
	d1^a	d2^b				Ebind	Eint	ECCSD(T)/CBS	Edef
a d1 represents the F–I and O–Xe intra-molecular distances that are equal to 1.83 and 1.71 Å for the isolated systems, respectively.b d2 represents the I/Xe⋯LB/X^− inter-molecular distance.c ∑rvdW and ∑rcovalent represent the sum of van der Waals and covalent radii of the interacting atoms, respectively.
IF5⋯NH3	1.84	2.92	3.53	2.08	141.43	−8.87	−9.30	−10.28	0.43
IF5⋯NCH	1.83	3.19	3.53	2.08	179.99	−5.53	−5.65	−6.00	0.12
[IF6]^−	1.99	1.99	3.45	2.04	179.99	−64.72	−91.02	−94.76	26.30
IF5⋯Cl^−	1.90	2.67	3.73	2.39	180.00	−35.46	−45.05	−47.00	9.59
IF5⋯Br^−	1.90	2.83	3.83	2.61	180.00	−33.59	−40.37	−42.11	6.78
IF5⋯I^−	1.89	3.10	3.96	2.80	180.00	−28.21	−33.64	−35.41	5.43
XeF4O⋯NH3	1.71	2.83	3.71	2.18	179.95	−11.42	−12.06	−11.97	0.64
XeF4O⋯NCH	1.71	2.94	3.71	2.18	179.87	−7.89	−8.04	−7.75	0.15
[XeF5O]^−	1.76	2.08	3.63	2.14	179.99	−65.89	−74.21	−72.26	8.32
XeF4O⋯Cl^−	1.74	2.68	3.91	2.49	179.99	−40.59	−44.57	−43.33	3.98
XeF4O⋯Br^−	1.74	2.84	4.01	2.71	179.99	−36.19	−39.94	−38.77	3.75
XeF4O⋯I^−	1.74	3.09	4.14	2.90	179.99	−30.43	−33.65	−33.02	3.22

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As evident in Fig. 5, optimized structures were obtained for all complexes, indicating the potency of the IF₅ and XeF₄O molecules within the square pyramidal geometry to interact favorably via σ-hole site with the studied LBs and X⁻. The inspected interactions were characterized with a highly directional character where all F–I⋯N and O–Xe⋯N angles within the optimized complexes were nearly equal to 180°, except for IF₅⋯NH₃ one. The F–I⋯N angle within the IF₅⋯NH₃ complex was identified to be nearly 141.43°, which was in synchronic with the previous reports.³⁷

From Table 2, a boosting in the F–I and O–Xe intra-molecular distances (d₁) was uncovered after the interaction of IF₅ and XeF₄O molecules with X⁻. In contrast, negligible changes in the d₁ were found in the case of interactions with LBs. With respect to the inter-molecular distances (d₂), they were found to be shorter and longer than the sum of the vdW and covalent radii, respectively (Table 2).

Regarding IF₅⋯ and XeF₄O⋯LB complexes, negative E_int and E_bind values were denoted with higher preferentiality for the latter complexes rather than the former candidates, indicating the occurrence of favorable interactions between the interacting species (Table 2). Notably, the energetic features were in line with the EP upshots. Illustratively, E_bind/E_int values were −11.42/−12.06 and −8.87/−9.30 kcal mol⁻¹ for IF₅⋯ and XeF₄O⋯NH₃ complexes, accompanied by V_s,max values of 63.7 and 71.5 kcal mol⁻¹ for IF₅ and XeF₄O molecules, respectively. Moreover, negligible geometrical deformation was denoted for all IF₅⋯ and XeF₄O⋯LB complexes where E_def values were aligned in the range from 0.12 to 0.64 kcal mol⁻¹.

Turning to IF₅⋯ and XeF₄O⋯X⁻ complexes, a direct correlation was noted between the E_bind/E_int upshots and the V_s,max claims. Clearly, more negative E_bind values were disclosed for XeF₄O⋯X⁻ complexes than the IF₅⋯X⁻ complexes, while higher negative E_int values were observed in the case of the latter complexes than the former one. For instance, E_bind and E_int were computed to be −35.46/−40.59 and −45.05/−44.57 kcal mol⁻¹ for IF₅/XeF₄O⋯Cl⁻ complexes, accompanied by V_s,max values of 63.7 and 71.5 kcal mol⁻¹ for IF₅ and XeF₄O molecules, respectively. This finding could be explained by observing higher deformation energies in the case of IF₅⋯X⁻ complexes (E_def = 5.43–26.30 kcal mol⁻¹) than the XeF₄O⋯X⁻ candidates (E_def = 3.22–8.32 kcal mol⁻¹). Generally, the considerable E_bind and E_int relevant to the IF₅/XeF₄O⋯X⁻ complexes declared the formation of coordinative covalent bonds, as previously documented.³⁵ It is worth mentioning that the extremely high E_bind/E_int of the IF₅⋯ and XeF₄O⋯F⁻ complexes uncovered the formation of I–F⁻ and Xe–F⁻ covalent bonds and hence the [IF₆]⁻ and [XeF₅O]⁻ molecules were obtained.

Notably, a direct correlation between MP2 energies of IF₅⋯ and XeF₄O⋯LB/X⁻ complexes and the nucleophilicity of the studied LBs. The E_bind and E_int values were denoted to increase with increasing nucleophilicity of the studied LBs as follows: IF₅/XeF₄O⋯NCH < ⋯NH₃ < ⋯I⁻ < ⋯Br⁻ < ⋯Cl⁻ < ⋯F⁻ complexes. This finding could be explained due to increasing the attractive forces between the positive regions relevant to the IF₅/XeF₄O molecules (i.e., σ-hole site) and the negative portions of the studied LBs and X⁻. For example, E_int values of IF₅⋯Cl⁻, ⋯Br⁻, ⋯I⁻, ⋯NH₃ and ⋯NCH complexes were −45.05, −40.37, −33.64, −9.30 and −5.65 kcal mol⁻¹ along with V_s,min values of −183.1 and −151.0, −142.1, −130.1, −44.1, −36.0 kcal mol⁻¹ for F⁻, Cl⁻, Br⁻, I⁻, NH₃, and NCH molecules. Clearly, this observation was also in coincidence with the PoC claims (Table 1/Fig. 2).

Noteworthy, the energetic results at the CCSD(T)/CBS level of theory showed similar trends with the outcomes related to the MP2/aug-cc-PVTZ(PP) counterparts. For instance, E_CCSD(T)/CBS values were −47.00 and −43.33 kcal mol⁻¹, along with E_bind/E_int of −35.46/−45.05 and −40.59/−44.57 kcal mol⁻¹ for IF₅⋯ and XeF₄O⋯Cl⁻ complexes, respectively.

QTAIM analysis

Quantum theory of atoms in molecules (QTAIM), established by Bader et al.,⁵⁷ is regarded as a reliable method for providing comprehensive insights into the nature of intermolecular interactions.⁶⁷ Therefore, QTAIM analysis was herein conducted for IF₅⋯LB/X⁻ and XeF₄O⋯LB/X⁻ containing complexes. Fig. 6 delineates the QTAIM portrays of IF₅⋯ and XeF₄O⋯LB/X⁻ complexes, and Table 3 lists the relevant topological parameters along the corresponding bond paths and bond critical points.

Fig. 6 QTAIM scheme of the optimized IF₅⋯ and XeF₄O⋯LB/X⁻ complexes.

Table 3 The QTAIM parameters of the optimized IF₅⋯ and XeF₄O⋯LB/X⁻ complexes

Complex	ρb	∇^2ρb	Hb	Gb	Vb	−Gb/Vb
IF5⋯NH3	0.0244	0.0610	−0.0001	0.0154	−0.0155	0.9914
IF5⋯NCH	0.0140	0.0445	0.0016	0.0095	−0.0078	1.2081
[IF6]^−	0.1235	0.2859	−0.0615	0.1329	−0.1944	0.6838
IF5⋯Cl^−	0.0578	0.0868	−0.0137	0.0354	−0.0492	0.7207
IF5⋯Br^−	0.0504	0.0698	−0.0100	0.0275	−0.0375	0.7324
IF5⋯I^−	0.0398	0.0489	−0.0064	0.0187	−0.0251	0.7435
XeF4O⋯NH3	0.0317	0.0807	−0.0012	0.0214	−0.0226	0.9459
XeF4O⋯NCH	0.0216	0.0705	0.0014	0.0163	−0.0149	1.0916
[XeF5O]^−	0.1090	0.2578	−0.0458	0.1206	−0.1855	0.6501
XeF4O⋯Cl^−	0.0577	0.1000	−0.0127	0.0377	−0.0503	0.7483
XeF4O⋯Br^−	0.1348	0.2292	−0.0751	0.1324	−0.2075	0.6381
XeF4O⋯I^−	0.0407	0.0526	−0.0068	0.1345	−0.2114	0.6364

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As manifested in Fig. 6, single BCP and BP within the optimized IF₅⋯ and XeF₄O⋯LB/X⁻ complexes were observed, which in turn confirmed the occurrence of attractive interactions between the interacting species. Clearly, for IF₅/XeF₄O⋯LB complexes, more positive ρ_b and ∇²ρ_b along with more negative H_b and V_b values were recorded when LB = NH₃ compared to NCH. Moreover, values of −G_b/V_b were found to be lower and higher than unity for the IF₅/XeF₄O⋯NH₃ and ⋯NCH complexes (Table 3), respectively. These findings announced the open- and closed-shell nature of the studied interactions within the IF₅/XeF₄O⋯NH₃ and ⋯NCH complexes, respectively. Illustratively, ρ_b, ∇²ρ_b, H_b, V_b, and −G_b/V_b values of XeF₄O⋯NH₃/NCH complexes were 0.0317/0.0216, 0.0807/0705, −0.0012/0.0014, −0.0226/−0.0149, and 0.9459/1.0916 a.u., respectively. Accordingly, among the investigated complexes, only IF₅⋯ and XeF₄O⋯NCH complexes exhibited true halogen and aerogen bonds, respectively.

With respect to IF₅⋯ and XeF₄O⋯X⁻ complexes, the topological parameters generally demonstrated an increase in the coordinative covalent nature of the studied interactions on going from X⁻ = I⁻ to Br⁻, Cl⁻, and F⁻ due to the following annotations: more negative values of H_b and V_b along with more positive ρ_b and ∇²ρ_b values whereas the −G_b/V_b were found to be less than unity. For example, the ρ_b, ∇²ρ_b, H_b, V_b, and −G_b/V_b values of IF₅⋯Br⁻/Cl⁻ were 0.0504/0.0578, 0.0698/0.0868, −0.0100/−0.0137, −0.0375/0.0492, and 0.7324/0.7207 a.u., respectively.

Generally, all the topological parameters coincided with the energetic patterns for all the complexes under investigation. Illustratively, the topological parameters outlined the preference of the IF₅/XeF₄O⋯X⁻ complexes over the IF₅/XeF₄O⋯LBs candidates, which was in synchronic with the energetic findings. For instance, ρ_b values were 0.0244/0.1235 and 0.0317/0.1090 a.u. accompanied by E_int of −9.30/−91.02 and −12.06/−74.21 kcal mol⁻¹ for IF₅⋯ and XeF₄O⋯NH₃/F⁻ complexes, respectively.

NCI-RDG analysis

The NCI-RDG index is documented as a punctilious tool to delicately indicate the nature of intermolecular interactions.⁵⁸ Fig. 7 shows the 2D and 3D NCI plots for the optimized IF₅⋯ and XeF₄O⋯LB/X⁻ complexes. In 3D NCI plots, the color scale of the isosurfaces ranged from green (i.e., noncovalent nature) to the blue (i.e., covalent nature).

Fig. 7 2D and 3D NCI diagrams for the optimized IF₅⋯ and XeF₄O⋯LB/X⁻ complexes depending on the sign (λ₂)ρ.

With respect to the studied complexes, all spikes in the RDG plots were shifted towards a more negative (λ₂)ρ sign (i.e., broader), along with ameliorating the interaction energies (Fig. 7). For example, in the case of IF₅/XeF₄O⋯X⁻ complexes, spikes became broader on going from X⁻ = I⁻, to Br⁻, Cl⁻, and F⁻. Regarding the 3D NCI plots, the appearance of green-coded surfaces within the IF₅/XeF₄O⋯NCH complexes outlined the noncovalent character of the investigated interactions. While in the case of the IF₅/XeF₄O⋯NH₃ complexes, green-bluish surfaces were noticed, announcing the partial covalent nature of the emerging interactions. Besides, for the IF₅⋯NH₃ complex, green isosurface was also observed between the F atom of IF₅ and the H atom of NH₃, announcing the role of F⋯H attractive interactions in stabilizing the IF₅⋯NH₃ complex. On the other side, a blue isosurface region was recorded within the IF₅⋯ and XeF₄O⋯X⁻ complexes, pinpointing the existence of maximal attractive forces (i.e., coordinative covalent nature) between the interacting molecules.

Remarkably, QTAIM and NCI upshots were significantly consistent with the energy upshots, clarifying the potency of the considered molecules to form varied-in-strength interactions via σ-hole site depending on the nature of the nucleophilic system.

SAPT calculations

SAPT method was herein employed to energetically elaborate the forces that contribute to the inter-molecular interactions within the optimized IF₅⋯ and XeF₄O⋯LB/X⁻ complexes.⁶⁸ Table 4 illustrates the attractive and repulsive energetic components along with the total SAPT2+(3)dMP2 energy for optimized IF₅⋯ and XeF₄O⋯LB/X⁻ complexes.

Table 4 E_elst, E_ind, E_disp, E_exch, and E_{SAPT2+(3)dMP2} along with the energy difference (ΔΔE) between the MP2 and SAPT2+(3)dMP2 energies of the optimized IF₅⋯ and XeF₄O⋯LB/X⁻ complexes. All energies are in kcal mol⁻¹

Complex	Eelst	Eind	Edisp	Eexch	ESAPT2+(3)dMP2^a	ΔΔE^b
a ESAPT2+(3)dMP2 = Eind + Eexch + Eelst + Edisp.b ΔΔE = EMP2/aug-cc-pVTZ(PP) − ESAPT2+(3)dMP2.
IF5⋯NH3	−18.92	−5.54	−6.42	21.15	−9.98	−0.68
IF5⋯NCH	−7.87	−1.91	−3.02	7.12	−5.68	−0.03
[IF6]^−	−158.25	−118.45	−24.63	204.26	−97.07	−6.05
IF5⋯Cl^−	−73.45	−42.74	−15.00	84.63	−46.55	−1.50
IF5⋯Br^−	−62.67	−38.64	−14.61	73.84	−42.09	−1.72
IF5⋯I^−	−50.69	−30.69	−13.19	59.49	−35.09	−1.45
XeF4O⋯NH3	−22.91	−8.14	−6.81	25.54	−12.32	−0.26
XeF4O⋯NCH	−11.71	−3.69	−4.74	12.17	−7.98	0.06
[XeF5O]^−	−131.70	−84.42	−20.80	157.14	−79.79	−5.58
XeF4O⋯Cl^−	−69.83	−39.23	−15.26	77.74	−46.58	−2.01
XeF4O⋯Br^−	−60.76	−35.89	−15.10	69.78	−41.97	−2.03
XeF4O⋯I^−	−50.27	−29.80	−14.15	58.85	−35.37	−1.72

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Among all the attractive energetic forces, the E_elst was observed as the dominant component for all optimized complexes, as demonstrated in Fig. 8. The E_disp and E_ind were denoted with different contributions within all IF₅/XeF₄O⋯LB and ⋯X⁻ complexes. This observation outlined the attractive nature of such forces and hence their contributions in stabilizing the investigated complexes. On the other hand, positive values of E_exch proclaimed the repulsive nature of such forces. For instance, E_elst, E_ind, E_disp, and E_exch were −73.45, −42.74, −15.00, and 84.63 kcal mol⁻¹.

Fig. 8 Bar chart of SAPT energetic component for the optimized IF₅⋯ and XeF₄O⋯LB/X⁻ complexes.

According to data tabulated in Table 4, negative values for the E_elst/E_disp/E_ind components were disclosed, unveiling their attractive nature. On the other hand, unfavorable positive E_exch values were found for all complexes, pinpointing the repulsive nature of E_exch. Among the attractive forces, the electrostatics were the predominant attractive forces within all the IF₅⋯ and XeF₄O⋯LB/X⁻ complexes. Generally, the attractive energetic components for IF₅⋯ and XeF₄O⋯LB complexes were ordered as follows: E_ind < E_disp < E_elst. For instance, E_elst, E_disp, and E_ind values were −18.92, −6.42, and −5.54 kcal mol⁻¹ for IF₅⋯NH₃ complex. For the IF₅/XeF₄O⋯X⁻ complexes, the attractive forces were denoted to increase in the following E_disp < E_ind < E_elst sequence. For example, E_elst, E_ind, and E_disp were −69.83, −39.23, and −15.26 kcal mol⁻¹ for XeF₄O⋯Cl⁻ complex, respectively. Basically, the variation in the trends relevant to the attractive forces could be attributed to the high ability of X⁻ compared to the LBs to polarize the σ-hole of IF₅/XeF₄O molecules more favorably.^51,69

Clearly, great compatibility between SAPT-based results and MP2 energy-based counterparts. Illustratively, for XeF₄O⋯X⁻ complexes, the negative E_elst, E_ind, and E_disp values were observed to increase on going from X⁻ = I⁻ < Br⁻ < Cl⁻ < F⁻. For instance, E_elst/E_ind/E_disp of XeF₄O⋯I⁻, ⋯Br⁻, ⋯Cl⁻, and ⋯F⁻ complexes were −50.27/−29.80/−14.15, −60.76/−35.89/−15.10, −69.83/−39.23/−15.26, and −131.70/−84.24/−20.80 kcal mol⁻¹, respectively. Moreover, SAPT results were in agreement with the QTAIM and NCI claims. Evidently, the coordinative covalent nature of the IF₅⋯ and XeF₄O⋯X⁻ complexes was also confirmed by observing significant negative E_elst, E_ind, and E_disp values. Overall, the low values of ΔΔE ensured the reliability of the selected SAPT level (Table 4).

Conclusion

The tendency of the hypervalent IF₅ and XeF₄O molecules within the square pyramidal geometry to interact via σ-hole site with Lewis bases (LB = NH₃ and NCH) and anions (X⁻ = F⁻, Cl⁻, Br⁻, and I⁻) was inspected. For all IF₅⋯ and XeF₄O⋯LB/X⁻ complexes, significant interaction and binding (i.e., E_int and E_bind, respectively) energies were detected in the range from −5.65 to −91.02 kcal mol⁻¹ and from −5.53 to −65.89 kcal mol⁻¹, respectively. Clearly, more negative E_int and E_bind values for the XeF₄O⋯LB complexes were noticed compared to the IF₅⋯LB candidates, outlining the preferentiality of the former complexes over the latter ones. In addition, all IF₅⋯ and XeF₄O⋯LB complexes were characterized by meager deformation energies. Regarding IF₅⋯ and XeF₄O⋯X⁻ complexes, E_bind declared that the anterior complexes were more favorable than posterior candidates, whereas the vice versa observations were noted in the case of E_int values. This annotation could be explained as an upshot of the significant deformation energies in the 5.43–26.30 kcal mol⁻¹ energetic ambit for the IF₅⋯X⁻ complexes versus 3.22–8.32 kcal mol⁻¹ one for the XeF₄O⋯X⁻ counterparts. Moreover, the energy features were noted to increase in line with the Lewis basicity strength as follows: IF₅/XeF₄O⋯NCH < ⋯NH₃ < ⋯I⁻ < ⋯Br⁻ < ⋯Cl⁻ < ⋯F⁻ complexes. QTAIM and NCI results announced that the interactions between the IF₅/XeF₄O molecules via σ-hole site with the NH₃ and NCH were characterized with the open- and closed-shell nature, respectively. In comparison, the IF₅/XeF₄O⋯X⁻ complexes were generally characterized by the coordinative covalent nature. SAPT upshots outlined that the driving force behind the occurrence of the inspected interactions was the electrostatic one. These results will help facilitate the comprehension of the investigated interactions and pave the way for several future applications in material science and crystal engineering fields.

Author contributions

Mahmoud A. A. Ibrahim: conceptualization, methodology, software, resources, project administration, supervision, writing—review and editing. Asmaa M. M. Mahmoud: data curation, formal analysis, investigation, visualization, writing—original draft. Rehab R. A. Saeed: methodology, investigation, project administration, writing—review and editing. Mohammed N. I. Shehata: methodology, investigation, project administration, writing—review and editing. Tamer Shoeib: software, resources, writing—review and editing. Jabir H. Al-Fahemi: resources, project administration, writing—review and editing.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

The data supporting this article have been included as part of the SI. See DOI: https://doi.org/10.1039/d5ra04648c.

Acknowledgements

The authors extend their appreciation to Umm Al-Qura University, Saudi Arabia for funding this research work through grant number: 25UQU4200274GSSR04.

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