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. 2020 Aug 19;5(34):21631–21640. doi: 10.1021/acsomega.0c02362

σ-Hole and Lone-Pair Hole Interactions in Chalcogen-Containing Complexes: A Comparative Study

Mahmoud A A Ibrahim 1,*, Ebtisam M Z Telb 1
PMCID: PMC7469375  PMID: 32905338

Abstract

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The potentiality of sp3-hybridized chalcogen-containing molecules to participate in lone-pair (lp) hole interactions was reported for the first time. lp hole interactions were characterized and compared to σ-hole ones for OF2 and SF2 molecules as a case study. Various quantum mechanical calculations, including molecular electrostatic potential (MEP), maximum positive electrostatic potential (Vs,max), point of charge (PoC), symmetry-adapted perturbation theory (SAPT), quantum theory of atoms in molecule (QTAIM), and reduced density gradient–noncovalent interaction (RDG-NCI) calculations, were carried out. The more significant findings to emerge from this study are the following: (i) the Vs,max calculation was proved to be an unreliable method to determine the precise σ-hole and lp hole locations. (ii) The maximum positive electrostatic potential of the σ hole and lp hole was found to be at the F–Chal···PoC angle (θ) of 180° and at the centroid of XYlp plane, respectively. (iii) Lewis basicity has a significant effect on the strength of σ-hole and lp hole interactions. (iv) The studied molecules more favorably interact with Lewis bases via the σ hole compared to the lp hole, and (v) stabilization of the σ-hole and lp hole interactions stems from the electrostatic and dispersion forces, respectively.

1. Introduction

Recently, the nature and characteristics of σ-hole interactions have become the center of attraction among experimentalists and theoreticians.1−8 A σ-hole refers to an electron-deficient outer lope of a p orbital that consequently results in forming a positive or less negative region along the extension of the covalently bonded group IV–VII elements.5−7 Therefore, the covalently bonded group IV–VII elements can act as Lewis acids via the σ-hole and, in turn, interact with Lewis bases forming tetrel,9−13 pnicogen,14−16 chalcogen,17−22 and halogen bonds.23−26

Among these noncovalent interactions, the chalcogen bond in sp2- and sp3-hybridized chalcogen-containing molecules has attracted immense interest due to its significant role in crystal engineering and protein–ligand interactions.27−29 In addition to the chalcogen bond, chalcogen-containing molecules can act as an electron donor as a result of the occurrence of two lone pairs (lp’s) on the chalcogen atom (Chal).30−33

Very recently, an enthralling study argued the ability of chalcogen-containing molecules in trigonal pyramidal geometry to form an unconventional type of noncovalent interaction called an lp hole interaction.34 This type of interaction was exposed as a result of the presence of a positive electrostatic region opposite to the lp (termed lp hole). According to their findings, for instance, the lp hole interaction energy was observed with a notable value of −2.03 kcal/mol for the SF2O···F– complex. Taking the role of hybridization into account, a question arises as to whether there is any potentiality for sp3-hybridized chalcogen-containing molecules (ChalX2) to act as Lewis acids via the lp hole and interact with Lewis bases.

Accordingly, the aim of the current study is to (i) assess the occurrence of lp hole interactions and (ii) compare the strength and nature of lp hole interactions with σ-hole interactions in ChalX2···Lewis base complexes. An lp–Chal–XYlp···B nomenclature will be proposed to describe the lp hole interaction in sp3-hybridized chalcogen-containing molecules where XY are two atoms on the same side of the lp-hole and B is a Lewis base. The σ-hole and lp hole interactions will first be investigated from the electrostatic perspective via the point-of-charge (PoC) approach.12,13,18,34,35 In addition, the PoC approach will be utilized to precisely define lp, lp hole, and σ-hole locations. Moreover, the Lewis basicity effect on the strength of the σ-hole and lp hole interactions will be also examined. All PoC-based results will be validated in ChalF2···F– complexes. To provide an insight into the nature and characteristics of σ-hole and lp-hole interactions, the results of the symmetry-adapted perturbation theory (SAPT), quantum theory of atoms in molecules (QTAIM), and the reduced density gradient–noncovalent interaction (RDG-NCI) will be analyzed. The emerging findings from the current study provide a base for future studies concerning the interactions of sp3-hybridized chalcogen-containing molecules with Lewis bases.

2. Computational Methods

To characterize σ-hole and lp hole interactions of sp3-hybridized chalcogen-containing molecules in bent molecular geometry, quantum mechanical calculations were performed on two molecular systems, namely, OF2 and SF2. The investigated molecules were first optimized at the MP2/aug-cc-pVTZ level of theory.36−38 Upon the optimized geometries, molecular electrostatic potential (MEP) maps were generated and then mapped on 0.002 au electron density contours as previously recommended where the 0.001 au isodensity envelope may provide incorrect information about the complete nature of the surface reactive sites.7,39 Moreover, the maximum positive electrostatic potential (Vs,max) values at the σ-hole and lp hole were estimated using Multiwfn3.5 software.40

To achieve the purpose of the study, the σ-hole and lp hole locations on the molecular surfaces were precisely determined with the help of the point-of-charge (PoC) approach. For the lp hole location, positions of the two lp’s on the chalcogen atom were first located by scanning the van der Waals (vdW) surface of the chalcogen atom by −0.01 au PoC with an increment angle value of 2.5° (see Figure 1i). The vdW radii of oxygen and sulfur atoms were set to 1.52 and 1.80 Å, respectively.

Figure 1.

Figure 1

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Schematic representation of implemented PoC-based calculations employed for investigation of (a) σ-hole and (b) lp hole interactions.

To determine the σ-hole and lp hole locations, the studied molecules were aligned to the x axis and the YZ plane was then scanned by −0.01 au PoC with a step size of 0.1 Å. The PoC was placed at a distance of 2.0 Å from the chalcogen atom and moved along both y and zdirections in the range from 1.6 to −1.6 Å, generating 2D molecular stabilization energy surfaces (see Figure 1ii).

The effect of the Lewis basicity on the σ-hole and lp hole interactions was investigated using the PoC approach.12,13,18,34,35 In the PoC approach, different degrees of negatively charged points stimulating Lewis bases were used to inspect the potentiality of the studied molecules to electrostatically interact with Lewis bases. The studied molecules were first optimized in the presence of −0.10, −0.25, −0.50, and −1.00 au PoC values, and the Chal···PoC distance effect on the strength of interactions was then determined in the range of 2.5–5.0 Å from the chalcogen atom (see Figure 1iii). The value of the employed PoC to investigate the Chal···PoC distance effect was made equal to the one used in optimization. The strength of the σ-hole and lp hole interactions was estimated in terms of the molecular stabilization energy (Establization) according to the following equation:12,13,18,34,35

2.

To validate the PoC-based results, the negative PoC was replaced with a fluoride ion (F–) and the corresponding interaction energy curves were generated. Furthermore, full geometrical optimization was performed for OF2··· and SF2···N2/NCH complexes and the interaction energies were then estimated at the MP2/aug-cc-pVTZ level of theory. The frozen-core (FC) approximation was adopted for all MP2 calculations. Vibrational frequency calculations were not performed for the optimized complexes; thus, there was a possibility that the structures were not energetic minima. The counterpoise procedures were considered to correct the interaction energy for the basis set superposition error (BSSE).41 Moreover, the interaction energies were computed for the optimized complexes at the CCSD(T)/CBS level of theory. The CCSD(T)/CBS energies were constructed based on the following equation:42

2.

where

2.
2.

To inspect the physical nature of the σ-hole and lp hole interactions in the optimized complexes, the symmetry-adapted perturbation theory-based energy decomposition analysis (SAPT-EDA) was performed using the PSI4 code.43,44 This method furnishes a separation of interaction energies into four physically meaningful components, such as those arising from electrostatics (Eelst), exchange (Eexch), induction (Eind), and dispersion (Edisp). The interaction energies were estimated at one of the truncations of SAPT, denoted as SAPT2 + (CCD)δMP2,45−47 given as follows:

2.

where

2.
2.
2.
2.

Moreover, the topological properties of electron density and its derivatives were investigated using the quantum theory of atoms in molecules (QTAIM) to explore the nature of the studied noncovalent interactions.48−50 The bond critical points (BCPs) and the bond paths (BPs) were depicted for all complexes discussed herein. Reduced density gradient–noncovalent interaction (RDG-NCI) indices were also analyzed for the investigated complexes and the NCI plots were generated.51 The gradient isosurfaces are colored on the blue-green-red (BGR) scale where blue surfaces signify strong attractions, green surfaces show weak interactions, and red surfaces imply strong repulsions. The coloring scale of electron density (ρ) was from −0.035 (blue) to 0.020 (red) au. The QTAIM and RDG-NCI analyses were performed using Multiwfn3.5 software and then visualized by VMD1.9.2 software.52 All quantum-mechanical calculations were performed at the same level of geometrical optimization using Gaussian09 software.53

3. Results and Discussion

3.1. MEP and Vs,max Calculations

A molecular electrostatic potential (MEP) map is a widely used index for molecular charge distribution in three-dimensions.54 MEP maps were therefore generated for the investigated sp3-hybridized chalcogen-containing molecules to illustrate the occurrence of σ-hole and lp hole regions. The MEP maps were supplemented by estimating the Vs,max values at the σ-hole and lp hole using Multiwfn3.5 software. The generated MEP maps and the estimated Vs,max values for the studied molecules are depicted in Figure 2.

Figure 2.

Figure 2

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Molecular electrostatic potential (MEP) maps of the investigated OF2 and SF2 molecules plotted at 0.002 au electron density contours. The electrostatic potentials vary from −0.01 au (red) to 0.01 au (blue). The calculated maximum positive electrostatic potential (Vs,max, kcal/mol) at the σ-hole and lp hole is also shown.

According to the data presented in Figure 2, variable-in-size σ-holes were observed along the Chal–F bond extensions in the studied molecules. The size of the σ-hole was increased from lighter to heavier chalcogen atoms. The Vs,max values at the σ-hole were found to be 23.3 and 49.3 kcal/mol for OF2 and SF2 molecules, respectively. Moreover, a positive region opposite to the lp (i.e., lp-hole) was observed in all investigated molecules. The magnitude of Vs,max at the lp hole increased in the order of S > O with values of 15.4 and 8.9 kcal/mol for SF2 and OF2 molecules, respectively. Comparing these results, it was noted that the Vs,max values at the σ-hole were larger compared to the ones at the lp hole. Overall, the sp3-hybridized chalcogen-containing molecules may have the potentiality to participate in noncovalent interactions with Lewis bases via both the σ-hole and lp hole.

3.2. σ-Hole and lp Hole Locations

Generally, it has been established from a variety of studies that the chalcogen bond angle (i.e. A–Chal···B bond angle, θ) can range from 160° to 180°.17,55,56 To determine the precise σ-hole location, 2D molecular stabilization energy surfaces were generated for the studied molecules using a PoC value of −0.01 au. The generated 2D molecular stabilization energy surfaces are illustrated in Figure 3i.

Figure 3.

Figure 3

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Generated 2D-molecular stabilization energy surfaces for the investigated (a) OF2 and (b) SF2 molecules in the presence of −0.01 au PoC at a Chal···PoC distance of 2.0 Å along the x axis for determining (i) σ-hole and (ii) lp hole locations (see the Computational Methods section for details).

Based on the results presented in Figure 3i, the largest molecular stabilization energies were observed at a F–Chal···PoC angle (θ) of 180°. According to Vs,max calculations, the Vs,max of the σ-hole was observed at angles of 179° and 170° for OF2 and SF2 molecules, respectively. Thence, it may be claimed that Vs,max calculations are an unreliable method in determining the σ-hole location of the maximum positive electrostatic potential.

Similar to the σ-hole, the precise location of the lp hole remains to be determined. However, the lp location on the chalcogen atoms must be first detected. To tackle this issue, the vdW surfaces of the chalcogen atoms in the studied molecules were scanned by a −0.01 au PoC, generating 3D molecular stabilization energy surfaces (Figure 4).

Figure 4.

Figure 4

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Generated 3D molecular stabilization energy surfaces for the investigated (i) OF2 and (ii) SF2 molecules by employing −0.01 au PoC.

According to the obtained results in Figure 4, the lp was observed at a F–Chal···PoC angle (θ) of 101.10° and 99.75° with the lowest molecular stabilization energies of −0.26 and 0.04 kcal/mol for OF2 and SF2 molecules, respectively.

Based on the defined lp location, the maximum positive electrostatic potential of the lp-hole was then accurately determined by generating the 2D molecular stabilization energy surfaces using the PoC approach (Figure 3ii).

As can be seen from the data in Figure 3ii, the largest molecular stabilization energies were noted at the centroid of the XYlp plane. These results are in good accordance with previous work in which the optimum location of the lp hole was found to be at the centroid of the XYZ plane in the covalently bonded group V–VIII elements.34

3.3. σ-Hole and lp Hole Interactions

3.3.1. Lewis Basicity Effect

In this study, the Lewis basicity effect on the strength of σ-hole and lp hole interactions was investigated with the help of the PoC approach. For both σ-hole and lp hole interactions, the Chal···PoC distance effect was examined in a range of 2.5–5.0 Å and the corresponding stabilization energies were calculated. The molecular stabilization energy curves are illustrated in Figure 5, and Table 1 lists the values of molecular stabilization energies at a Chal···PoC distance of 2.5 Å.

Figure 5.

Figure 5

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Generated molecular stabilization energy curves for the investigated (a) OF2 and (b) SF2 molecules in the presence of −0.10, −0.25, −0.50, and −1.00 au PoCs at Chal···PoC distances ranging from 2.5 to 5.0 Å in the case of (i) σ-hole and (ii) lp hole interactions.

Table 1. Molecular Stabilization Energies (kcal/mol) of the Studied OF2 and SF2 Molecules with a Chal···PoC Distance of 2.5 Å in the Presence of −0.10, −0.25, −0.50, or −1.00 au PoCs.
molecule PoC = −0.10 au PoC = −0.25 au PoC = −0.50 au PoC = −1.00 au
molecular stabilization energies at 2.5 Å (σ-hole interactions)
OF2 –0.47 –1.43 –3.67 –10.44
SF2 –1.78 –4.94 –11.46 –28.94
molecular stabilization energies at 2.5 Å (lp hole interactions)
OF2 0.06 –0.17 –1.44 –7.07
SF2 –0.22 –1.17 –4.27 –15.77
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With regard to σ-hole interactions, it can be seen from the data in Figure 5i that the observed molecular stabilization energies decreased with increasing Chal···PoC distances. Moreover, molecular stabilization energies remain to be observed at long Chal···PoC distances indicating the dominance of the attractive electrostatic force between the negative PoC and the positive σ-hole.

In addition, it was noticed that the greater the negativity of the PoC (i.e., Lewis basicity), the more the molecular stabilization energies (i.e., became more negative). For example, in the case of SF2, the molecular stabilization energies obtained at a Chal···PoC distance of 2.5 Å were −1.78, −4.94, −11.46, and −28.94 kcal/mol in the presence of −0.10, −0.25, −0.50, and −1.00 au PoCs, respectively (Table 1).

For lp hole interactions, molecular stabilization energies were clearly shown at short Chal···PoC distances for all investigated molecules (Figure 5ii). For instance, in the case of −1.00 au PoC, molecular stabilization energies were obtained at a Chal···PoC distance of 2.5 Å with values of −7.07 and −15.77 kcal/mol for OF2 and SF2 molecules, respectively (Table 1). These results indicate a consistent association between the molecular stabilization energies and Vs,max values at the lp holes.

Similar to the σ-hole interactions, the raise in the negativity of the PoC led to greater molecular stabilization energies. For SF2, as an exemplar, the molecular stabilization energies were noted at a Chal···PoC distance of 2.5 Å with values of −0.22, −1.17, −4.27, and −15.77 kcal/mol in the presence of −0.10, −0.25, −0.50, and −1.00 au PoCs, respectively (Table 1). On the other hand, molecular destabilization energies were noticed at long Chal···PoC distances as a result of the prevalence of repulsive electrostatic forces between the negative XYlp plane and the negative PoC.

Overall, the propensity of sp3-hybridized chalcogen-containing molecules to form a favorable electrostatic interaction with Lewis bases via both a σ-hole and lp hole was demonstrated.

3.3.2. PoC Validation

To validate the PoC-based results, the negative PoC was replaced with a fluoride ion (F–) and the corresponding interaction energy curves were generated. The interaction energy curves were generated upon the optimized molecules in the presence of −1.00 au PoC. The interaction energy curves are presented in Figure 6.

Figure 6.

Figure 6

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Interaction energy curves of (a) OF2··· and (b) SF2···F– complexes at Chal···F– distances in the range of 2.5–5.0 Å for (i) σ-hole···F– and (ii) lp hole···F– interactions.

As shown in Figure 6i, for σ-hole···F– interactions, favorable interaction energies with notable values were observed and declined with increasing Chal···F– distances. For instance, interaction energies were noticed at 2.5 Å with values of −6.80 and −27.69 kcal/mol for OF2··· and SF2···F– complexes, respectively.

As can be seen from Figure 6ii, favorable lp hole···F– interactions were obtained for studied complexes with binding energies values of −0.32 and −1.93 kcal/mol at 3.52 and 3.13 Å for OF2··· and SF2···F– complexes, respectively. Notwithstanding, unfavorable interactions were observed at short and long Chal···F– distances.

These intriguing results reported here suggest that the strength of the lp hole···Lewis base interaction is exclusive not only to the attractive electrostatic interaction between the lp hole and Lewis base but also to repulsive/attractive electrostatic interactions and vdW interactions with XY atoms.

Comparing the lp hole interactions to the σ-hole ones, it can be seen that the sp3-hybridized chalcogen-containing molecules more favorably interact with Lewis bases via the σ-hole.

3.4. Chalcogen···Lewis Base Complexes

3.4.1. Interaction Energy

The potentiality of diflouro-chalcogen (ChalF2) molecules to participate in lp hole interactions was proved from an electrostatic perspective with the help of the PoC approach. Further investigations in ChalF2···Lewis base complexes were needed to reveal the characteristics and nature of such interactions. Full geometrical optimization was carried out for OF2··· and SF2···N2/NCH complexes that in turn underlines whether these complexes can participate in σ-hole and lp hole interactions. The interaction energies were then estimated at MP2/aug-cc-pVTZ as well as CCSD(T)/CBS levels of theory to reveal the accuracy of the former. Table 2 presents the interaction energies and the ChalF2···N bond lengths of studied complexes.

Table 2. Interaction Energies (kcal/mol) Evaluated at MP2/aug-cc-pVTZ and CCSD(T)/CBS Levels of Theory for the Optimized OF2··· and SF2···NCH/N2 complexes and the Chal···N Distance (d, Å).
noncovalent interactions complexes EMP2/aug-cc-pVTZ ECCSD(T)/CBS bond length dChal···N
σ-hole interaction OF2···N2 –0.62 –0.56 3.01
SF2···N2 –1.39 –1.31 3.05
OF2···NCH –1.28 –1.17 2.89
SF2···NCH –3.93 –3.72 2.79
lp hole interaction OF2···N2 –0.41 –0.42 3.23
SF2···N2 –0.60 –0.61 3.49
OF2···NCH –0.42 –0.46 3.20
SF2···NCH –0.64 –0.66 3.42
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As can be seen from Table 2, favorable interactions were found for all analyzed complexes and stronger σ-hole and lp hole interactions were observed for SF2 complexes than for OF2 ones. This may be traced back to the considerable Vs,max values at σ-hole and lp hole locations for the SF2 molecule (see Figure 2). Furthermore, the interaction energies increased in the order of OF2···N2 < OF2···NCH < SF2···N2 < SF2···NCH demonstrating the ability of NCH to more favorably interact compared to N2 as a Lewis base.

For σ-hole interactions, the CCSD(T)/CBS interaction energies were found to be −0.56, −1.17, −1.31 and −3.72 for OF2···N2, OF2···NCH, SF2···N2, and SF2···NCH complexes, respectively, with Chal···N distances varying from 2.79 to 3.05 Å (Table 2). These findings match those observed in earlier studies, which demonstrate that OF2 and SF2 molecules are indeed capable of forming chalcogen bonds with Lewis bases.20,21,56−60

For lp hole interactions, the obtained interaction energies at the CCSD(T)/CBS level of theory were −0.42, −0.46, −0.61, and −0.66 kcal/mol for OF2···N2, OF2···NCH, SF2···N2, and SF2···NCH complexes, respectively (Table 2). Interestingly, the Chal···N intermolecular distances ranged from 3.20 to 3.49 Å, which are higher than the sum of the vdW radii of chalcogen and nitrogen atoms.

Remarkably, the summarized interaction energies in Table 2 indicate that the change from the BSSE-corrected MP2/aug-cc-pVTZ to the CCSD(T)/CBS level of theory leads to marginal changes in interaction energies, less than −0.20 kcal/mol, signifying good convergence. Moreover, these results parallel those obtained from a previous study confirming the reliability of the MP2 method for studying chalcogen bonds.61

3.4.2. SAPT-EDA Calculation

Symmetry-adapted perturbation theory-based energy decomposition analysis (SAPT-EDA) is considered a proper method to reflect the nature of interactions.43 Thus, SAPT calculations were carried out to uncover the major driving force participating considerably in the interaction energies associated with the OF2··· and SF2···N2/NCH complexes. The total SAPT2 + (CCD)δMP2 interaction energy as well as its components are compiled in Table 3.

Table 3. Estimated SAPT2 + (CCD)δMP2 Interaction Energy and its Components Eelst, Eexch, Eind, and Edisp for the Investigated Complexes.
noncovalent interactions complexes Eelst Eexch EinddMP2 EdispCCD EintSAPT2 + (CCD)dMP2
σ-hole interaction OF2···N2 –0.63 1.11 –0.02 –1.01 –0.57
SF2···N2 –1.94 2.93 –0.46 –1.86 –1.36
OF2···NCH –1.60 2.02 –0.23 –1.37 –1.21
SF2···NCH –6.87 8.47 –2.05 –3.43 –3.90
lp hole interaction OF2···N2 –0.35 0.88 0.06 –0.99 –0.43
SF2···N2 –0.59 1.30 0.02 –1.31 –0.59
OF2···NCH –0.40 1.13 –0.01 –1.13 –0.44
SF2···NCH –0.74 1.95 –0.14 –1.65 –0.63
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According to the data in Table 3, the total obtained SAPT2 + (CCD)δMP2 interaction energies are similar to the corresponding MP2/aug-cc-PVTZ and CCSD/CBS interaction energies, demonstrating the reliability of the implemented SAPT level of theory.

Generally, for σ-hole interactions, the electrostatic force (Eelst) appears to be the predominant one followed by the dispersion force (Edisp) and induction force (Eind). For instance, in the case of the SF2···NCH complex, the Eelst, Edisp, and Eind forces were observed with values of −6.87, −3.43, and −2.05 kcal/mol, respectively.

Surprisingly, for lp-hole interactions, the Edisp was found to be the dominant force and exceeded the Eelst contribution with values in the range of 0.17–0.73 kcal/mol. For instance, in the case of the SF2···NCH complex, the Edisp and Eelst forces were observed with values of −1.65 and −0.74 kcal/mol, respectively.

Generally, these results disclose that the σ-hole and lp hole interactions are chiefly stabilized by the electrostatic and dispersion forces, respectively.

3.4.3. QTAIM Analysis

To analyze the characteristics of σ-hole and lp hole interactions in more depth, the quantum theory of atoms in molecules (QTAIM) study was carried out for the optimized OF2··· and SF2···N2/NCH complexes.48 Through the QTAIM analysis, the bond critical points (BCPs) and bond paths (BPs) were generated, and the topological parameters were investigated. The BPs and BCPs for the complexes are set out in Figure 7. The electron density (ρb), laplacian (∇2ρb), and total energy density (Hb) values are compared in Table 4.

Figure 7.

Figure 7

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QTAIM diagrams of OF2··· and SF2···N2/NCH binary complexes for (i) σ-hole and (ii) lp hole interactions, computed at the MP2/aug-cc-pVTZ level of theory. Bond paths between bonded atomic basins and bond critical points are illustrated by solid lines and tiny red spheres, respectively.

Table 4. Characteristics of the Bond Critical Point (BCP) Corresponding to the Bond Path Linking the Chalcogen Atom with the Nitrogen Atom in the Studied Optimized Dimmers: The Electron Density (ρb, au.), its Laplacian (∇2ρb, au), and the Total Electron Energy Density (Hb, au).
noncovalent interactions complexes Hb (au) ∇2ρb (au) ρb (au)
σ-hole interaction OF2···N2 0.0018 0.0272 0.0053
SF2···N2 0.0020 0.0388 0.0089
OF2···NCH 0.0023 0.0374 0.0074
SF2···NCH 0.0018 0.0639 0.0168
lp hole interaction OF2···N2 0.0011 0.0190 0.0042
SF2···N2 0.0011 0.0189 0.0044
OF2···NCH 0.0011 0.0202 0.0048
SF2···NCH 0.0012 0.0216 0.0055
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The inference of σ-hole and lp hole interactions was concluded based on the existence of BPs linking the two interacting monomers in the formation of complexes and the existence of BCPs in the middle of the bond paths that are visible in all molecular graphs (Figure 7). As shown in Table 4, the values of Hb are positive ranging from 0.0011 to 0.0023 au, indicating the closed-shell nature of σ-hole and lp hole interactions in OF2··· and SF2···N2/NCH complexes. Also, the comparatively low value of ρb and positivity of ∇2ρb report also direct evidence of the closed-shell nature of the investigated interactions. For instance, the positivity of ρb was found in the range of 0.0053–0.0168 and 0.0042–0.0055 au for σ-hole and lp hole interactions, respectively.

3.4.4. RDG-NCI Analysis

Noncovalent interaction analysis (NCI) is considered as a powerful tool for visualization of weak noncovalent interactions present in weakly bound molecular complexes.51 Here, the NCI calculations were performed for the optimized OF2··· and SF2···N2/NCH complexes to further reveal the characteristics of σ-hole and lp hole interactions. NCI isosurfaces and plots of the reduced density gradient (RDG) versus the electron density (ρ) multiplied by the sign of the second Hessian eigenvalue (λ2) are shown in Figure 8.

Figure 8.

Figure 8

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NCI isosurfaces of OF2··· and SF2···N2/NCH complexes for (i) σ-hole and (ii) lp hole interactions. They are colored on the blue-green-red (BGR) scale with blue and red for attractive and repulsive interactions, respectively. The corresponding sign(λ2) × ρ vs RDG plots for the NCI isosurfaces are also depicted.

From the NCI isosurfaces in Figure 8, it can be seen that green areas appear between the interacting monomers, thus confirming favorable σ-hole and lp hole interactions. Moreover, a larger noticeable area of green isosurfaces was observed for σ-hole interactions compared with the lp hole ones, indicating more favorable σ-hole interactions than lp hole ones. Spikes of sign(λ2)ρ at low densities assert attractive interaction (sign(λ2)ρ < 0), corresponding to the green areas in the NCI isosurfaces (see Figure 8). A remarkable finding here is that the location of the spike depends on the interaction strength; i.e., it shifts toward the more negative sign(λ2)ρ region as the value of the interaction energy increases. For example, the spike becomes broader for SF2···N2/NCH in the case of both σ-hole and lp hole interactions compared to OF2···N2/NCH complexes.

4. Conclusions

The present study was designed to uncover the nature and characteristics of the lp hole and σ-hole interactions for sp3-hybridized chalcogen-containing complexes. The following conclusions can be drawn from the MEP, Vs,max, PoC, interaction energy, and SAPT-based results: (i) the Vs,max calculation is considered an unreliable method to determine optimum σ-hole and lp hole locations. (ii) The maximum positive electrostatic potential of the σ-hole and lp hole was found to be at the F–Chal···PoC angle (θ) of 180° and at the centroid of XYlp plane, respectively. (iii) The studied molecules can participate in favorable electrostatic interactions with Lewis bases via the positive σ-hole and lp hole. (iv) The studied molecules more favorably interact with Lewis bases via the σ-hole compared to the lp hole. (v) The strength of σ-hole and lp hole interactions increased as Lewis basicity increased, and (vi) the electrostatic and dispersion forces play a critical role in the formation of the σ-hole and lp hole interactions, respectively. The QTAIM and NCI-based analyses provided evidence of the presence of σ-hole and lp hole interactions for the complexes under study and characterized the closed-shell nature of these interactions. In summary, the findings from this study make several contributions to the current literature and will also be of advantage to the materials design and crystal engineering fields.

Acknowledgments

The computational work was completed with resources supported by the Science and Technology Development Fund, STDF, Egypt (grants nos. 5480 and 7972).

The authors declare no competing financial interest.

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