On the Potentiality of X-T-X3 Compounds (T = C, Si, and Ge, and X = F, Cl, and Br) as Tetrel- and Halogen-Bond Donors.

The versatility of the X-T-X3 compounds (where T = C, Si, and Ge, and X = F, Cl, and Br) to participate in tetrel- and halogen-bonding interactions was settled out, at the MP2/aug-cc-pVTZ level of theory, within a series of configurations for (X-T-X3)2 homodimers. The electrostatic potential computations ensured the remarkable ability of the investigated X-T-X3 monomers to participate in σ-hole halogen and tetrel interactions. The energetic findings significantly unveil the favorability of the tetrel···tetrel directional configuration with considerable negative binding energies over tetrel···halogen, type III halogen···halogen, and type II halogen···halogen analogs. Quantum theory of atoms in molecules and noncovalent interaction analyses were accomplished to disclose the nature of the tetrel- and halogen-bonding interactions within designed configurations, giving good correlations between the total electron densities and binding energies. Further insight into the binding energy physical meanings was invoked through using symmetry-adapted perturbation theory-based energy decomposition analysis, featuring the dispersion term as the most prominent force beyond the examined interactions. The theoretical results were supported by versatile crystal structures which were characterized by the same type of interactions. Presumably, the obtained findings would be considered as a solid underpinning for future supramolecular chemistry, materials science, and crystal engineering studies, as well as a fundamental linchpin for a better understanding of the biological activities of chemicals.

Introduction

Noncovalent interactions are prevalent in chemical and biological systems and play an influential role in a substantial number of fields, including supramolecular chemistry,[1−3] molecular recognition,[4−7] materials science,[8,9] and drug discovery.[10−12] In common with hydrogen bonds, σ-hole interactions have been seen in recent years with upsurge interest, and outstanding efforts have been devoted to understanding their characteristics deeply. The occurrence of σ-hole interactions is primarily ascribed to the existence of an electron depletion portion coined as ″σ-hole″ that is located along the extension of covalently bonded atoms of groups IV–VII (called σ-atoms).[13−15] Initially, the σ-hole was alluded to be positive by nature. Up to date terminologies were then introduced to describe the nature of the σ-hole based on the sign of maximum positive electrostatic potential (VS,max) values.[16−18] It was found that the negative and positive signs of VS,max values pinpointed the occurence of negative σ-holes and positive σ-holes, respectively. When the VS,max value was zero, the neutral σ-hole was obviously obtained. Groups IV–VII atoms have the ability to interact through their σ-holes as Lewis acid centers, with Lewis bases forming tetrel,[19−21] pnicogen,[22−24] chalcogen,[25−28] and halogen[13,29,30] bonds, respectively. It is now well established from several studies that the size and magnitude of the σ-hole relied basically on the electronegativity of the σ-atom and the electron-withdrawing power of the attached atoms/groups.[31−33]

More recently, like···like noncovalent interactions have attracted tremendous attention because of their ubiquitous roles in material and crystal design.[34−37] The interactions involving the covalently bonded univalent group VII atoms constitute the most well-established and utilized type of like···like interactions.[16,17,38−42] For halogen···halogen (A-X···X-A) interactions (where A referred to the attached atom to halogen (X) atom), three types were identified based on the A-X···X (θ1) and X···X-A (θ2) angles (Figure ).[36,37,43,44] Generally, the θ1 and θ2 angles are with nearly equal values for type I halogen···halogen interactions, while the θ1 angle is about 180° and θ2 is about 90° for type II halogen···halogen interactions (Figure ). Turning to type III halogen···halogen interactions, the θ1 and θ2 angles are with a similar value of 180°, representing a linear geometrical structure (Figure ).

Figure 1

Schematic representation for (a) PoC calculations for X–T–X3 systems (where T = C, Si, and Ge, and X = F, Cl, and Br), and (b) PES scan for the investigated (i) tetrel···tetrel, (ii) tetrel···halogen, (iii) type III halogen···halogen, and (iv) type II halogen···halogen homodimers.

In close analogy to halogen···halogen interactions, it has been reported that chalcogens and pnicogens can engage in like···like noncovalent interactions.[45,46] Similarly, the potentiality of tetravalent group IV atoms to participate in like···like interactions has been recently examined.[47,48] Indeed, the occurrence of tetrel···tetrel interactions has been a subject of intense, controversial debate within the scientific community. This discrepancy was attributed to the domination of the repulsive forces between the noticeable positive σ-holes of the interacting tetrel-containing molecules.[49] Nevertheless, the point-of-charge (PoC) approach emphasized scant inclination of the tetrel-containing molecules to electrostatically interact with positively charged points, and its results were validated with the obtained substantial negative interaction energies of tetrel-containing molecule···Lewis acid complexes.[50] On the other hand, the occurrence of ditetrel bonds between two different charged tetrel-containing molecules was clearly unveiled and reported.[48] Scheiner proposed that tetrel (T) atoms could acquire a partial negative charge by bonding to a highly electropositive metal (M) atom, acting as a Lewis base center and then be able to interact with a positive σ-hole of a tetrel-containing molecule (i.e., Lewis acid).[47]

As another issue, the contribution of the three coplanar X3 atoms in the F-T-X3 molecules (where X = F, Cl, Br, and I) on the tetrel···Lewis base/acid interactions was thoroughly explored.[50] It has been reported that the strength of the tetrel-based interactions was governed by (i) repulsive forces between the negative X3 atoms and Lewis base, (ii) repulsive forces between the positive σ-hole and Lewis acid, (iii) attractive forces between the positive σ-hole and negative Lewis base, and (iv) attractive forces between negative X3 atoms and positive Lewis acid.

The present work addresses, for the first time, a delineated evaluation for the potentiality of X-T-X3 compounds (where T = C, Si, and Ge, and X = F, Cl, and Br) to participate in tetrel- and halogen-based interactions within the tetrel···tetrel, tetrel···halogen, type III halogen···halogen, and type II halogen···halogen configurations. Herein, the fulfillment of this investigation was conclusively put forward through a set of quantum mechanical calculations. For the explored monomers, molecular electrostatic potential (MEP) maps, maximum positive electrostatic potential (Vs,max) values, and molecular stabilization energy curves with the incorporation of PoC approach were generated and investigated. A potential energy surface (PES) scan was established for the (X-T-X3)2 homodimers in a specific orientation to fulfill the purpose of the current study (see Figure ). In addition, the quantum theory of atoms in molecules (QTAIM) and noncovalent interaction (NCI) index analyses were conducted. To reveal the nature of the inspected interactions, the symmetry-adapted perturbation theory-based energy decomposition analysis (SAPT-EDA) was performed. As well, a survey of the Cambridge Structure Database (CSD) was accomplished to give experimental evidence for the inspected halogen- and tetrel-based interactions in crystal structures. The results of the current work will be a foundation for a wide range of applications of crystal engineering and future studies of materials science.

Results and Discussion

MEP, Vs,max, and ±σ-Hole Test

Several studies have addressed MEP as a reliable tool to elucidate the convenient sites on the molecular surfaces for noncovalent interactions.[51−53] Herein, MEPs were plotted for all optimized monomers at the MP2/aug-cc-pVTZ (with PP functions for Ge and Br atoms) level of theory and then mapped onto 0.002 au electron density contours. Such a value of electron density contour was recommended to evade any misleading for the obtained results.[54] In addition, maximum positive electrostatic potential (Vs,max) calculations were carried out to compute the σ-hole magnitude and reinforce MEP results with quantitative evidence. For all the studied monomers, MEP maps are displayed in Figures S1 and S2 for the σ-hole on the inspected tetrel and halogen bond donors, respectively. Vs,max values are gathered in Table S1. Figure demonstrates the MEP results for Cl–T–Cl3 and X–Si–X3 molecules, as a case study for the studied tetrel- and halogen-containing molecules as σ-hole donors, respectively.

Figure 2

MEP maps plotted onto 0.002 au electron density contours for Cl–T–Cl3 and X-Si-X3 molecules (where T = C, Si, and Ge, and X = F, Cl, and Br) as tetrel and halogen bond donors, respectively. The electrostatic potential varies from −0.01 (red) to +0.01 (blue) au. The maximum positive electrostatic potentials (Vs,max) at σ-hole of the tetrel and halogen atoms in kcal/mol.

According to Figures S1 and S2, apparent σ-holes with considerable sizes were observed along the extension of the covalently bonded tetrel and halogen atoms in the Cl-T-Cl3 and X-Si-X3 monomers, respectively. The occurrence of such σ-holes would foretell the potentiality of the tetrel- and halogen-containing monomers to participate as Lewis acids in noncovalent interactions with Lewis bases .

Looking at the Vs,max values listed in Table S1, the orders of σ-hole magnitude of tetrel and halogen atoms in X-T-X3 systems were X-C-X3 < X-Si-X3 < X-Ge-X3 and F-T-F3 < Cl-T-Cl3 < Br-T-Br3, respectively. For example, tetrels’ σ-hole exhibited Vs,max values of 13.7, 31.5, and 36.7 kcal/mol in Cl-C-Cl3, Cl-Si-Cl3, and Cl-Ge-Cl3 molecules, respectively, while Vs,max values of 2.6, 25.9, and 31.6 kcal/mol were obtained at halogens’ σ-hole of F-C-F3, Cl-C-Cl3, and Br-C-Br3, respectively. Conspicuously, σ-hole magnitude increased as the electronegativity of the σ-atom decreased (i.e., the atomic size increased), and, in turn, the ability of the tetrel- and halogen-containing molecules to act as Lewis acids increased in line with their atomic size level up.

From compiled data in Table S1, the σ-hole magnitude of tetrel and halogen atoms in the studied systems generally increased with increasing the electron-withdrawing power of the attached atoms/groups. For instance, Vs,max values at tetrels’ σ-hole were 25.3, 31.5, and 64.1 kcal/mol in Br-Si-Br3, Cl-Si-Cl3, and F-Si-F3, respectively. For halogens’ σ-hole, Vs,max values were 25.9, 14.4, and 15.0 kcal/mol in Cl-C-Cl3, Cl-Si-Cl3, and Cl-Ge-Cl3, respectively. Such irregular trend might be in line with the van der Waals (vdW) radii order of tetrels, confirming the effect of tetrels’ vdW radii on the anisotropic distribution of the electron density on the molecular surface of tetrel-containing molecules. Apparently, there is a clear correlation between the numerical values of Vs,max and the visualized maps of MEP for all the inspected monomers, ensuring the ascending order of σ-holes’ size and magnitude according to the corresponding atomic size of tetrels and halogens.

Parallel to the π- and lone-pair (lp)-hole tests,[55−57]±σ-hole tests were advanced to critically examine the potentiality of σ-atom-containing molecules to engage in noncovalent interactions with the help of PoC approach.[57−59] In ±σ-hole tests, the correlation between the T/X···PoC distance and the molecular stabilization energy was established in the presence of ±0.50 au PoC (see the Computational Methodology section for more details). Figure displays the molecular stabilization energy curves for X-T-X3···PoC systems that were generated in a T/X···PoC distance range of 2.5–5.5 Å. Molecular stabilization energies for the studied X-T-X3···PoC systems in the presence of ±0.50 au PoC at T/X···PoC distance of 2.5 Å are collected in Table .

Figure 3

Molecular stabilization energies of the X-T-X3···PoC systems (where T = C, Si, and Ge, and X = F, Cl, and Br) in the presence of ±0.50 au PoC with the X-T···/T-X···PoC angle of 180° and T/X···PoC distance ranging from 2.5 to 5.5 Å.

Table 1

Molecular Stabilization Energies of the X-T-X3···PoC Systems (Where T = C, Si, and Ge, and X = F, Cl, and Br) Computed (in kcal/mol) in the Presence of ±0.50 au PoC at a T/X···PoC Distance of 2.5 Å and an X-T···/T-X···PoC Angle of 180°

	molecular stabilization energy (Estabilization, kcal/mol)
	PoC = −0.50 au			PoC = +0.50 au
	tetrel interactions
system···PoC	F	Cl	Br	F	Cl	Br
X-C-X3···PoC	–5.58	–7.46	–8.77	0.30	–7.54	–10.23
X-Si-X3···PoC	–11.57	–12.19	–12.68	5.12	–3.34	–6.36
X-Ge-X3···PoC	–13.56	–13.31	–13.53	6.68	–2.07	–5.20
	halogen interactions
system···PoC	C	Si	Ge	C	Si	Ge
F-T-F3···PoC	–0.79	0.55	0.53	–1.40	–2.81	–3.12
Cl-T-Cl3···PoC	–7.08	–5.34	–5.64	–0.11	–2.01	–2.20
Br-T-Br3···PoC	–10.11	–8.22	–8.62	0.27	–1.88	–2.08

At first glance, the molecular stabilization energies were found to decrease in the order T···–PoC < X···–PoC < T···+PoC < X···+PoC, demonstrating the ability of the T and X atoms to interact more preferentially with Lewis bases than Lewis acids. For example, molecular stabilization energy of the Cl-Si-Cl3···PoC system emphasized the latter order with values of −12.19, −5.34, −3.34, and – 2.01 kcal/mol for Si···–PoC, Cl···–PoC, Si···+PoC, and Cl···+PoC, respectively.

According to data shown in Figure , it can be affirmed that almost all the studied X-T-X3 molecules had a salient capability to engage in pure electrostatic interactions through their tetrels’ and halogens’ σ-holes with negative PoC and exhibited substantial molecular stabilization energy with an exception for fluorine in F-T-F3 where T = Si and Ge. Molecular destabilization energies were found with values of 0.55 and 0.53 kcal/mol at an X···PoC distance of 2.5 Å in the presence of −0.50 au PoC for F-Si-F3··· and F-Ge-F3···PoC systems, respectively.

Furthermore, a proportional intercorrelation between the molecular stabilization energy and the atomic size was denoted, which confirmed to a large extent the results of MEP analysis. From Table , the molecular stabilization energies were −7.46, −12.19, and −13.31 kcal/mol for Cl-C-Cl3···, Cl-Si-Cl3···, and Cl-Ge-Cl3···PoC systems, respectively, at a T···PoC distance of 2.5 Å, in the presence of PoC with a value of −0.50 au. These results also accord with our earlier observations, which showed that the molecular stabilization energy was inversely correlated with σ-atom electronegativity and σ-atom···PoC distance.[32,59]

Regarding the results of the +σ-hole test, molecular stabilization energies decreased with increasing the atomic size of the interacted σ-atom and vanished for tetrels’ interactions of the F-T-F3···PoC systems. For the latter systems, at a T···PoC distance of 2.5 Å, molecular destabilization energies were observed with values of 0.30, 5.12, and 6.68 kcal/mol for F-C-F3···PoC, F-Si-F3···PoC, and F-Ge-F3···PoC, respectively, pinpointing the direct correlation between the molecular destabilization energy and the σ-holes’ size of the considered systems. Turning to the remaining systems, molecular stabilization energies showed an upward trend in line with the electronegativity of the explored tetrel atoms. As an illustration, the Cl-T-Cl3···PoC systems exhibited molecular stabilization energies with values of −2.07, −3.34, and −7.54 kcal/mol where T = Ge, Si, and C, respectively, in the presence of the +0.50 PoC value.

Interestingly, carbon-containing molecules showed more preferential molecular stabilization energies in the presence of positively charged PoC, compared to the negative one. Numerically, the molecular stabilization energies of the Cl-C-Cl3···PoC tetrel bonding system were found with values of −7.46 and −7.54 kcal/mol in the presence of −0.50 and +0.50 au PoC, respectively. Similar findings were explored for F-T-F3···PoC halogen bonding systems.

In all instances, the most prominent σ-hole was generally denoted on tetrels showing significant molecular stabilization energies with negative PoCs, prominent destabilization energies with positive PoCs, noticeable blue color in MEP maps, and considerable values of Vs,max. These results reflect the favorability of tetrels to engage in noncovalent interactions rather than halogens.

PES Scan

To rigorously assess the versatility of the X-T-X3 molecules (where T = C, Si, and Ge, and X = F, Cl, and Br) to engage in tetrel- and halogen-based interactions, a PES scan was performed for the (X-T-X3)2 homodimers within the designed configurations (see Figure ). PES scan at the MP2/aug-cc-pVTZ(PP) level of theory was carried out at the T/X···T/X distance in the range of 2.5–5.5 Å with a step size of 0.1 Å (see the Computational Methodology section for more details). PES scan graphs for the homodimers under study are pictured in Figure . Binding energies at the most favorable T/X···T/X distances are collected in Table .

Figure 4

Binding energies calculated at the MP2/aug-cc-pVTZ(PP) level of theory for (X-T-X3)2 homodimers (where T = C, Si, and Ge; and X = F, Cl, and Br) at a T/X···T/X distance ranging from 2.5 to 5.5 Å with a step size of 0.1 Å.

Table 2

Binding Energies Calculated (in kcal/mol) at the MP2/aug-cc-pVTZ(PP) and CCSD(T)/CBS Levels of Theory for the (X-T-X3)2 Homodimers (Where T = C, Si, and Ge, and X = F, Cl, and Br) at the Most Favorable T/X···T/X Distances (in Å)

homodimer	distancea (Å)	EMP2/aug – cc–pVTZb (kcal/mol)	ECCSD(T)/CBS (kcal/mol)	distancea (Å)	EMP2/aug – cc–pVTZb (kcal/mol)	ECCSD(T)/CBS (kcal/mol)
	tetrel···tetrel			tetrel···halogen
(F-C-F3)2	4.03	–0.60	–0.74	3.37	–0.49	–0.60
(Cl-C-Cl3)2	4.69	–2.99	–2.53	3.91	–2.00	–1.75
(Br-C-Br3)2	4.95	–3.96	–3.52	4.05	–2.98	–2.67
(F-Si-F3)2	4.78	–0.05	–0.14	3.25	–1.01	–1.26
(Cl-Si-Cl3)2	4.79	–3.17	–2.77	4.00	–1.70	–1.49
(Br-Si-Br3)2	4.98	–4.42	–3.98	4.14	–2.51	–2.25
(F-Ge-F3)2	noc	noc	noc	3.17	–1.34	–1.68
(Cl-Ge-Cl3)2	4.79	–3.27	–2.92	3.98	–1.79	–1.57
(Br-Ge-Br3)2	5.00	–4.57	–4.13	4.11	–2.63	–2.37
	type III halogen···halogen			type II halogen···halogen
(F-C-F3)2	2.96	–0.27	–0.32	3.09	–0.52	–0.64
(Cl-C-Cl3)2	3.44	–0.74	–0.68	3.45	–2.19	–1.95
(Br-C-Br3)2	3.54	–1.01	–0.92	3.49	–3.41	–3.06
(F-Si-F3)2	3.25	–0.08	–0.14	3.01	–0.87	–1.06
(Cl-Si-Cl3)2	3.56	–0.80	–0.77	3.56	–1.78	–1.61
(Br-Si-Br3)2	3.66	–1.12	–1.05	3.66	–2.60	–2.34
(F-Ge-F3)2	3.18	–0.10	–0.16	2.95	–1.06	–1.31
(Cl-Ge-Cl3)2	3.50	–0.90	–0.86	3.51	–1.91	–1.75
(Br-Ge-Br3)2	3.60	–1.26	–1.18	3.61	–2.79	–2.55

The most favorable T/X···T/X distances were determined according to the corresponding PES curves (see Figure ).

PP functions were implemented for Ge and Br atoms.

No local energy minimum was observed in the corresponding PES curve (see Figure ).

According to data presented in Figure and Table , almost all the examined (X-T-X3)2 homodimers exhibited an impressive inclination to engage in tetrel- and halogen-based interactions within tetrel···tetrel, tetrel···halogen, type III halogen···halogen, and type II halogen···halogen configurations.

With regard to tetrel···tetrel configuration, a direct correlation was detected between the atomic size of the tetrels and the obtained negative binding energies for all the considered homodimers with an exception for (F-T-F3)2 homodimers. The interpretation of the abovementioned correlation could be relevant to the significant influence of vdW on the strength of the tetrel···tetrel homodimers. For example, the (Br-T-Br3)2 homodimers, which recorded the most significant binding energies among all the investigated halogens in tetrel···tetrel configurations, were observed with MP2 binding energies of −3.96, −4.42, and −4.57 kcal/mol for T = C, Si, and Ge, respectively. In line with the literature, these energetic results of the tetrel···tetrel homodimers confirmed the occurrence of like···like interactions for tetrel-containing molecules.[47,48] Unexpectedly, the descending pattern of binding energies was highly consistent with the ascending order of the halogens’ electronegativity of the (X-T-X3)2 homodimers. Evidently, the binding energy progressively declined as the electronegativity of the halogens increased (i.e., the tetrels’ σ-hole decreased) and faded in the case of the (F-Ge-F3)2 homodimer with the largest tetrel’s σ-hole size. For instance, the MP2 binding energies of the (X-C-X3)2 homodimers were denoted with values of −3.96, −2.99, and −0.60 kcal/mol for X = Br, Cl, and F, respectively. The positive binding energy observed in (F-Ge-F3)2 homodimer supports previous pretinent research, which links the lack of tetrels’ ability to engage in like···like interactions with the domination of the repulsive forces between the two eminent positive σ-holes.[49]

For tetrel···halogen configurations, the binding energies of the investigated homodimers were found to increase as the halogens’ electronegativity decreased. For instance, the MP2 binding energies of the (X-C-X3)2 homodimers where X = F, Cl, and Br were −0.49, −2.00, and −2.98 kcal/mol, respectively. Interestingly, the binding energies of the tetrel···halogen interactions in the (F-T-F3)2 homodimers were directly and inversely correlated along with the σ-hole size of the examined tetrels and halogens, respectively. The latter trend confirms the substantial role of the σ-hole of tetrels and the negative belt of the interacted fluorine atom on the strength of the tetrel···halogen interaction. For (F-T-F3)2 homodimers, the MP2 binding energies were noted to be −0.49, −1.01, −1.34 kcal/mol, where T = C, Si, and Ge, respectively. In line with the Vs,max remarkable trend, the strength of interaction between the tetrel···halogen homodimers decreased in the order (X-C-X3)2 > (X-Ge-X3)2 > (X-Si-X3)2 (where X = Cl and Br). Quantitatively speaking, as an example, the MP2 binding energies were – 2.00, −1.70, and −1.79 kcal/mol for (Cl-C-Cl3)2, (Cl-Si-Cl3)2, and (Cl-Ge-Cl3)2 homodimers, respectively.

Apart from the obscure trends of the abovementioned interactions, there is a direct correlation between the halogens’ σ-hole size and the binding energy in type III halogen···halogen and type II halogen···halogen configurations. Considering the (X-C-X3)2 type III halogen···halogen configuration, as an example, the MP2 binding energies were found to be −0.27, −0.74, and −1.01 kcal/mol for X = F, Cl, and Br, respectively. In general, an inverse correlation was denoted between the electronegativity of tetrels in the type III halogen···halogen configuration and binding energy. For example, the (Cl-T-Cl3)2 showed MP2 binding energies of −0.74, −0.80, and −0.90 kcal/mol for T = C, Si, and Ge, respectively. An unexpected pattern for the tetrels’ atomic size with binding energies was noticed in type II halogen···halogen configurations. In detailed, the computed binding energies were found to be decreased in the order (X-C-X3)2 > (X-Ge-X3)2 > (X-Si-X3)2 where X = Cl and Br. This observed trend is in obvious consistency with the Vs,max and MEP results (see Table S1 and Figures S1 and S2).

Generally, the (X-T-X3)2 homodimers showed the most favorable binding energies in the tetrel···tetrel configuration followed by type II halogen···halogen, tetrel···halogen, and type III halogen···halogen configurations. For instance, the binding energies of the (F-C-F3)2 homodimers were – 0.74, −0.64, −0.60, and −0.32 kcal/mol for the tetrel···tetrel, type II halogen···halogen, tetrel···halogen, and type III halogen···halogen homodimers, respectively.

Furthermore, the benchmarking of the binding energies was executed for all the investigated interactions at the CCSD/CBS level of theory (Table ). Inspecting data presented in Table , an apparent similarity was noticed between the binding energy values computed at the MP2/aug-cc-pVTZ(PP) and CCSD(T)/CBS levels of theory.

QTAIM Analysis

To present detailed analysis of the origin and nature of the designed interactions between (X-T-X3)2 homodimers from a topological perspective, QTAIM was incorporated.[60−62] Within the context of the QTAIM, the strength of the noncovalent interactions could be detected from the electron density (ρb) values at bond critical points (BCPs) along bond paths (BPs) between the interacting species. The positive values of both Laplacian (∇2ρb) and total energy density (Hb) were deemed ample evidence for the closed-shell nature of the interactions under investigation. In this study, BCPs and BPs were generated for the considered homodimers at the most favorable T/X···T/X distance (Figure S3). BCPs and BPs for the four examined configurations of the (X-Si-X3)2 homodimers (where X = F, Cl, and Br) are displayed in Figure . The topological parameters, including electron density (ρb), Laplacian (∇2ρb), and total energy density (Hb), at the BCPs are listed in Table .

Figure 5

QTAIM diagrams for the investigated interactions within (X-Si-X3)2 homodimers (where X = F, Cl, and Br). Red dots indicate the locations of BCPs at the BPs between the monomers at the most favorable T/X···T/X distance.

Table 3

Topological Parameters Including Total Energy Density (Hb, au), Laplacian (∇2ρb, au), and Electron Density (ρb, au) at BCPs for the (X-T-X3)2 Homodimers (where T = C, Si, and Ge, and X = F, Cl, and Br) at the Most Favorable T/X···T/X Distances

homodimer	ρb	∇2ρb	Hb	ρb	∇2ρb	Hb
	tetrel···tetrel			tetrel···halogen
(F-C-F3)2	0.0021	0.0102	0.0005	0.0028	0.0143	0.0007
(Cl-C-Cl3)2	0.0038	0.0124	0.0008	0.0043	0.0157	0.0010
(Br-C-Br3)2	0.0041	0.0121	0.0007	0.0052	0.0159	0.0008
(F-Si-F3)2	0.0005	0.0030	0.0003	0.0043	0.0199	0.0009
(Cl-Si-Cl3)2	0.0036	0.0115	0.0007	0.0037	0.0131	0.0008
(Br-Si-Br3)2	0.0041	0.0121	0.0007	0.0043	0.0136	0.0008
(F-Ge-F3)2	noa	noa	noa	0.0051	0.0224	0.0009
(Cl-Ge-Cl3)2	0.0036	0.0114	0.0007	0.0038	0.0132	0.0008
(Br-Ge-Br3)2	0.0040	0.0119	0.0007	0.0045	0.0139	0.0007
	type III halogen···halogen			type II halogen···halogen
(F-C-F3)2	0.0035	0.0197	0.0011	0.0034	0.0170	0.0008
(Cl-C-Cl3)2	0.0049	0.0228	0.0015	0.0067	0.0265	0.0015
(Br-C-Br3)2	0.0063	0.0234	0.0011	0.0097	0.0297	0.0009
(F-Si-F3)2	0.0021	0.0108	0.0006	0.0048	0.0221	0.0010
(Cl-Si-Cl3)2	0.0045	0.0196	0.0013	0.0058	0.0221	0.0013
(Br-Si-Br3)2	0.0058	0.0206	0.0010	0.0073	0.0230	0.0010
(F-Ge-F3)2	0.0025	0.0125	0.0007	0.0056	0.0251	0.0010
(Cl-Ge-Cl3)2	0.0052	0.0221	0.0014	0.0064	0.0244	0.0014
(Br-Ge-Br3)2	0.0065	0.0227	0.0010	0.0081	0.0248	0.0009

No local energy minimum was observed in the corresponding PES curve (see Figure ).

As illustrated in Figure S3, all the studied homodimers showed different numbers of BCPs and BPs that varied based on the configuration of the interacting species. For tetrel···tetrel homodimers, six BCPs and BPs were denoted between the three coplanar halogen atoms in each interacting molecule, indicating the prominent contribution of the attractive forces between halogen atoms over tetrels’ counterparts (Figure S3). Three BCPs and BPs were formed between halogen of one interacting molecule and three coplanar ones on the other molecule within tetrel···halogen configuration. For such homodimers, the absence of BPs involving a tetrel atom was considered as a strong affirmation for the favorable contribution of the three coplanar atoms to the overall noncovalent interaction that was in accordance with our previous work.[57] In type III halogen···halogen interactions, only one BCP and BP were displayed between the interacting species that was in great agreement with the previously reported results that emphasis the potentiality of halogens to form σ-hole···σ-hole interactions.[43] Remarkably, the number of the generated BPs and BCPs between the halogens of the two interacted species within type II halogen···halogen configuration increased as the halogens’ σ-hole became more prominent.

From the inspection of compiled results in Table , a direct correlation between the binding energy of the homodimers and the ρb of the BCP was denoted in tetrel···tetrel, type II halogen···halogen, and type III halogen···halogen configurations, whereas the tetrel···halogen configuration was observed with an irregular trend. For instance, ρb values in (X-Si-X3)2 homodimers within the tetrel···tetrel configuration were 0.0005, 0.0036, and 0.0041 au with binding energies of −0.05, −3.14, and −4.42 kcal/mol for (F-Si-F3)2, (Cl-Si-Cl3)2, and (Br-Si-Br3)2 homodimers, respectively. Inspecting the positive sign of ∇2ρb and Hb values, the closed-shell nature of the four studied configurations of the (X-T-X3)2 homodimers was announced.

NCI-RDG Analysis

Noncovalent interaction-based reduced density gradient (NCI-RDG) analysis was earlier described as a potent index to identify the existence of weak noncovalent interactions.[63] As previously repoted, the NCI-RDG was perceived to be a more flexible tool to identify long-range chemical bonding than QTAIM analog.[64] 3D color-mapped NCI plots of noncovalent interaction regions for the studied homodimers at the most favorable T/X···T/X distances were generated (Figure S4). The color scale of sign(λ2)ρ was set to be from −0.035 (blue) to 0.020 (red), where λ2 is the second eigenvalue of the Hessian matrix and ρ is the electron density. For all discussed (X-Si-X3)2 interactions, the 3D color-mapped NCI plots are given in Figure .

Figure 6

NCI isosurfaces of the four types of the (X-Si-X3)2 homodimers (where X = F, Cl, and Br). The isosurfaces are plotted with a reduced density gradient value of 0.50 au and colored from blue to red according to sign(λ2)ρ ranging from −0.035 to 0.020 au.

From Figure S4, NCI graphs unveiled the occurrence of the tetrel- and halogen-bonding interactions between the examined (X-T-X3)2 homodimers within the four investigated configurations, which was in line with the QTAIM affirmations. As can be noticed from Figure , weak attractive interactions between the interacting molecules within the studied homodimers were disclosed through the perceived green regions. Such regions’ size was deemed strong evidence for the position and strength of the investigated interactions.

SAPT-EDA Calculations

To adequately scrutinize the nature of tetrel- and halogen-bonding interactions in the designed configurations, SAPT-EDA was utilized. SAPT was reported as a well-established method to evaluate accurate intermolecular interaction energies in terms of their physical meanings that were labeled as electrostatic (Eelst), dispersion (Edisp), induction (Eind), and exchange (Eexch). For the homodimers under study, at the most favorable distance, the total binding energy was decomposed and computed as the sum of the abovementioned meaningful physical terms at the SAPT2 level of truncation. Total SAPT-based binding energy and its basic components (calculated in kcal/mol) are compiled in Table .

Table 4

Electrostatic (Eelst), Dispersion (Edisp), Induction (Eind), and Exchange (Eexch) Interactions Contributions to the Binding Energies of the (X-T-X3)2 Homodimers (Where T = C, Si, and Ge; and X = F, cl, and Br) Gleaned from SAPT-EDA

homodimer	Eelst	Edisp	Eind	Eexch	ESAPT2	Eelst	Edisp	Eind	Eexch	ESAPT2
	tetrel···tetrel					tetrel···halogen
(F-C-F3)2	–0.03	–1.24	–0.02	0.66	–0.64	–0.16	–0.87	–0.03	0.55	–0.51
(Cl-C-Cl3)2	–1.63	–5.91	–0.23	4.53	–3.24	–0.92	–3.64	–0.28	2.70	–2.13
(Br-C-Br3)2	–2.21	–7.95	–0.35	6.40	–4.12	–1.54	–5.24	–0.57	4.31	–3.04
(F-Si-F3)2	0.39	–0.51	–0.02	0.08	–0.06	–1.02	–1.18	–0.19	1.32	–1.07
(Cl-Si-Cl3)2	–1.44	–6.16	–0.22	4.40	–3.42	–0.58	–3.31	–0.19	2.26	–1.81
(Br-Si-Br3)2	–2.28	–8.69	–0.36	6.73	–4.60	–0.99	–4.74	–0.34	3.48	–2.59
(F-Ge-F3)2	noa	noa	noa	noa	noa	–1.44	–1.49	–0.37	1.89	–1.41
(Cl-Ge-Cl3)2	–1.42	–6.41	–0.24	4.57	–3.50	–0.57	–3.52	–0.22	2.42	–1.89
(Br-Ge-Br3)2	–2.28	–8.92	–0.37	6.85	–4.72	–0.99	–5.06	–0.39	3.77	–2.68
	type III halogen···halogen					type II halogen···halogen
(F-C-F3)2	–0.07	–0.47	–0.01	0.28	–0.28	–0.21	–0.92	–0.03	0.61	–0.55
(Cl-C-Cl3)2	0.17	–1.84	–0.23	1.09	–0.80	–1.36	–4.13	–0.41	3.55	–2.35
(Br-C-Br3)2	0.42	–2.70	–0.51	1.76	–1.03	–2.50	–6.33	–1.06	6.42	–3.48
(F-Si-F3)2	0.07	–0.28	–0.01	0.12	–0.09	–0.72	–0.99	–0.12	0.92	–0.92
(Cl-Si-Cl3)2	–0.21	–1.54	–0.11	1.01	–0.85	–0.82	–3.25	–0.21	2.38	–1.90
(Br-Si-Br3)2	–0.20	–2.31	–0.28	1.64	–1.15	–1.32	–4.66	–0.43	3.74	–2.66
(F-Ge-F3)2	0.08	–0.35	–0.02	0.18	–0.11	–0.91	–1.13	–0.20	1.13	–1.10
(Cl-Ge-Cl3)2	–0.27	–1.77	–0.16	1.27	–0.94	–0.96	–3.48	–0.27	2.70	–2.01
(Br-Ge-Br3)2	–0.26	–2.64	–0.38	2.01	–1.27	–1.51	–4.97	–0.54	4.21	–2.81

No local energy minimum was observed in the corresponding PES curve (see Figure ).

SAPT-EDA results collected in Table addressed the dispersion forces (Edisp) as the most prominent physical term that contributed to the total binding energies for all the investigated configurations of the (X-T-X3)2 homodimers. Conspicuously, the Edisp contribution became more striking as the atomic size of the interacted halogens increased in line with the binding energy pattern. For instance, for tetrel···tetrel configuration of the (X-C-X3)2 homodimers, the Edisp values were −1.24, −5.91, and −7.95 kcal/mol for (F-C-F3)2, (Cl-C-Cl3)2, and (Br-C-Br3)2 with binding energies of −0.60, −2.99, and −3.96 kcal/mol, respectively.

Evidently, electrostatic forces had an indispensable contribution to the total binding energies of the (X-T-X3)2 homodimers within tetrel···tetrel, tetrel···halogen, and type II halogen···halogen configurations (Table ). In comparison, a weak electrostatic contribution was denoted for the type III halogen···halogen configurations, which agrees with the reported SAPT-EDA results for the type III halogen···halogen complexes.[43] For instance, the Eelst exhibited values of −1.44, −0.58, −0.21, and −0.82 for the (Cl-Si-Cl3)2 homodimers within the tetrel···tetrel, tetrel···halogen, type III halogen···halogen, and type II halogen···halogen configurations, respectively. The aforesaid Eelst pattern showed general accordance with the favorable precedence of tetrel···tetrel configurations over the rest of explored counterparts. Little contribution for induction term (Eind) was seen whereas ignored one was relevant to the repulsive Eexch forces.

In accordance with the literature, a slight difference was detected between the MP2 and total SAPT2 energies, which was presumably ascribed to the difference in the description of the two variant utilized computational levels.[65,66]

CSD Survey

To elucidate the relative experimental importance of the tetrel- and halogen-bonding interactions, the Cambridge Structural Database (CSD) was thoroughly explored for the (X-T-X3)2 homodimers within the tetrel···tetrel, tetrel···halogen, type III halogen···halogen, and type II halogen···halogen configurations. The CSD survey disclosed crystal structures with the standard geometric requirements for designed configurations except for type II halogen···halogen (see Computational Methodology section for details). A visual representation of the obtained CSD models can be seen in Figure.

Figure 7

Interactions of tetrel···tetrel, tetrel···halogen, and type III halogen···halogen configurations in crystal structures. Systems were truncated for better visualization.

As can be seen from Figure, interactions within tetrel···tetrel, tetrel···halogen, and type III halogen···halogen configurations were observed in BODBUT, TERQIQ03, and BEPZED hits, respectively. Clear reliability was accordingly unveiled for the explored interactions within the modeled configurations.

Conclusions

A thorough investigation was conducted to assess the versatility of the tetrel- and halogen-containing molecules to engage in tetrel- and halogen-based interactions within tetrel···tetrel, tetrel···halogen, type III halogen···halogen, and type II halogen···halogen configurations. MEP analyes claimed the occurrence of obvious σ-holes over the molecular surfaces of all the selected tetrel- and halogen-containing molecules with variable sizes and magnitudes. Evidently, PoC calculations revealed the electrostatic potentiality of almost all the studied monomers to favorably interact as Lewis acid and base centers with negatively and positively charged points, respectively. Preeminent negative binding energies were preferentially noted for almost all the inspected homodimers, demonstrating the tendency of the considered molecular systems to engage in the explored interactions within the designed configurations. Generally, the (X-T-X3)2 homodimers within the tetrel···tetrel configuration were recognized with the most substantial binding energies followed by type II halogen···halogen, tetrel···halogen, and finally, type III halogen···halogen configurations. SAPT-EDA results affirmed that the binding energies of the investigated interactions were governed by the dispersion forces. Therefore, the results of the current study provide a convincing affirmation for advancing the understanding of the tetrel- and halogen-bonding interactions via variant configurations that may be helpful in the forthcoming studies in the materials science and crystal engineering.

Computational Methodology

The potentiality of the X-T-X3 model (where T = C, Si, and Ge, and X = F, Cl, and Br) to engage in tetrel- and halogen-based interactions within tetrel···tetrel, tetrel···halogen, type III halogen···halogen, and type II halogen···halogen configurations was comparatively investigated (see Figure ). Geometrical optimization was first performed for the studied monomers at the MP2/aug-cc-pVTZ (with PP functions for Ge and Br) level of theory.[67−70] On the optimized monomers, MEP maps were generated and plotted onto 0.002 au electron density contours. Along with that, maximum positive electrostatic potential (Vs,max) calculations were carried out with the help of Multiwfn 3.5 software.[71]±σ-hole tests were also invoked via the incorporation of the PoC approach to assess the electrostatic potentiality of the X-T-X3 molecules to participate in the tetrel- and halogen-based interactions.[55,72,73] In the ±σ-hole tests, the effect of T/X···PoC distance was investigated within a distance range of 2.5–5.5 Å along the x-axis with a step size of 0.1 Å and X-T···/T-X···PoC angle of 180° in the presence of ±0.50 au PoCs (see Figure ). Molecular stabilization energies (Estabilization) of the tetrel··· and halogen···PoC systems were estimated as follows:

To pursue the aim of the current study, the optimized monomers were placed in a way to form a staggered form of tetrel···tetrel, tetrel···halogen, type III halogen···halogen, and type II halogen···halogen homodimers (see Figure ). PES scan was then performed for all the investigated homodimers at a distance ranging from 2.5 to 5.5 Å in the x-direction of the σ-atom with a step size of 0.1 Å. No vibrational frequency calculations were executed for the inspected complexes, giving the possibility that the such structures were not energetic minima. With this in mind, binding energies were estimated as the difference between the energy of the complex and the sum of energies of its monomers. The computed binding energies were corrected from the basis set superposition error via the counterpoise correction procedure.[74] Moreover, the CCSD(T)/CBS binding energies (ECCSD(T)/CBS) were computed for the studied homodimers solely at the most favorable distance as follows:[75]where

To firmly investigate the nature of interactions within the tetrel···tetrel, tetrel···halogen, and halogen···halogen configurations, the QTAIM was incorporated.[62] Through QTAIM, BCPs were identified, and BPs were generated. In addition, the characteristics of BCPs were investigated through a diversity of topological parameters, including electron density (ρb), Laplacian (∇2ρb), and total energy density (Hb). NCI index analysis was also established, and the corresponding NCI plots were depicted.[63] QTAIM and NCI index analyses were executed using Multiwfn 3.5 software[71] and the related plots were graphed with the help of Visual Molecular Dynamics software.[76]

Toward a more in-depth insight into the energetic origin of the considered interactions, SAPT-EDA was performed at the SAPT2 level of truncation using a truncated aug-cc-PVTZ basis set with the help of the PSI4 code.[77,78] The total SAPT2 binding energy for the studied homodimers was estimated as the sum of the electrostatic (Eelst), dispersion (Edisp), induction (Eind), and exchange energy (Eexch) according to the following equation:[79]where

MEP analysis, ±σ-hole tests, PES scan, QTAIM, and NCI analysis calculations were executed at the MP2/aug-cc-pVTZ (with PP functions for Ge and Br) level of theory. Gaussian 09 software was adopted to carry out all geometrical optimizations and energy calculations.[80] The CSD version 5.41,[81,82] (updates November 2019) survey was ultimately devoted to unveiling the manifestation of the studied interactions in crystal structures. In the CSD survey, the intermolecular distances and angles were defined using the ″3D″ function of Conquest.[83]