Noncovalent Bonds between Tetrel Atoms

Attraction versus Repulsion between Methyl and Related Groups: (CH3NHCH3)2 and (CH3SeBr2CH3)2

The starting point for this work was a set of crystal structures containing the motif of interaction between methyl groups in homodimers. Two structures were selected for which QTAIM, NCI and NBO analyses suggested an attractive interaction. However, the calculated interaction energy was negative for only one of these systems. The ability of methyl groups to interact with one another is then examined by DFT calculations. A series of (CH3PnHCH3)2 homodimers were allowed to interact with each other for a range of Pn atoms N, P, As, and Sb. Interaction energies of these C⋅⋅⋅C tetrel-bonded species were below 1 kcal/mol, but could be raised to nearly 3 kcal/mol if the C atom was changed to a heavier tetrel. A strengthening of the C⋅⋅⋅C intermethyl bonds can also be achieved by introducing an asymmetry via an electron-withdrawing substituent on one unit and a donor on the other. The attractions between the methyl and related groups occur in spite of a coulombic repulsion between σ-holes on the two groups. NBO, AIM, and NCI tools must be interpreted with caution as they can falsely suggest bonding when the potentials are repulsive.

σ-Hole, lone-pair-hole, and π-hole site-based interactions in aerogen-comprising complexes: a comparative study

Herein, the potential of ZO3 and ZF2 aerogen-comprising molecules (where Z = Ar, Kr, and Xe) to engage in σ-, lp-, and π-hole site-based interactions was comparatively studied using various ab initio computations. For the first time, a premier in-depth elucidation of the external electric field (EEF) influence on the strength of the σ-, lp-, and π-hole site-based interactions within the ZO3/ZF2⋯NH3 and ⋯NCH complexes was addressed using oriented EEF with disparate magnitude. Upon the energetic features, σ-hole site-based interactions were noticed with the most prominent preferability in comparison to lp- and π-hole analogs. This finding was ensured by the negative interaction energy values of -11.65, -3.50, and -2.74 kcal mol-1 in the case of σ-, lp-, and π-hole site-based interactions within the XeO3⋯ and XeF2⋯NH3 complexes, respectively. Detailedly, the strength of the σ- and lp-hole site-based interactions directly correlated with the atomic size of the aerogen atoms and the magnitude of the positively oriented EEF. Unexpectedly, an irregular correlation was noticed for the interaction energies of the π-hole site-based interactions with the size of the π-hole. Interestingly, the π-hole site-based interactions within Kr-comprising complexes exhibited higher negative interaction energies than the Ar- and Xe-comprising counterparts. Notwithstanding, a direct proportion between the interaction energies of the π-hole site-based interactions and π-hole size was obtained by employing EEF along the positive orientation with high strength. The present outcomes would be a fundamental basis for forthcoming progress in studying the σ-, lp-, and π-hole site-based interactions within aerogen-comprising complexes and their pertinent applications in materials science and crystal engineering.

Transition from covalent to noncovalent bonding between tetrel atoms

The strength and nature of the bonding between tetrel (T) atoms in R2T⋯TR2 is examined by quantum calculations. T atoms cover the range of Group 14 atoms from C to Pb, and substituents R include Cl, F, and NH2. Systems vary from electrically neutral to both positive and negative overall charged radicals. There is a steady weakening progression in T-T bond strength as the tetrel atom grows larger, transitioning smoothly from a strong covalent to a much weaker noncovalent bond for the larger T atoms. The latter have some of the characteristics of a ditetrel bond, but there are also significant deviations from a classic bond of this type. The T2Cl4- anions are more strongly bonded than the corresponding cations, which are in turn stronger than the neutrals.

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

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

Types of noncovalent bonds within complexes of thiazole with CF4 and SiF4

The five-membered heteroaromatic thiazole molecule contains a number of electron-rich regions that could attract an electrophile, namely the N and S lone pairs that lie in the molecular plane, and π-system areas above the plane. The possibility of each of these sites engaging in a tetrel bond (TB) with CF4 and SiF4, as well as geometries that encompass a CH⋯F H-bond, was explored via DFT calculations. There are a number of minima that occur in the pairing of thiazole with CF4 that are very close in energy, but these complexes are weakly bound by less than 2 kcal mol-1 and the presence of a true TB is questionable. The inclusion of zero-point vibrational energies alters the energetic ordering, which is further modified when entropic effects are added. The preferred geometry would thus be sensitive to the temperature of an experiment. Replacement of CF4 by SiF4 leaves intact most of the configurations, and their tight energetic clustering, the ordering of which is again altered as the temperature rises. But there is one exception in that by far the most tightly bound complex involves a strong Si⋯N TB between SiF4 and the lone pair of the thiazole N, with an interaction energy of 30 kcal mol-1. Even accounting for its high deformation energy and entropic considerations, this structure remains as clearly the most stable at any temperature.

Heavy pnicogen atoms as electron donors in sigma-hole bonds

DFT calculations evaluate the strength of σ-hole bonds formed by ZH3 and ZMe3 (Z = N, P, As, Sb) acting as electron donor. Bond types considered include H-bond, halogen, chalcogen, pnicogen, and tetrel bond to perfluorinated Lewis acids FH, FBr, F2Se F3As, F4Ge, respectively, as well as their monofluorinated analogues. All of the Z atoms can engage in bonds of at least moderate strength, varying from 3 to more than 40 kcal mol-1. In most cases, N forms the strongest bonds, but the falloff from P to Sb is quite mild. However, this pattern is not characteristic of all cases, as for example in the halogen bonds, where the heavier Z atoms are comparable to, or even stronger than N. Most of the bonds are strengthened by replacing the three H atoms of ZH3 by methyl groups, better simulating the situation that would be generally encountered. Structural and NMR shielding data ought to facilitate the identification of these bonds within crystals or in solution.

Influence of Internal Noncovalent Bonds on Rotational Dynamics

While a good deal of information has accumulated concerning the manner in which an intramolecular noncovalent bond can affect the relative energies of various conformers, less is known about how such bonds might affect the dynamics of interconversion between them. A series of molecules are constructed in which symmetrically equivalent conformers containing a noncovalent bond can be interconverted by a bond rotation, the energy barrier to which is computed by quantum chemical methods. The rotation of a CF3 group attached to a phenyl ring is speeded up if a Se··F chalcogen bond can be formed with a SeH or SeF group placed in an ortho position, a bond that is present in and stabilizes the rotational transition state. The analogous SnF3 group can, on the other hand, engage in a Sn··Se tetrel bond in its global minimum. The energetic cost of breakage of this bond is not fully compensated by the appearance of a Se··F chalcogen bond in the rotational transition state. Other systems were designed by placing two phenyl rings on opposite ends of an octahedrally disposed SeF4 group. A high barrier inhibits their rotation with bulky Br atoms in ortho positions, but this barrier is lowered if Br is replaced by groups that can engage in either chalcogen (SeH or SeF) or pnicogen (AsH2) bonds with the F atoms in the rotational transition state. The barrier reduction is closely related to the strength of these noncovalent bonds.

Stabilizing σ-hole Dimethyl Interactions

Methyl groups bound to electronegative atoms, such as N or O, are recognized to participate in tetrel bonding as Lewis acids. On the other hand, the capability of methyl groups bound to electropositive atoms, such as B or Al, to act as Lewis bases has been recently reported. Herein, we analyze the combination of these two behaviors to establish attractive methyl···methyl interactions. We have explored the Cambridge Structural Database to find experimental examples of these dimethyl-bound systems, finding a significant degree of directionality in the relative disposition of the two methyl groups. Moreover, we have carried out a comprehensive computational analysis at the DFT level of the dimethyl interactions, including the natural bond orbital, energy decomposition analysis, and topological analysis of the electron density (QTAIM and NCI). The dimethyl interaction is characterized as weak yet attractive and based on electrostatics, with a non-negligible contribution from orbital charge transfer and polarization.

Effects of Lewis Basicity and Acidity on σ-Hole Interactions in Carbon-Bearing Complexes: A Comparative Ab Initio Study

The effects of Lewis basicity and acidity on σ-hole interactions were investigated using two sets of carbon-containing complexes. In Set I, the effect of Lewis basicity was studied by substituting the X3/X atom(s) of the NC-C6H2-X3 and NCX Lewis bases (LB) with F, Cl, Br, or I. In Set II, the W-C-F3 and F-C-X3 (where X and W = F, Cl, Br, and I) molecules were utilized as Lewis acid (LA) centers. Concerning the Lewis basicity effect, higher negative interaction energies (Eint) were observed for the F-C-F3∙∙∙NC-C6H2-X3 complexes compared with the F-C-F3∙∙∙NCX analogs. Moreover, significant Eint was recorded for Set I complexes, along with decreasing the electron-withdrawing power of the X3/X atom(s). Among Set I complexes, the highest negative Eint was ascribed to the F-C-F3∙∙∙NC-C6H2-I3 complex with a value of -1.23 kcal/mol. For Set II complexes, Eint values of F-C-X3 bearing complexes were noted within the -1.05 to -2.08 kcal/mol scope, while they ranged from -0.82 to -1.20 kcal/mol for the W-C-F3 analogs. However, Vs,max quantities exhibited higher values in the case of W-C-F3 molecules compared with F-C-X3; preferable negative Eint were ascribed to the F-C-X3 bearing complexes. These findings were delineated as a consequence of the promoted contributions of the X3 substituents. Dispersion forces (Edisp) were identified as the dominant forces for these interactions. The obtained results provide a foundation for fields such as crystal engineering and supramolecular chemistry studies that focus on understanding the characteristics of carbon-bearing complexes.

Experimental and Theoretical Evidence of a Pb⋅⋅⋅Pb Ditetrel Bond Without a σ-Hole

The crystal structure of a newly synthesized compound, [PbL(Ac)]₂ , (where L=2 (amino(pyrazin-2-yl) methylene) hydrazinecarbothioamide, Ac=acetate anion) exhibits a close contact between pairs of Pb atoms, suggesting a ditetrel bond, in addition to two Pb⋅⋅⋅O tetrel bonds, and two C-H⋅⋅⋅O H-bonds. The presence of this ditetrel bond as an attractive component is confirmed by various quantum chemical methods. This novelty of this particular bond is its existence even in the absence of a σ-hole on the Pb atom, which is typically considered a prerequisite for a bond of this type. From a wider perspective, a survey of the Cambridge Structural Database suggests this bond may be more common than was hitherto thought, with 44 examples of Pb⋅⋅⋅Pb contacts amongst a total number of 219 examples of T⋅⋅⋅T interactions in general (T=Si, Ge, Sn, Pb).

External Electric Field Effect on the Strength of σ-Hole Interactions: A Theoretical Perspective in Like⋯Like Carbon-Containing Complexes

For the first time, σ-hole interactions within like⋯like carbon-containing complexes were investigated, in both the absence and presence of the external electric field (EEF). The effects of the directionality and strength of the utilized EEF were thoroughly unveiled in the (F-C-F₃)₂, (F-C-H₃)₂, and (H-C-F₃)₂ complexes. In the absence of the EEF, favorable interaction energies, with negative values, are denoted for the (F-C-F₃)₂ and (H-C-F₃)₂ complexes, whereas the (F-C-H₃)₂ complex exhibits unfavorable interactions. Remarkably, the strength of the applied EEF exhibits a prominent role in turning the repulsive forces within the latter complex into attractive ones. The symmetrical nature of the considered like⋯like carbon-containing complexes eradicated the effect of directionality of the EEF. The quantum theory of atoms in molecules (QTAIM), and the noncovalent interaction (NCI) index, ensured the occurrence of the attractive forces, and also outlined the substantial contributions of the three coplanar atoms to the total strength of the studied complexes. Symmetry-adapted perturbation theory (SAPT) results show the dispersion-driven nature of the interactions.

σ-Hole and LP-Hole Interactions of Pnicogen···Pnicogen Homodimers under the External Electric Field Effect: A Quantum Mechanical Study

σ-Hole and lone-pair (lp)-hole interactions within σ-hole···σ-hole, σ-hole···lp-hole, and lp-hole···lp-hole configurations were comparatively investigated on the pnicogen···pnicogen homodimers (PCl3)2, for the first time, under field-free conditions and the influence of the external electric field (EEF). The electrostatic potential calculations emphasized the impressive versatility of the examined PCl3 monomers to participate in σ-hole and lp-hole pnicogen interactions. Crucially, the sizes of σ-hole and lp-hole were enlarged under the influence of the positively directed EEF and decreased in the case of reverse direction. Interestingly, the energetic quantities unveiled more favorability of the σ-hole···lp-hole configuration of the pnicogen···pnicogen homodimers, with significant negative interaction energies, than σ-hole···σ-hole and lp-hole···lp-hole configurations. Quantum theory of atoms in molecules and noncovalent interaction index analyses were adopted to elucidate the nature and origin of the considered interactions, ensuring their closed shell nature and the occurrence of attractive forces within the studied homodimers. Symmetry-adapted perturbation theory-based energy decomposition analysis alluded to the dispersion force as the main physical component beyond the occurrence of the examined interactions. The obtained findings would be considered as a fundamental underpinning for forthcoming studies pertinent to chemistry, materials science, and crystal engineering.

Effect of External Electric Field on Tetrel Bonding Interactions in (FTF3···FH) Complexes (T = C, Si, Ge, and Sn)

A quantum chemical study was accomplished on the σ-hole interactions of the barely explored group IV elements, for the first time, in the absence and presence of the positively and negatively directed external electric field (EEF). The analyses of molecular electrostatic potential addressed the occurrence of the σ-hole on all the inspected tetrel atoms, confirming their salient versatility to engage in σ-hole interactions. MP2 energetic findings disclosed the occurrence of favorable σ-hole interactions within the tetrel bonding complexes. The tetrel bonding interactions became stronger in the order of C < Si < Ge < Sn for F-T-F3···FH complexes with the largest interaction energy amounting to -19.43 kcal/mol for the optimized F-Sn-F3···FH complex under the influence of +0.020 au EEF. The interaction energy conspicuously evolved by boosting the magnitude of the positively directed EEF value and declining the negatively directed EEF one. The decomposition analysis for the interaction energies was also executed in terms of symmetry-adapted perturbation theory, illuminating the dominant electrostatic contribution to all the studied complexes' interactions except carbon-based interactions controlled by dispersion forces. The outcomes that emerged from the current work reported significantly how the direction and strength of the EEF affect the tetrel-bonding interactions, leading to further improvements in the forthcoming studies of supramolecular chemistry and materials science.

Molecular Electrostatic Potential and Noncovalent Interactions in Derivatives of Group 8 Elements

This communication reports experimental and theoretical evidences of σ‐hole interactions in adducts between nitrogen or oxygen nucleophiles and tetroxides of osmium or other group 8 elements. Cocrystals between pyridine or pyridine N‐oxide derivatives and osmium tetroxide are characterized through various techniques and rationalized as σ‐hole interactions using DFT calculations and several other computational tools. We propose the term “osme bond” (OmB, Om=Fe, Ru, Os, (Hs)) for naming the noncovalent interactions wherein group 8 elements have the role of the electrophile. The word osme is the transcription of ὀσμή, the ancient Greek word for smell that was used to name the heaviest group 8 element in relation to the smoky odor of its tetroxide.

Quantification of the electric field inside protein active sites and fullerenes

While electrostatic interactions are exceedingly accountable for biological functions, no simple method exists to directly estimate or measure the electrostatic field in protein active sites. The electrostatic field inside the protein is generally inferred from the shift in the vibrational stretching frequencies of nitrile and thionitrile probes at the active sites through several painstaking and time-consuming experiments like vibrational Stark effect spectroscopy (VSS). Here we present a simple, fast, and reliable methodology, which can efficiently predict the vibrational Stark tuning rates (VSRs) of a large variety of probes within 10% error of the reported experimental data. Our methodology is based on geometry optimization and frequency calculations in the presence of an external electric field to predict the accurate VSR of newly designed nitrile/thionitrile probes. A priori information of VSRs is useful for difficult experiments such as catalytic/enzymatic study and in structural biology. We also applied our methodology successfully to estimate the electric field inside fullerenes and nano-onions, which is encouraging for researchers to adopt it for further applications in materials science and supramolecular chemistry.

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.

Competition between Inter and Intramolecular Tetrel Bonds: Theoretical Studies Complemented by CSD Survey

Crystal structures document the ability of a TF₃ group (T=Si, Ge, Sn, Pb) situated on a naphthalene system to engage in an intramolecular tetrel bond (TB) with an amino group on the adjoining ring. Ab initio calculations evaluate the strength of this bond and evaluate whether it can influence the ability of the T atom to engage in a second, intermolecular TB with another nucleophile. A very strong CN^- anionic base can approach the T either along the extension of a T-C or T-F bond and form a strong TB with an interaction energy approaching 100 kcal/mol, although this bond is weakened a bit by the presence of the internal T⋅⋅⋅N bond. The much less potent NCH base engages in a correspondingly longer and weaker TB, less than 10 kcal/mol. Such an intermolecular TB is weakened by the presence of the internal TB, to the point that it only occurs for the two heavier tetrel atoms Sn and Pb.

Relative Strengths of a Pnicogen and a Tetrel Bond and Their Mutual Effects upon One Another

The ability of the T and Z atoms of TR₃ZR₂ to engage in a noncovalent interaction with NH₃ is assessed by DFT calculations, where the T atom refers to C, Si, and Ge; Z = As, Sb, and P; and substituents R = H and F. In most instances, the tetrel bond (TB) is both stronger and shorter than the pnicogen bond (ZB). These two bond strengths can be equalized, or preference shifted to the ZB, if F substituents are placed on the Z and H on the T atoms. Employing C as the T atom results in a very weak TB, with the ZB clearly favored energetically. The simultaneous formation of both TB and ZB weakens both, particularly the latter, but both bonds survive intact. Geometric and spectroscopic perturbations of the subunits reflect the two types of noncovalent bonds.

DFT and IsoStar Analyses to Assess the Utility of σ- and π-Hole Interactions for Crystal Engineering

The interpretation of 36 charge neutral 'contact pairs' from the IsoStar database was supported by DFT calculations of model molecules 1-12, and bimolecular adducts thereof. The 'central groups' are σ-hole donors (H2 O and aromatic C-I), π-hole donors (R-C(O)Me, R-NO2 and R-C6 F5 ) and for comparison R-C6 H5 (R=any group or atom). The 'contact groups' are hydrogen bond donors X-H (X=N, O, S, or R2 C, or R3 C) and lone-pair containing fragments (R3 C-F, R-C≡N and R2 C=O). Nearly all the IsoStar distributions follow expectations based on the electrostatic potential of the 'central-' and 'contact group'. Interaction energies (ΔEBSSE ) are dominated by electrostatics (particularly between two polarized molecules) or dispersion (especially in case of large contact area). Orbital interactions never dominate, but could be significant (∼30 %) and of the n/π→σ*/π* kind. The largest degree of directionality in the IsoStar plots was typically observed for adducts more stable than ΔEBSSE ≈-4 kcal⋅mol-1 , which can be seen as a benchmark-value for the utility of an interaction in crystal engineering. This benchmark could be met with all the σ- and π-hole donors studied.

Origins and properties of the tetrel bond

The tetrel bond (TB) recruits an element drawn from the C, Si, Ge, Sn, Pb family as electron acceptor in an interaction with a partner Lewis base. The underlying principles that explain this attractive interaction are described in terms of occupied and vacant orbitals, total electron density, and electrostatic potential. These principles facilitate a delineation of the factors that feed into a strong TB. The geometric deformation that occurs within the tetrel-bearing Lewis acid monomer is a particularly important issue, with both primary and secondary effects. As a first-row atom of low polarizability, C is a reluctant participant in TBs, but its preponderance in organic and biochemistry make it extremely important that its potential in this regard be thoroughly understood. The IR and NMR manifestations of tetrel bonding are explored as spectroscopy offers a bridge to experimental examination of this phenomenon. In addition to the most common σ-hole type TBs, discussion is provided of π-hole interactions which are a result of a common alternate covalent bonding pattern of tetrel atoms.