Systematic Elucidation of Factors That Influence the Strength of Tetrel Bonds

Tetrel Bonding of the Carbenium Ion Forms a Pentacoordinate Carbon Atom

As a flat trigonal species, the CR3 + carbenium ion contains a pair of deep π-holes above and below its molecular plane. In the case of CH3 + a first base will form a covalent bond with the central C, making the combined species tetrahedral. Approach of a second base to the opposite side results in a longer but rather strong noncovalent tetrel bond (TB). While CMe3 + can also form a similar asymmetric complex with a pair of bases, it also has the capacity to form a pair of nearly equivalent TBs, such that the resulting symmetric trigonal bipyramid configuration is only slightly higher in energy. When the three substituents on the central C are phenyl rings, the symmetric configuration with two TBs predominates. These tetrel bonds are quite strong, reaching up to 20 kcal/mol. Adding OPH2 or OCH substituents to the phenyl rings permits the formation of intramolecular C⋅⋅O TBs to the central C, very similar in many respects to the case where these TBs are intermolecular.

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.

Metal-Induced Enhancement of Tetrel Bonding. The Case of C⋅⋅⋅X-IrIII (X=Cl, Br) Tetrel Bond Involving a Methyl Group

In X-ray structures of the isomorphic mer-[IrX3(THT)(CNXyl)2] (X=Cl 1, Br 2; THT=tetrahydrothiophene; Xyl=2,6-Me2C6H3-) complexes, we revealed short intermolecular contacts between the C-atom of an isocyanide methyl group and halide ligands of another molecule. Geometrical consideration of the X-ray data and analysis of appropriate DFT studies allowed the attribution of these contacts to CMe⋅⋅⋅X-IrIII (X=Cl, Br) tetrel bond. Specifically, through the application of DFT calculations and various theoretical models, the presence of tetrel bonding interactions was validated, and the contribution of the CMe⋅⋅⋅X-IrIII interaction was assessed. The reinforcement of the tetrel bond upon the isocyanide coordination to iridium(III) is substantiated by molecular electrostatic potential (MEP) surface calculations. To distinguish the tetrel bonding characteristics of CMe⋅⋅⋅X-IrIII (X=Cl, Br) interactions from conventional hydrogen bonding, we employed multiple computational methodologies, including Natural Bond Orbital (NBO) analysis and Electron Localization Function (ELF) analysis. Additionally, Energy Decomposition Analysis (EDA) was applied to selected model systems to explore the underlying physical nature of these interactions.

Exploring the Structural Attributes of Yoda1 for the Development of New-Generation Piezo1 Agonist Yaddle1 as a Vaccine Adjuvant Targeting Optimal T Cell Activation

Piezo1, a mechano-activated ion channel, has wide-ranging physiological and therapeutic implications, with the ongoing development of specific agonists unveiling cellular responses to mechanical stimuli. In our study, we systematically analyzed the chemical subunits in Piezo1 protein agonist Yoda1 to comprehend the structure-activity relationship and push forward next-generation agonist development. Preliminary screening assays for Piezo1 agonism were performed using the Piezo1-mCherry-transfected HEK293A cell line, keeping Yoda1 as a positive control. We introduce a novel Piezo1 agonist Yaddle1 (34, 0.40 μM), featuring a trifluoromethyl group, with further exploration through in vitro studies and density functional theory calculations, emphasizing its tetrel interactions, to act as an ambidextrous wedge between the domains of Piezo1. In contrast to the poor solubility of the established agonist Yoda1, our results showed that the kinetic solubility of Yaddle1 (26.72 ± 1.8 μM at pH 7.4) is 10-fold better than that of Yoda1 (1.22 ± 0.11 μM at pH 7.4). Yaddle1 (34) induces Ca2+ influx in human CD4+ T cell, suggesting its potential as a vaccine adjuvant for enhanced T cell activation.

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.

Double Centrosymmetric Si···π Tetrel Bonds as New Synthons─Evidence from Crystal Structures and DFT Calculations

The crystal structure of bis((μ2-ethynylsilyloxo)-dichloro-aluminum), BEDCA, and a few related structures are characterized by the occurrence of tetrel bonds that link molecules. Particularly, centosymmetric dimers in such structures occur that are connected by two equivalent Si···π tetrel bonds. The dimer of BEDCA and dimers of other model species that similarly are linked by two equivalent Si···π tetrel bonds are analyzed theoretically. Some of the complexes calculated here are also characterized by the occurrence of triel bonds. Thus, ωB97XD/aug-cc-pVTZ calculations are performed and these DFT results are further supported by calculations with the use of other theoretical approaches: the quantum theory of atoms in molecules, QTAIM; the natural bond orbital, NBO; the energy decomposition analysis, EDA; and the noncovalent interactions method, NCI. The results show that the tetrel bonds analyzed here are rather weak, and they are not detected by the QTAIM approach; however, they are detected by other approaches, like NBO, for example. On the other hand, the triel bonds that occur in a few complexes discussed here are very strong and possess characteristics of covalent bonds.

Revisiting conventional noncovalent interactions towards a complete understanding: from tetrel to pnicogen, chalcogen, and halogen bond

Typical noncovalent interactions, including tetrel (TtB), pnicogen (PniB), chalcogen (ChalB), and halogen bonds (HalB), were systematically re-investigated by modeling the N⋯Z interactions (Z = Si, P, S, Cl) between NH3 - as a nucleophilic, and SiF4, PF3, SF2, and ClF - as electrophilic components, employing highly reliable ab initio methods. The characteristics of N⋯Z interactions when Z goes from Si to Cl, were examined through their changes in stability, vibrational spectroscopy, electron density, and natural orbital analyses. The binding energies of these complexes at CCSD(T)/CBS indicate that NH3 tends to hold tightly most with ClF (-34.7 kJ mol-1) and SiF4 (-23.7 kJ mol-1) to form N⋯Cl HalB and N⋯Si TtB, respectively. Remarkably, the interaction energies obtained from various approaches imply that the strength of these noncovalent interactions follows the order: N⋯Si TtB > N⋯Cl HalB > N⋯S ChalB > N⋯P PniB, that differs the order of their corresponding complex stability. The conventional N⋯Z noncovalent interactions are characterized by the local vibrational frequencies of 351, 126, 167, and 261 cm-1 for TtB, PniB, ChalB, and HalB, respectively. The SAPT2+(3)dMP2 calculations demonstrate that the primary force controlling their strength retains the electrostatic term. Accompanied by the stronger strength of N⋯Si TtB and N⋯Cl HalB, the AIM and NBO results state that they are partly covalent in nature with amounts of 18.57% and 27.53%, respectively. Among various analysis approaches, the force constant of the local N⋯Z stretching vibration is shown to be most accurate in describing the noncovalent interactions.

The Tetrel Bonds of Hypervalent Halogen Compounds

The tetrel bond between PhXF2Y(TF3) (T = C and Si; X = Cl, Br, and I; Y = F and Cl) and the electron donor MCN (M = Li and Na) was investigated at the M06-2X/aug-cc-pVDZ level of theory. As the electronegativity of the halogen atom X increases, the strength of the tetrel bond also increases, but as the electronegativity of the halogen atom Y increases, the strength of the tetrel bond decreases. The magnitude of the interaction energy in most -CF3 complexes was found to be less than 10 kcal/mol, but to exceed 11 kcal/mol for PhClF2Cl(CF3)⋯NCNa. The tetrel bond is greatly enhanced when the -SiF3 group interacts with LiCN or NaCN, with the largest interaction energy approaching 100 kcal/mol and displaying a covalent Si⋯N interaction. Along with this enhancement, the Si⋯N distance was found to be less than the X-Si bond length, the -SiF3 group to be closer to the N atom, and in most -SiF3 systems, the X-Si-F angle to be less than 90°; the -SiF3 group therefore undergoes inversion and complete transfer in some systems.

C∙∙∙O and Si∙∙∙O Tetrel Bonds: Substituent Effects and Transfer of the SiF3 Group

The tetrel bond (TB) between 1,2-benzisothiazol-3-one-2-TF3-1,1-dioxide (T = C, Si) and the O atom of pyridine-1-oxide (PO) and its derivatives (PO-X, X = H, NO2, CN, F, CH3, OH, OCH3, NH2, and Li) is examined by quantum chemical means. The Si∙∙∙O TB is quite strong, with interaction energies approaching a maximum of nearly 70 kcal/mol, while the C∙∙∙O TB is an order of magnitude weaker, with interaction energies between 2.0 and 2.6 kcal/mol. An electron-withdrawing substituent on the Lewis base weakens this TB, while an electron-donating group has the opposite effect. The SiF3 group transfers roughly halfway between the N of the acid and the O of the base without the aid of cooperative effects from a third entity.

The Tetrel Bond and Tetrel Halide Perovskite Semiconductors

The ion pairs [Cs+•TtX3−] (Tt = Pb, Sn, Ge; X = I, Br, Cl) are the building blocks of all-inorganic cesium tetrel halide perovskites in 3D, CsTtX3, that are widely regarded as blockbuster materials for optoelectronic applications such as in solar cells. The 3D structures consist of an anionic inorganic tetrel halide framework stabilized by the cesium cations (Cs+). We use computational methods to show that the geometrical connectivity between the inorganic monoanions, [TtX3−]∞, that leads to the formation of the TtX64− octahedra and the 3D inorganic perovskite architecture is the result of the joint effect of polarization and coulombic forces driven by alkali and tetrel bonds. Depending on the nature and temperature phase of these perovskite systems, the Tt···X tetrel bonds are either indistinguishable or somehow distinguishable from Tt–X coordinate bonds. The calculation of the potential on the electrostatic surface of the Tt atom in molecular [Cs+•TtX3−] provides physical insight into why the negative anions [TtX3−] attract each other when in close proximity, leading to the formation of the CsTtX3 tetrel halide perovskites in the solid state. The inter-molecular (and inter-ionic) geometries, binding energies, and charge density-based topological properties of sixteen [Cs+•TtX3−] ion pairs, as well as some selected oligomers [Cs+•PbI3−]n (n = 2, 3, 4), are discussed.

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.

Structural, vibrational and electronic properties of some tetrel-bonded complexes of the fluorinated methanes methyl fluoride, difluoromethane and fluoroform: an ab initio study

A search has been conducted, by means of ab initio molecular orbital theory, for potential tetrel-bonded complexes formed between the fluorinated methanes methyl fluoride, difluoromethane and fluoroform, and the related hydrides ammonia, water, hydrogen fluoride, phosphine, hydrogen sulphide and hydrogen chloride. Eleven such complexes have been identified, six containing CH₃F and five CH₂F₂. The complexes are typically less strongly bound than their hydrogen-bonded counterparts, and the interaction energies vary in a consistent way with the periodic trend of the electron donors. The intermolecular separations and changes of the relevant intramolecular bond lengths, the wavenumber shifts of the critical vibrational modes and the extents of charge transfer correlate, by and large, with the strengths of interaction.

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.

Strongly Bound π-Hole Tetrel Bonded Complexes between H2SiO and Substituted Pyridines. Influence of Substituents

Ab initio calculation at the MP2/aug-cc-pVTZ level has been performed on the π-hole based N … Si tetrel bonded complexes between substituted pyridines and H 2 SiO. The primary aim of the study is to find out the effect of substitution on the strength and nature of this tetrel bond, and its similarity/difference with the N … C tetrel bond. Correlation between the strength of the N … Si bond and several molecular properties of the Lewis acid (H 2 SiO) and base (pyridines) are explored. The properties of the tetrel bond are analyzed using AIM, NBO, and symmetry-adapted perturbation theory calculations. The complexes are characterized with short N … Si intermolecular distances and high binding energies ranging between -142.72 and -115.37 kJ/mol. The high value of deformation energy indicates significant geometrical distortion of the monomer units. The AIM and NBO analysis reveal significant coordinate covalent  bond character of the N … Si π-hole bond.  Sharp differences are also noticed in the orbital interactions present in the N … Si and N … C tetrel bonds.

Unusual chalcogen⋯chalcogen interactions in like⋯like and unlike YCY⋯YCY complexes (Y = O, S, and Se)

Chalcogen⋯chalcogen interactions were investigated within four types of like⋯like and unlike YCY⋯YCY complexes (where Y = O, S, or Se). A plethora of quantum mechanical calculations, including molecular electrostatic potential (MEP), surface electrostatic potential extrema, point-of-charge (PoC), quantum theory of atoms in molecules (QTAIM), noncovalent interaction (NCI), and symmetry-adapted perturbation theory-based energy decomposition analysis (SAPT-EDA) calculations, were executed. The energetic findings revealed a preferential tendency of the studied chalcogen-bearing molecules to engage in type I, II, III, or IV chalcogen⋯chalcogen interactions. Notably, the selenium-bearing molecules exhibited the most potent ability to favorably participate in all the explored chalcogen⋯chalcogen interactions. Among like⋯like complexes, type IV interactions showed the most favorable negative binding energies, whereas type III interactions exhibited the weakest binding energies. Unexpectedly, oxygen-containing complexes within type IV interactions showed an alien pattern of binding energies that decreased along with an increase in the chalcogen atomic size level. QTAIM analysis provided a solo BCP, via chalcogen⋯chalcogen interactions, with no clues as to any secondary ones. SAPT-EDA outlined the domination of the explored interactions by the dispersion forces and indicated the pivotal shares of the electrostatic forces, except type III σ-hole⋯σ-hole and di-σ-hole interactions. These observations demonstrate in better detail all the types of chalcogen⋯chalcogen interactions, providing persuasive reasons for their more intensive use in versatile fields related to materials science and drug design.

Enhancement of tetrel bond involving tetrazole-TtR3 (Tt = C, Si; R = H, F). Promotion of SiR3 transfer by a triel bond

The combination of a CR3 (R = H, F) with a tetrazole can result in a moderate carbon bond, which can be further strengthened by a triel bond. On the other hand, SiR3 group is half transferred between the two N atoms in these conditions.

Maximal occupation by bases of π-hole bands surrounding linear molecules

Linear molecules such as CO₂ contain a positive π-hole ring that surrounds C on the molecule's equator. Quantum calculations examine the question as to how many bases can simultaneously bind to this ring. Linear molecules examined are TO₂ , where T = C, Si, Ge, Sn; bases are NCH and NH₃ . CO₂ engages in the weakest of the tetrel bonds, and can bind up to three NCH and two NH₃ . Unlike σ-hole tetrel bonds, Si forms the strongest tetrel bonds, with interaction energies as high as 43 kcal/mol with NH₃ . But like GeO₂ , SiO₂ can sustain only two bases in its equatorial ring. The π-hole ring of SnO₂ can engage in up to four tetrel bonds with either NCH or NH₃ , even though these bonds are weaker than those with GeO₂ or SiO₂ . As all of these complexes cast TO₂ in the role of multiple electron acceptor, the resulting negative cooperativity makes each successive bond weaker than its predecessor as bases are added, as well as reducing the magnitude of the central molecule's π-hole.

Enhancement of the Tetrel Bond by the Effects of Substituents, Cooperativity, and Electric Field: Transition from Noncovalent to Covalent Bond

The T⋅⋅⋅N tetrel bond (TB) formed between TX₃ OH (T=C, Si, Ge; X=H, F) and the Lewis base N≡CM (M=H, Li, Na) is studied by ab initio calculations at the MP2/aug-cc-pVTZ level. Complexes involving TH₃ OH contain a conventional TB with interaction energy less than 10 kcal/mol. This bond is substantially strengthened, approaching 35 kcal/mol and covalent character, when fluorosubstituted TF₃ OH is combined with NCLi or NCNa. Along with this enhanced binding comes a near equalization of the TB T⋅⋅⋅N and the internal T-O bond lengths, and the associated structure acquires a trigonal bipyramidal shape, despite a high internal deformation energy. This structural transformation becomes more complete, and the TB is further strengthened upon adding an electron acceptor BeCl₂ to the Lewis acid and a base to the NCM unit. This same TB strengthening can be accomplished also by imposition of an external electric field.

Comparison for Electron Donor Capability of Carbon-Bound Halogens in Tetrel Bonds

The tetrel bond formed by HC≡CX, H₂C=CHX, and H₃CCH₂X (X=F, Cl, Br, I) as an electron donor and TH₃F (T=C, Si, Ge) was explored by ab initio calculations. The tetrel bond formed by H₃CCH₂X is the strongest, as high as -3.45 kcal/mol for the H₃CCH₂F···GeH₃F dimer, followed by H₂C=CHX, and the weakest bond is from HC≡CX, where the tetrel bond can be as small as -0.8 kcal/mol. The strength of the tetrel bond increases in the order of C < Si < Ge. For the H₃CCH₂X and HC≡CX complexes, the tetrel bond strength shows a similar increasing tendency with the decrease of the electronegativity of the halogen atom. Electrostatic interaction plays the largest role in the stronger tetrel bonds, while dispersion interaction makes an important contribution to the H₂C=CHX complexes.

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.

Examining a Transition from Supramolecular Halogen Bonding to Covalent Bonds: Topological Analysis of Electron Densities and Energies in the Complexes of Bromosubstituted Electrophiles

The transition from weak (noncovalent) interactions to fully developed covalent bonds is examined using the quantum theory of atoms in molecules in a series of halogen-bonded (XB) complexes of bromosubstituted electrophiles, RBr, with 1,4-diazabicyclo[2.2.2]octane (DABCO) and Cl^- and Br^- anions. The gradual decrease in the XB lengths in these associations, d _Br···Y (where Y = Cl^-, Br^-, or N), was accompanied by the exponential increase in the binding energies and charge transfer, as well as electron densities and magnitudes of the kinetic and potential energy densities at the bond critical points (BCPs) on the Br···Y bond path. These indices, as well as characteristics of the adjacent bonds in the XB donor, followed remarkably close trend lines when plotted against the normalized XB length R _BrY = d _Br···Y/(r _Br + r _Y) (where r _Br and r _Y are the van der Waals radii) regardless of the methods [MP2/6-311+G(d,p) or M062X/6-311+G(d,p)], media (gas phase or dichloromethane), and nucleophiles (Cl^-, Br^-, or DABCO). In the systems with an R _BrY higher than about 0.78, the energy densities H(r) at BCPs at the Br···Y bond path were small and positive, and XBs did not substantially affect the characteristics of the adjacent R-Br covalent bond in the XB donor. Accordingly, the XB can be identified as noncovalent in this range. In the complexes with R _BrY values between about 0.67 and 0.78, energy densities H(r) at Br···Y BCPs were negative, and their magnitudes increased with the decrease in the Br···Y separation. In this range, formation of XBs was accompanied by the increase in the R-Br bond length in the XB donor and the decrease in the magnitude of the (negative) H(r) values at the BCPs of the R-Br bonds. XBs can be classified as partially covalent in this R _BrY range. At an R _BrY less than about 0.67, electron densities were larger, and energy densities were more negative at BCPs of the Br···Y bond than those at BCPs of the R-Br bond in the XB donor. This indicates that Br···Y bonds were stronger than R-Br bonds, and these (Br···Y) XBs can be regarded as essentially covalent. The synchronous change of a variety of (R-Br and Br···Y) bonding characteristics with R _BrY suggests that the normalized XB bond length can be used as a basic parameter in the identification of the type of intermolecular interaction. A continuity of these characteristics suggests an inherent relationship between limiting (covalent and noncovalent) types of XBs and thus an onset of molecular-orbital interactions in the weaker bonds.

The Effects of Electronegativity of X and Hybridization of C on the X-C⋅⋅⋅O Interactions: A Statistical Analysis on Tetrel Bonding

Cone and distance-cone corrected statistical analyses have been performed on X-C⋅⋅⋅O (X=H, B, C, N, O and F; the C atom is sp² and sp³ hybridized) tetrel bonds. The sp³ -C and sp² -C prefer to form the interactions through σ-hole (∠XCO≈180°) and π-hole (∠XCO≈90°), respectively. With the increase in electronegativity of X, the preference for the particular angles of the respective geometries increases and the C⋅⋅⋅O distance becomes shorter. The angular preference is found to be more prominent in the cases of π-hole interactions than that in the σ-hole interactions. A similar distance-cone corrected statistical analysis on O=C⋅⋅⋅O interaction also suggests that the preferred ∠OCO angle is ∼90° and the preferred C⋅⋅⋅O distance is around the sum of van der Waals radii (3.22 Å) of the C and O atoms. However, a cone-corrected statistical analysis on X-Si⋅⋅⋅O interactions suggests that the preference for linearity in this case is much higher than that for the X-C⋅⋅⋅O σ-hole interactions.

Dissection of the Origin of π-Holes and the Noncovalent Bonds in Which They Engage

Accompanying the rapidly growing list of σ-hole bonds has come the acknowledgment of parallel sorts of noncovalent bonds which owe their stability in large part to a deficiency of electron density in the area above the molecular plane, known as a π-hole. The origins of these π-holes are probed for a wide series of molecules, comprising halogen, chalcogen, pnicogen, tetrel, aerogen, and spodium bonds. Much like in the case of their σ-hole counterparts, formation of the internal covalent π-bond in the Lewis acid molecule pulls density toward the bond midpoint and away from its extremities. This depletion of density above the central atom is amplified by an electron-withdrawing substituent. At the same time, the amplitude of the π*-orbital is enhanced in the region of the density-depleted π-hole, facilitating a better overlap with the nucleophile's lone pair orbital and a stabilizing n → π* charge transfer. The presence of lone pairs on the central atom acts to attenuate the π-hole and shift its position somewhat, resulting in an overall weakening of the π-hole bond. There is a tendency for π-hole bonds to include a higher fraction of induction energy than σ-bonds with proportionately smaller electrostatic and dispersion components, but this distinction is less a product of the σ- or π-character and more a function of the overall bond strength.

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.

Noncovalent bond between tetrel π-hole and hydride

The π-hole above the plane of the X2T'Y molecule (T' = Si, Ge, Sn; X = F, Cl, H; Y = O, S) was allowed to interact with the TH hydride of TH(CH3)3 (T = Si, Ge, Sn). The resulting THT' tetrel bond is quite strong, with interaction energies exceeding 30 kcal mol-1. F2T'O engages in the strongest such bonds, as compared to F2T'S, Cl2T'O, or Cl2T'S. The bond weakens as T' grows larger as in Si > Ge > Sn, despite the opposite trend in the depth of the π-hole. The reverse pattern of stronger tetrel bond with larger T is observed for the Lewis base TH(CH3)3, even though the minimum in the electrostatic potential around the H is nearly independent of T. The THT' arrangement is nonlinear which can be understood on the basis of the positions of the extrema in the molecular electrostatic potentials of the monomers. The tetrel bond is weakened when H2O forms an OT' tetrel bond with the second π-hole of F2T'O, and strengthened if H2O participates in an OHO H-bond.

Study of Beryllium, Magnesium, and Spodium Bonds to Carbenes and Carbodiphosphoranes

The aim of this article is to present results of theoretical study on the properties of C⋯M bonds, where C is either a carbene or carbodiphosphorane carbon atom and M is an acidic center of MX2 (M = Be, Mg, Zn). Due to the rarity of theoretical data regarding the C⋯Zn bond (i.e., the zinc bond), the main focus is placed on comparing the characteristics of this interaction with C⋯Be (beryllium bond) and C⋯Mg (magnesium bond). For this purpose, theoretical studies (ωB97X-D/6-311++G(2df,2p)) have been performed for a large group of dimers formed by MX2 (X = H, F, Cl, Br, Me) and either a carbene ((NH2)2C, imidazol-2-ylidene, imidazolidin-2-ylidene, tetrahydropyrymid-2-ylidene, cyclopropenylidene) or carbodiphosphorane ((PH3)2C, (NH3)2C) molecule. The investigated dimers are characterized by a very strong charge transfer effect from either the carbene or carbodiphosphorane molecule to the MX2 one. This may even be over six times as strong as in the water dimer. According to the QTAIM and NCI method, the zinc bond is not very different than the beryllium bond, with both featuring a significant covalent contribution. However, the zinc bond should be definitely stronger if delocalization index is considered.

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.

Zero-, one-, two- and three-dimensional supramolecular architectures sustained by Se…O chalcogen bonding: A crystallographic survey

The Cambridge Structural Database was evaluated for crystals containing Se…O chalcogen bonding interactions. These secondary bonding interactions are found to operate independently of complementary intermolecular interactions in about 13% of the structures they can potentially form. This number rises significantly when more specific interactions are considered, e.g. Se…O(carbonyl) interactions occur in 50% of cases where they can potentially form. In about 55% of cases, the supramolecular assemblies sustained by Se…O(oxygen) interactions are one-dimensional architectures, with the next most prominent being zero-dimensional assemblies, at 30%.

Comparison of Bifurcated Halogen with Hydrogen Bonds

Bifurcated halogen bonds are constructed with FBr and FI as Lewis acids, paired with NH₃ and NCH bases. The first type considered places two bases together with a single acid, while the reverse case of two acids sharing a single base constitutes the second type. These bifurcated systems are compared with the analogous H-bonds wherein FH serves as the acid. In most cases, a bifurcated system is energetically inferior to a single linear bond. There is a larger energetic cost to forcing the single σ-hole of an acid to interact with a pair of bases, than the other way around where two acids engage with the lone pair of a single base. In comparison to FBr and FI, the H-bonding FH acid is better able to participate in a bifurcated sharing with two bases. This behavior is traced to the properties of the monomers, in particular the specific shape of the molecular electrostatic potential, the anisotropy of the orbitals of the acid and base that interact directly with one another, and the angular extent of the total electron density of the two molecules.

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.

Carbon (sp3) tetrel bonding mediated BODIPY supramolecular assembly via unprecedented synergy of Csp3⋯N and Csp3⋯F pair interactions

Here, we present the first example of sp³ hybridized carbon centered (C_sp3) tetrel bonding mediated 3D BODIPY assembly via the exceptional synergy of C_sp3⋯N and C_sp3⋯F pair interactions.

Understanding noncovalent bonds and their controlling forces

The fundamental underpinnings of noncovalent bonds are presented, focusing on the σ-hole interactions that are closely related to the H-bond. Different means of assessing their strength and the factors that control it are discussed. The establishment of a noncovalent bond is monitored as the two subunits are brought together, allowing the electrostatic, charge redistribution, and other effects to slowly take hold. Methods are discussed that permit prediction as to which site an approaching nucleophile will be drawn, and the maximum number of bonds around a central atom in its normal or hypervalent states is assessed. The manner in which a pair of anions can be held together despite an overall Coulombic repulsion is explained. The possibility that first-row atoms can participate in such bonds is discussed, along with the introduction of a tetrel analog of the dihydrogen bond.

Dominance of unique Pπ phosphorus bonding with π donors: evidence using matrix isolation infrared spectroscopy and computational methodology

Albeit the first account of hypervalentπ interactions has been reported with halogenπ interactions, the feasibility of their extension to other hypervalent atoms as possible Lewis acids is still open. In this work, the role of phosphorus as an acceptor from the π electron cloud (Pπ pnicogen or phosphorus bonding) in PCl3-C2H2 and PCl3-C2H4 heterodimers is explored, by combining matrix isolation infrared spectroscopy with ab initio and DFT computational methodologies. The respective potential energy surfaces of the PCl3-C2H2 and PCl3-C2H4 heterodimers reveal unique minima stabilized by a concert of reasonably strong to weak interactions, of which Pπ phosphorus bonding was energetically dominant. Heterodimers, trimers and tetramers bound primarily by this unique phosphorus bond were generated at low temperatures. The dominance of phosphorus bonding in the PCl3-C2H2 and PCl3-C2H4 heterodimers over other interactions (such as Hπ, HCl, HP, Clπ and lone pair-π interactions) was confirmed and substantiated using extended quantum theory of atoms in molecules, natural bond orbital, electrostatic potential mapping and energy decomposition analyses. The following inferences in correlation with results from non-covalent-interaction analysis offer a complete understanding of the nature of the Pπ phosphorus bonding interactions. The significance of electrostatic forces kinetically favoring the formation of phosphorus bonded heterodimers, in addition to thermodynamic stabilization, is demonstrated experimentally.

Interactions in Model Ionic Dyads and Triads Containing Tetrel Atoms

The interactions in model ionic YTX₃···Z (Y = NC, F, Cl, Br; X = F, Cl, Br, Z = F^-, Cl^-, Br^-, Li⁺) dyads containing the tetrel atoms, T = C, Si, Ge, were studied using ab initio computational methods, including an energy decomposition analysis, which found that the YTX₃ molecules were stabilized by both anions (via tetrel bonding) and cations (via polarization). For the tetrel-bonded dyads, both the electrostatic and polarization forces make comparable contributions to the binding in the C-containing dyads, whereas, electrostatic forces are by far the largest contributor to the binding in the Si- and Ge-containing analogues. Model metastable Li⁺···NCTCl₃···F^- (T = C, Si, Ge) triads were found to be lower in energy than the combined energy of the Li⁺ + NCTCl₃ + F^- fragments. The pair energies and cooperative energies for these highly polar triads were also computed and discussed.

Influence of alkali substituents on the strength, properties, and nature of tetrel bond between TH3F and pyridine

Ab initio calculations have been performed for the complexes of TH₃F (T=C, Si, and Ge) with pyridine and its alkali derivatives to study the influence of an alkali substituent on the strength, properties, and nature of tetrel bond. The introduction of an alkali atom into the electron donor has a prominent enhancing effect on the strength of tetrel bond, which depends on the T atom as well as the alkali atom and its substitution position. The enhancing effect becomes larger in the C < Ge < Si, Li < Na < K, and para- < meta- < ortho- patterns. The interaction energy varies in a wide range from 2 to 40 kcal/mol. Both electrostatic and polarization including charge transfer are responsible for the enhancing effect of an alkali atom. The formation of a tetrel bond results in an elongation of F-T bond and a red shift of F-T stretch vibration, which is big enough to be detected with infrared spectroscopy. Electrostatic interaction is dominant in all complexes, while polarization is smaller or larger than dispersion in the complexes of CH₃F or TH₃F(T=Si and Ge).