Pnicogen and tetrel bonds—tetrahedral Lewis acid centres

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.

Hole interactions of aerogen oxides with Lewis bases: an insight into σ-hole and lone-pair-hole interactions

σ-Hole and lone-pair (lp)-hole interactions of aerogen oxides with Lewis bases (LB) were comparatively inspected in terms of quantum mechanics calculations. The ZOn ⋯ LB complexes (where Z = Kr and Xe, n = 1, 2, 3 and 4, and LB = NH3 and NCH) showed favourable negative interaction energies. The complexation features were explained in light of σ-hole and lp-hole interactions within optimum distances lower than the sum of the respective van der Waals radii. The emerging findings outlined that σ-hole interaction energies generally enhanced according to the following order: KrO4 ⋯ < KrO⋯ < KrO3⋯ < KrO2⋯LB and XeO4⋯ < XeO⋯ < XeO2⋯ < XeO3⋯LB complexes with values ranging from -2.23 to -12.84 kcal mol-1. Lp-hole interactions with values up to -5.91 kcal mol-1 were shown. Symmetry-adapted perturbation theory findings revealed the significant contributions of electrostatic forces accounting for 50-65% of the total attractive forces within most of the ZOn⋯LB complexes. The obtained observations would be useful for the understanding of hole interactions, particularly for the aerogen oxides, with application in supramolecular chemistry and crystal engineering.

Influence of Internal Angular Arrangement on Pnicogen Bond Strength

The three Z-X covalent bonds of a ZX3 unit (Z = P, As, Sb, Bi) are normally arranged in a pyramidal structure. Quantum chemical calculations show that pnicogen bonds (ZBs) to the central Z are weakened if ZX3 is flattened, as in the opening of an umbrella. The partial closing of the umbrella has the opposite effect of substantially strengthening these ZBs, even amounting to a 2- or 3-fold magnification in certain cases. The strongest such bonds, wherein Sb and Bi are in a strained configuration within a ZO3CH model system, have interaction energies of 20 kcal/mol with an NH3 base. Most of these systems, whether flattened or more pyramidal, are capable of engaging in three ZBs simultaneously, despite a certain amount of negative cooperativity.

Transition between the Noncovalency and Covalency of σ-Hole Bonds

The properties of the bond between a N-ligand and a Lewis acid containing a σ-hole are studied by quantum chemical methods. Interactions considered include pnicogen bonds involving SbX5, PX5, and PX3, where X represents any of the halogen atoms F, Cl, Br, or I. Also studied are the tetrel bonds of PbX4 and SiX4, as well as the chalcogen bond involving TeOX4. Both NH3 and NCH are applied as two possible bases of differing potency. Some of the bonds are very strong with interaction energies easily exceeding 25 kcal/mol and with AIM bond critical point densities much higher than 0.04 au, suggesting their classification as coordinate covalent bonds. The pentavalent SbX5 and PX5 fall into this category when combined with NH3, as does TeOX4. Although the tetrel bonds involving PbX4 are only slightly weaker, they are probably better viewed as a strong noncovalent bond on the cusp of covalency. Changing the internal bonding of hypervalent SbX5 to the more conventional SbX3 weakens the interaction to a classical noncovalent pnicogen bond. Reducing the base nucleophilicity from NH3 to NCH weakens the bonds so that they are clearly noncovalent.

Relation between Halogen Bond Strength and IR and NMR Spectroscopic Markers

The relationship between the strength of a halogen bond (XB) and various IR and NMR spectroscopic quantities is assessed through DFT calculations. Three different Lewis acids place a Br or I atom on a phenyl ring; each is paired with a collection of N and O bases of varying electron donor power. The weakest of the XBs display a C-X bond contraction coupled with a blue shift in the associated frequency, whereas the reverse trends occur for the stronger bonds. The best correlations with the XB interaction energy are observed with the NMR shielding of the C atom directly bonded to X and the coupling constants involving the C-X bond and the C-H/F bond that lies ortho to the X substituent, but these correlations are not accurate enough for the quantitative assessment of energy. These correlations tend to improve as the Lewis acid becomes more potent, which makes for a wider range of XB strengths.

The borderless world of chemical bonding across the van der Waals crust and the valence region

The definition of the van der Waals crust as the spherical section between the atomic radius and the van der Waals radius of an element is discussed and a survey of the application of the penetration index between two interacting atoms in a wide variety of covalent, polar, coordinative or noncovalent bonding situations is presented. It is shown that this newly defined parameter permits the comparison of bonding between pairs of atoms in structural and computational studies independently of the atom sizes.

Static and Dynamical Quantum Studies of CX3-AlX2 and CSiX3-BX2 (X = F, Cl, Br) Complexes with Hydrocyanic Acid: Unusual Behavior of Strong π-Hole at Triel Center

The set of TX₃-TrX₂ (T = C, Si, Ge; Tr = B, Al, Ga; X = F, Cl, Br) molecules offers a rather unique opportunity to study both σ-hole and π-hole dimerization on the tetrel and triel ends, respectively. According to the molecular electrostatic potential (MEP) distribution, the π-hole extrema (acidic sites) were more intense than their σ-hole counterparts. The molecules owning the most (CX₃-AlX₂) and least (SiX₃-BX₂) intense π-holes were chosen to evaluate their capacities to attract one and two HCN molecules (Lewis bases). We discovered that the energetic characteristics of π-hole dimers severely conflict with the monomers MEP pattern since the weakest π-hole monomer forms a dimer characterized by interaction energy compared to those created by the monomers with noticeably greater power in the π-hole region. This outcome is due to the deformation of the weakest π-hole donor. Furthermore, the MEP analysis for monomers in the geometry of respective dimers revealed a "residual π-hole" site that was able to drive second ligand attachment, giving rise to the two "unusual trimers" examined further by the NCI and QTAIM analyses. Apart from them, the π-hole/π-hole and σ-hole/π-hole trimers have also been obtained throughout this study and described using energetic and geometric parameters. The SAPT approach revealed details of the bonding in one of the "unusual trimers". Finally, Born-Oppenheimer Molecular Dynamics (BOMD) simulations were carried out to investigate the time evolution of the interatomic distances of the studied complexes as well as their stability.

Factors contributing to halogen bond strength and stretch or contraction of internal covalent bond

The halogen bond formed by a series of Lewis acids TF₃X (T = C, Si, Ge, Sn, Pb; X = Cl, Br, I) with NH₃ is studied by quantum chemical calculations. The interaction energy is closely mimicked by the depth of the σ-hole on the X atom as well as the full electrostatic energy. There is a first trend by which the hole is deepened if the T atom to which X is attached becomes more electron-withdrawing: C > Si > Ge > Sn > Pb. On the other hand, larger more polarizable T atoms are better able to transmit the electron-withdrawing power of the F substituents. The combination of these two opposing factors leaves PbF₃X forming the strongest XBs, followed by CF₃X, with SiF₃X engaging in the weakest bonds. The charge transfer from the NH₃ lone pair into the σ*(TX) antibonding orbital tends to elongate the covalent TX bond, and this force is largest for the heavier X and T atoms. On the other hand, the contraction of this bond deepens the σ-hole at the X atom, which would enhance both the electrostatic component and the full interaction energy. This bond-shortening effect is greatest for the lighter X atoms. The combination of these two opposing forces leaves the T-X bond contracting for X = Cl and Br, but lengthening for I.

Adjusting the balance between hydrogen and chalcogen bonds

A complex is assembled which pairs a carboxyl group of X₁COOH with a 1,2,5-chalcogenadiazole ring containing substituents on its C atoms. The OH of the carboxyl group donates a proton to a N atom of the ring to form a OH⋯N H-bond (HB), while its carbonyl O engages in a Y⋯O chalcogen bond (ChB) with the ring in which Y = S, Se, Te. The ChB is strengthened by enlarging the size of the Y atom from S to Se to Te. Placement of an electron-withdrawing group (EWG) X₁ on the acid strengthens the HB while weakening the ChB; the reverse occurs when EWGs are placed on the ring. By selection of the proper substituents on the two units, it is possible to achieve a near perfect balance between the strengths of these two bonds. These bond strengths are also reflected in the NMR spectroscopic properties of the chemical shielding of the various atoms and the coupling between the nuclei directly involved in each bond.

Properties and Stabilities of Cyclic and Open Chains of Halogen Bonds

Open and cyclic chains from two to eight units of ICl and IF are constructed and examined by density functional theory (DFT) calculations. These chains contain either I···I or I···X halogen bonds (XBs) where X refers to Cl or F. The closed rings are more stable than the open chains due to the presence of an additional XB and enhanced cooperativity. This pattern is true even for most trimers where there is sizable geometric distortion in the rings. I···F rings are generally more stable than the corresponding I···I cycles as the I···F bond is stronger than I···I even in the simple dimer. However, I···I rings are comparable in energy to I···Cl. It is possible to construct I···I rings of at least as large as eight units, which are held together exclusively by XBs. On the other hand, the maximum possible size of I···X rings is 6. Red shifts are observed in the I-X stretching frequency bands, which magnify as the chain, both cyclic and open, grows longer. The NMR chemical shielding of the I atoms increases for I···I chains but diminishes when I···Cl bonds are present.

The Pnictogen Bond: The Covalently Bound Arsenic Atom in Molecular Entities in Crystals as a Pnictogen Bond Donor

In chemical systems, the arsenic-centered pnictogen bond, or simply the arsenic bond, occurs when there is evidence of a net attractive interaction between the electrophilic region associated with a covalently or coordinately bound arsenic atom in a molecular entity and a nucleophile in another or the same molecular entity. It is the third member of the family of pnictogen bonds formed by the third atom of the pnictogen family, Group 15 of the periodic table, and is an inter- or intramolecular noncovalent interaction. In this overview, we present several illustrative crystal structures deposited into the Cambridge Structure Database (CSD) and the Inorganic Chemistry Structural Database (ICSD) during the last and current centuries to demonstrate that the arsenic atom in molecular entities has a significant ability to act as an electrophilic agent to make an attractive engagement with nucleophiles when in close vicinity, thereby forming σ-hole or π-hole interactions, and hence driving (in part, at least) the overall stability of the system’s crystalline phase. This overview does not include results from theoretical simulations reported by others as none of them address the signatory details of As-centered pnictogen bonds. Rather, we aimed at highlighting the interaction modes of arsenic-centered σ- and π-holes in the rationale design of crystal lattices to demonstrate that such interactions are abundant in crystalline materials, but care has to be taken to identify them as is usually done with the much more widely known noncovalent interactions in chemical systems, halogen bonding and hydrogen bonding. We also demonstrate that As-centered pnictogen bonds are usually accompanied by other primary and secondary interactions, which reinforce their occurrence and strength in most of the crystal structures illustrated. A statistical analysis of structures deposited into the CSD was performed for each interaction type As···D (D = N, O, S, Se, Te, F, Cl, Br, I, arene’s π system), thus providing insight into the typical nature of As···D interaction distances and ∠R–As···D bond angles of these interactions in crystals, where R is the remainder of the molecular entity.

σ-Hole Bonds and the VSEPR Model—From the Tetrahedral Structure to the Trigonal Bipyramid

Complexes linked by various interactions are analysed in this study. They are characterized by the tetrahedral configuration of the Lewis acid centre. Interactions, being a subject of this study, are classified as σ-hole bonds, such as the halogen, chalcogen, pnicogen, and tetrel bonds. In the case of strong interactions, the tetrahedral configuration of the Lewis acid centre changes into the trigonal bipyramid configuration. This change is in line with the Valence-Shell Electron-Pair Repulsion model, VSEPR, and this is supported here by the results of high-level ab initio calculations. The theoretical results concerning the geometries are supported mainly by the Natural Bond Orbital, NBO, method.

Influence of Substituents in the Benzene Ring on the Halogen Bond of Iodobenzene with Ammonia

The effects on the CI··N halogen bond between iodobenzene and NH3 of placing various substituents on the phenyl ring are monitored by quantum calculations. Substituents R = N(CH3)2, NH2, CH3, OCH3, COCH3, Cl, F, COH, CN, and NO2 were each placed ortho, meta, and para to the I. The depth of the σ-hole on I is deepened as R became more electron-withdrawing which is reflected in a strengthening of the halogen bond, which varied between 3.3 and 5.5 kcal/mol. In most cases, the ortho placement yields the largest perturbation, followed by meta and then para, but this trend is not universal. Parallel to these substituent effects is a progressive lengthening of the covalent C-I bond. Formation of the halogen bond reduces the NMR chemical shielding of all three nuclei directly involved in the C-I··N interaction. The deshielding of the electron donor N is most closely correlated with the strength of the bond, as is the coupling constant between I and N, so both have potential use as spectroscopic measures of halogen bond strength.

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.

A Combined Experimental/Quantum-Chemical Study of Tetrel, Pnictogen, and Chalcogen Bonds of Linear Triatomic Molecules

Linear triatomic molecules (CO₂, N₂O, and OCS) are scrutinized for their propensity to form perpendicular tetrel (CO₂ and OCS) or pnictogen (N₂O) bonds with Lewis bases (dimethyl ether and trimethyl amine) as compared with their tendency to form end-on chalcogen bonds. Comparison of the IR spectra of the complexes with the corresponding monomers in cryogenic solutions in liquid argon enables to determine the stoichiometry and the nature of the complexes. In the present cases, perpendicular tetrel and pnictogen 1:1 complexes are identified mainly on the basis of the lifting of the degenerate ν 2 bending mode with the appearance of both a blue and a red shift. Van ′t Hoff plots of equilibrium constants as a function of temperature lead to complexation enthalpies that, when converted to complexation energies, form the first series of experimental complexation energies on sp¹ tetrel bonds in the literature, directly comparable to quantum-chemically obtained values. Their order of magnitude corresponds with what can be expected on the basis of experimental work on halogen and chalcogen bonds and previous computational work on tetrel bonds. Both the order of magnitude and sequence are in fair agreement with both CCSD(T) and DFA calculations, certainly when taking into account the small differences in complexation energies of the different complexes (often not more than a few kJ mol⁻¹) and the experimental error. It should, however, be noted that the OCS chalcogen complexes are not identified experimentally, most probably owing to entropic effects. For a given Lewis base, the stability sequence of the complexes is first successfully interpreted via a classical electrostatic quadrupole–dipole moment model, highlighting the importance of the magnitude and sign of the quadrupole moment of the Lewis acid. This approach is validated by a subsequent analysis of the molecular electrostatic potential, scrutinizing the σ and π holes, as well as the evolution in preference for chalcogen versus tetrel bonds when passing to “higher” chalcogens in agreement with the evolution of the quadrupole moment. The energy decomposition analysis gives further support to the importance/dominance of electrostatic effects, as it turns out to be the largest attractive term in all cases considered, followed by the orbital interaction and the dispersion term. The natural orbitals for chemical valence highlight the sequence of charge transfer in the orbital interaction term, which is dominated by an electron-donating effect of the N or O lone-pair(s) of the base to the central atom of the triatomics, with its value being lower than in the case of comparable halogen bonding situations. The effect is appreciably larger for TMA, in line with its much higher basicity than DME, explaining the comparable complexation energies for DME and TMA despite the much larger dipole moment for DME.

Group 12 Carbonates and their Binary Complexes with Nitrogen Bases and FH2 Z Molecules (Z=P, As, Sb): Synergism in Forming Ternary Complexes

MCO₃ (M=Zn, Cd, Hg) forms a spodium bond with nitrogen-containing bases (HCN, NHCH₂ , NH₃ ) and a pnicogen bond with FH₂ Z (Z=P, As, Sb). The spodium bond is very strong with the interaction energy ranging from -31 kcal/mol to -56 kcal/mol. Both NHCH₂ and NH₃ have an equal electrostatic potential on the N atom, but the corresponding interaction energy is differentiated by 1.5-4 kcal/mol due to the existence of spodium and hydrogen bonds in the complex with NHCH₂ as the electron donor. The spodium bond is weakest in the HCN complex, which is not consistent with the change of the binding distance. The spodium bond becomes stronger in the CdCO₃ <ZnCO₃ <HgCO₃ sequence although the positive electrostatic potential on the Hg atom is smallest. This is because the electrostatic interaction is dominant in the spodium-bonded complexes of CdCO₃ and ZnCO₃ but the polarization interaction in that of HgCO₃ . The pnicogen bond is much weaker than the spodium bond and the former has a larger enhancement than the latter in the FH₂ Z⋅⋅⋅OCO₂ M⋅⋅⋅N-base ternary complexes.

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.

Proximity Effects of Substituents on Halogen Bond Strength

It is well known that the presence of an electron-withdrawing substituent (EWS) placed near the halogen (X) atom on a Lewis acid molecule amplifies the ability of this unit to engage in a halogen bond with a base. Quantum calculations are applied to examine how quickly these effects fade as the EWS is moved further and further from the X atom. Conjugated alkene and alkyne chains of varying lengths with a terminal C-I first facilitate analysis as to how the number of these multiple bonds affects the strength of CI··N XB to NH₃. Then, electron-withdrawing F and C≡N substituents are placed on the opposite end of the chain, and their effects on the XB properties are monitored as a function of their distance from I. These same EWSs are added to the ortho, meta, and para positions of aromatic iodobenzene. It is found that the XB grows in strength as more triple bonds are added to the alkyne, but there is little change caused by elongating an alkene. The cyano group has a much stronger effect than does F. While F strengthens the XB, its effects are quickly attenuated as it is moved further from I. The consequences of C≡N substitution are stronger and extend over a longer distance. Placement of an EWS on the phenyl ring diminishes with distance: o > m > p, and the effects of disubstitution are nearly additive. These trends apply not only to energetics but also to geometries, properties of the wave function, σ-hole depth, and NMR shielding.

Actual Symmetry of Symmetric Molecular Adducts in the Gas Phase, Solution and in the Solid State

This review discusses molecular adducts, whose composition allows a symmetric structure. Such adducts are popular model systems, as they are useful for analyzing the effect of structure on the property selected for study since they allow one to reduce the number of parameters. The main objectives of this discussion are to evaluate the influence of the surroundings on the symmetry of these adducts, steric hindrances within the adducts, competition between different noncovalent interactions responsible for stabilizing the adducts, and experimental methods that can be used to study the symmetry at different time scales. This review considers the following central binding units: hydrogen (proton), halogen (anion), metal (cation), water (hydrogen peroxide).

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.

Anion-Anion Interactions in Aerogen-Bonded Complexes. Influence of Solvent Environment

Ab initio calculations are applied to the question as to whether a AeX₅^- anion (Ae = Kr, Xe) can engage in a stable complex with another anion: F^-, Cl^-, or CN^-. The latter approaches the central Ae atom from above the molecular plane, along its C₅ axis. While the electrostatic repulsion between the two anions prevents their association in the gas phase, immersion of the system in a polar medium allows dimerization to proceed. The aerogen bond is a weak one, with binding energies less than 2 kcal/mol, even in highly polar aqueous solvent. The complexes are metastable in the less polar solvents THF and DMF, with dissociation opposed by a small energy barrier.

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.

Comparison of ±σ-hole and ±R˙-hole interactions formed by tetrel-containing complexes: a computational study

For the first time, unconventional ±R˙-hole interactions were unveiled in tetrel-containing complexes. The nature and characteristics of ±R˙-hole interactions were explored relative to their ±σ-hole counterparts for ˙TF3⋯ and W-T-F3⋯B/R˙/A complexes (where T = C, Si, and Ge, W = H and F, B = Lewis bases, R˙ = free radicals, and A = Lewis acids). In an effort to thoroughly investigate such interactions, a plethora of quantum mechanical calculations, including molecular electrostatic potential (MEP), maximum positive electrostatic potential (V s,max), point-of-charge (PoC), interaction energy, symmetry adapted perturbation theory (SAPT), and reduced density gradient-noncovalent interaction (RDG-NCI) calculations, were applied. The most notable findings to emerge from this study are that (i) from the electrostatic perspective, the molecular stabilization energies of ˙TF3 and W-T-F3 monomers became more negative as the Lewis basicity increased, (ii) the most stable complexes were observed for the ones containing Lewis bases, forming -σ-hole and -R˙-hole interactions, and the interaction energies systematically increased in the order H-T-F3⋯B < ˙TF3⋯B < F-T-F3⋯B, (iii) contrariwise, the +σ-hole and +R˙-hole interactions with Lewis acids are more energetically favorable in the order F-T-F3⋯A < ˙TF3⋯A < H-T-F3⋯A, and (iv) generally, the dispersion force plays a key role in stabilizing the tetrel-containing complexes, jointly with the electrostatic and induction forces for the interactions with Lewis bases and acids, respectively. Concretely, the findings presented in this paper add to our understanding of the characteristics and nature of such intriguing interactions.

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.

Chalcogen-Bonding Interactions in Telluroether Heterocycles [Te(CH2 )m ]n (n=1-4; m=3-7)

The Te⋅⋅⋅Te secondary bonding interactions (SBIs) in solid cyclic telluroethers were explored by preparing and structurally characterizing a series of [Te(CH2 )m ]n (n=1-4; m=3-7) species. The SBIs in 1,7-Te2 (CH2 )10 , 1,8-Te2 (CH2 )12 , 1,5,9-Te3 (CH2 )9 , 1,8,15-Te3 (CH2 )18 , 1,7,13,19-Te4 (CH2 )20 , 1,8,15,22-Te4 (CH2 )24 and 1,9,17,25-Te4 (CH2 )28 lead to tubular packing of the molecules, as has been observed previously for related thio- and selenoether rings. The nature of the intermolecular interactions was explored by solid-state PBE0-D3/pob-TZVP calculations involving periodic boundary conditions. The molecular packing in 1,7,13,19-Te4 (CH2 )20 , 1,8,15,22-Te4 (CH2 )24 and 1,9,17,25-Te4 (CH2 )28 forms infinite shafts. The electron densities at bond critical points indicate a narrow range of Te⋅⋅⋅Te bond orders of 0.12-0.14. The formation of the shafts can be rationalized by frontier orbital overlap and charge transfer.

Versatility of the Cyano Group in Intermolecular Interactions

Several cyano groups are added to an alkane, alkene, and alkyne group so as to construct a Lewis acid molecule with a positive region of electrostatic potential in the area adjoining these substituents. Although each individual cyano group produces only a weak π-hole, when two or more such groups are properly situated, they can pool their π-holes into one much more intense positive region that is located midway between them. A NH3 base is attracted to this site, where it forms a strong noncovalent bond to the Lewis acid, amounting to as much as 13.6 kcal/mol. The precise nature of the bonding varies a bit from one complex to the next but typically contains a tetrel bond to the C atoms of the cyano groups or the C atoms of the linkage connecting the C≡N substituents. The placement of the cyano groups on a cyclic system like cyclopropane or cyclobutane has a mild weakening effect upon the binding. Although F is comparable to C≡N in terms of electron-withdrawing power, the replacement of cyano by F substituents substantially weakens the binding with NH3.

Coordination of a Central Atom by Multiple Intramolecular Pnicogen Bonds

A central pnicogen Z atom (Z = Sb, As) is covalently attached to the O atom of three -O(CH₂)_nX chains where X represents either an aldehyde or amine group. The chain can fold around so that the basic X group can engage in a noncovalent pnicogen bond with the central Z. The formation of up to three pnicogen bonds is energetically favored. The amine appears to engage in stronger pnicogen bonds than does the aldehyde, and bonds to Sb are favored over As, but there is little dependence on the length of the chain. The formation of each successive pnicogen bond reduces the magnitude of the σ-holes surrounding the Z atom, which tends to weaken the attraction for the basic end of the chain.

Not Only Hydrogen Bonds: Other Noncovalent Interactions

In this review, we provide a consistent description of noncovalent interactions, covering most groups of the Periodic Table. Different types of bonds are discussed using their trivial names. Moreover, the new name “Spodium bonds” is proposed for group 12 since noncovalent interactions involving this group of elements as electron acceptors have not yet been named. Excluding hydrogen bonds, the following noncovalent interactions will be discussed: alkali, alkaline earth, regium, spodium, triel, tetrel, pnictogen, chalcogen, halogen, and aerogen, which almost covers the Periodic Table entirely. Other interactions, such as orthogonal interactions and π-π stacking, will also be considered. Research and applications of σ-hole and π-hole interactions involving the p-block element is growing exponentially. The important applications include supramolecular chemistry, crystal engineering, catalysis, enzymatic chemistry molecular machines, membrane ion transport, etc. Despite the fact that this review is not intended to be comprehensive, a number of representative works for each type of interaction is provided. The possibility of modeling the dissociation energies of the complexes using different models (HSAB, ECW, Alkorta-Legon) was analyzed. Finally, the extension of Cahn-Ingold-Prelog priority rules to noncovalent is proposed.

Directionality of P⋯O pnicogen bonding in light of geometry corrected statistical analysis

Cone corrected statistical analysis suggests that the X–P⋯O angle prefers linearity which is more prominent in the case of X₃P⋯O compared to X₄P⋯O pnicogen bonds. This preference also increases with an increase in the electronegativity of X.

The ditetrel bond: noncovalent bond between neutral tetrel atoms

The ability of a tetrel atom to serve in the capacity of electron donor in a σ-hole noncovalent bond is tested by quantum calculations.

Lead(ii) coordination polymers driven by pyridine-hydrazine donors: from anion-guided self-assembly to structural features

This work unveils an indispensable role of London dispersion forces and relativistic effects in tetrel and covalent bonds of the type Pb–X (X = O, N, S, I), which drives formation of extended architectures of lead(ii) coordination polymers.

Theoretical Studies of IR and NMR Spectral Changes Induced by Sigma-Hole Hydrogen, Halogen, Chalcogen, Pnicogen, and Tetrel Bonds in a Model Protein Environment

Various types of σ-hole bond complexes were formed with FX, HFY, H₂FZ, and H₃FT (X = Cl, Br, I; Y = S, Se, Te; Z = P, As, Sb; T = Si, Ge, Sn) as Lewis acid. In order to examine their interactions with a protein, N-methylacetamide (NMA), a model of the peptide linkage was used as the base. These noncovalent bonds were compared by computational means with H-bonds formed by NMA with XH molecules (X = F, Cl, Br, I). In all cases, the A-F bond, which lies opposite the base and is responsible for the σ-hole on the A atom (A refers to the bridging atom), elongates and its stretching frequency undergoes a shift to the red with a band intensification, much as what occurs for the X-H bond in a H-bond (HB). Unlike the NMR shielding decrease seen in the bridging proton of a H-bond, the shielding of the bridging A atom is increased. The spectroscopic changes within NMA are similar for H-bonds and the other noncovalent bonds. The C=O bond of the amide is lengthened and its stretching frequency red-shifted and intensified. The amide II band shifts to higher frequency and undergoes a small band weakening. The NMR shielding of the O atom directly involved in the bond rises, whereas the C and N atoms both undergo a shielding decrease. The frequency shifts of the amide I and II bands of the base as well as the shielding changes of the three pertinent NMA atoms correlate well with the strength of the noncovalent bond.

Effects of Halogen, Chalcogen, Pnicogen, and Tetrel Bonds on IR and NMR Spectra

Complexes were formed pairing FX, FHY, FH2Z, and FH3T (X = Cl, Br, I; Y = S, Se, Te; Z = P, As, Sb; T = Si, Ge, Sn) with NH3 in order to form an A⋯N noncovalent bond, where A refers to the central atom. Geometries, energetics, atomic charges, and spectroscopic characteristics of these complexes were evaluated via DFT calculations. In all cases, the A-F bond, which is located opposite the base and is responsible for the σ-hole on the A atom, elongates and its stretching frequency undergoes a shift to the red. This shift varies from 42 to 175 cm-1 and is largest for the halogen bonds, followed by chalcogen, tetrel, and then pnicogen. The shift also decreases as the central A atom is enlarged. The NMR chemical shielding of the A atom is increased while that of the F and electron donor N atom are lowered. Unlike the IR frequency shifts, it is the third-row A atoms that undergo the largest change in NMR shielding. The change in shielding of A is highly variable, ranging from negligible for FSnH3 all the way up to 1675 ppm for FBr, while those of the F atom lie in the 55-422 ppm range. Although smaller in magnitude, the changes in the N shielding are still easily detectable, between 7 and 27 ppm.