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

Different Stacking Types in a Single Hybrid Cocrystal System: π···π- and π-Hole-Based Organic-Inorganic Planar Assemblies

The planar bis-chelated complex [Pd(N∩O)2] (1; N∩O = 4-MeC5H3NNC(O)NMe2) exhibits two distinct stacking modes with electron-deficient aromatics: π···π stacking with hexafluorobenzene (C6F6) versus charge-transfer π-hole interactions with 1,2,4,5-tetracyanobenzene (TCB). Cocrystallization of the complex with C6F6 or TCB yields cocrystals 1·3(C6F6) and 1·2TCB, respectively, which display different colors and stacking patterns despite similar structural motifs. Comprehensive analysis using X-ray diffraction, combined with quantum theory of atoms-in-molecules (QTAIM), an independent gradient model based on Hirshfeld partition (IGMH), extended transition state natural orbital for chemical valence theory with charge displacement function (ETS-NOCV/CDF), many-body interaction analysis, and symmetry-adapted perturbation theory (SAPT), reveals fundamentally different interaction mechanisms. In 1·3(C6F6), the stacking is primarily governed by intermolecular polarization without significant charge transfer, with dispersion forces contributing approximately 70% of the attractive energy. In contrast, 1·2TCB exhibits pronounced charge transfer (35 me) and significant inductive components alongside dispersion forces, characteristic of π-hole interactions. This dichotomy in stacking behavior provides new insights into the nature of organic-inorganic planar assemblies and demonstrates that seemingly similar structural patterns can arise from distinctly different combinations of noncovalent forces, which is essential for rational crystal engineering of hybrid materials.

Diverse Cyclization Pathways Between Nitriles with Active α-Methylene Group and Ambiphilic 2-Pyridylselenyl Reagents Enabled by Reversible Covalent Bonding

Herein, we describe a novel coupling between ambiphilic 2-pyridylselenyl reagents and nitriles featuring an active α-methylene group. Depending on the solvent employed, this reaction can yield two distinct types of cationic pyridinium-fused selenium-containing heterocycles, 1,3-selenazolium or 1,2,4-selenadiazolium salts, in high yields. This is in contrast to what we observed before for other nitriles. Notably, the formation of selenadiazolium is reversible, gradually converting into the more thermodynamically stable selenazolium product in solution. Our findings reveal, for the first time, the reversible nature of 1,3-dipolar cyclization between the CN triple bond and 2-pyridylselenyl reagents. Nitrile substitution experiments in the adducts confirmed the dynamic nature of this cyclization, indicating potential applications in dynamic covalent chemistry. DFT calculations revealed the mechanistic pathways for new cyclizations, suggesting a concerted [3 + 2] cycloaddition for the formation of selenadiazolium rings and a stepwise mechanism involving a ketenimine intermediate for the formation of selenazolium rings. Natural bond orbital analysis confirmed the involvement of σ-hole interactions and lone pair to σ* electron donation in these processes. Additionally, theoretical investigations of σ-hole interactions were performed, focusing on the selenium-centered contacts within the new compounds.

Diverse Self-Assembled Molecular Architectures Promoted by C-H···O and C-H···Cl Hydrogen Bonds in a Triad of α-Diketone, α-Ketoimine, and an Imidorhenium Complex: A Unified Analysis Based on XRD, NEDA, SAPT, QTAIM, and IBSI Studies

X-ray structural elucidation, supramolecular self-assembly, and energetics of existential noncovalent interactions for a triad comprising α-diketone, α-ketoimine, and an imidorhenium complex are highlighted in this report. Molecular packing reveals a self-assembled 2D network stabilized by the C-H···O H-bonds for the α-diketone (benzil), and the first structural report of Brown and Sadanaga stressing on the prevalence of only the van der Waals forces seems to be an oversimplified conjecture. In the α-ketoimine, the imine nitrogen atom undergoes intramolecular N···H interaction to render itself inert toward intermolecular C-H···N interaction and exhibits two types of C-H···O H-bonds in consequence to generate a self-assembled 2D molecular architecture. The imidorhenium complex features a self-aggregated 3D packing engendered by the interplay of C-H···Cl H-bonds along with the ancillary C-H···π, C···C, and C···Cl contacts. To the best of our knowledge, in rhenium chemistry, this imidorhenium complex unravels the first example of self-associated 3D molecular packing constructed by the directional hydrogen bonds of C-H···Cl type. The presence of characteristic supramolecular synthons, viz., R2 2(12), R2 2(16), and R2 2(14), in the α-diketone, α-ketoimine, and imidorhenium complex, respectively, has prompted us to delve into the energetics of noncovalent interactions. Symmetry-adapted perturbation theory analysis has authenticated a stability order: R2 2(14) > R2 2(12) > R2 2(16) based on the interaction energy values of -25.97, -9.93, and -4.98 kcal/mol, respectively. The respective average contributions of the long-range dispersion, electrostatic, and induction forces are 58.5, 32.8, and 8.7%, respectively, for the intermolecular C-H···O interactions. The C-H···Cl interactions experience comparable contribution from the dispersion force (57.9% on average), although the electrostatic and induction forces contribute much less, 28.0 and 14.1%, respectively, on average. The natural energy decomposition analysis has further attested that the short-range, interfragment charge transfer occurring via the lp(O/Cl) → σ*(C-H) routes contributes 17-25% of the total attractive force for the C-H···O and C-H···Cl interactions. Quantum theory of atoms in molecules analysis unfolds a first-order exponential decay relation (y = 8.1043e -x/0.4095) between the electron density at the bond critical point and the distance of noncovalent interactions. The distances of noncovalent interactions in the lattices are internally governed by the individual packing patterns rather than the chemical nature of the H-bond donors and acceptors. Intrinsic bond strength index analysis shows promise to correlate the electron density at BCP with the SAPT-derived interaction energy for the noncovalent interactions. Two factors: (i) nearly half the HOMO-LUMO energy difference for the imidorhenium complex (∼30 kcal/mol) compared to the organics, and (ii) ∼60% localization of HOMO over the mer-ReCl3 moiety clearly indicate an enhanced polarizability of the complex facilitating the growth of weak C-H···Cl H-bonds.

Participation of transition metal atoms in noncovalent bonds

The existence of halogen, chalcogen, pnicogen, and tetrel bonds as variants of noncovalent σ and π-hole bonds is now widely accepted, and many of their properties have been elucidated. The ability of the d-block transition metals to potentially act as Lewis acids in a similar capacity is examined systematically by DFT calculations. Metals examined span the entire range of the d-block from Group 3 to 12, and are selected from several rows of the periodic table. These atoms are placed in a variety of neutral MXn molecules, with X = Cl and O, and paired with a NH3 nucleophile. The resulting M⋯N bonds tend to be stronger than their p-block analogues, many of them with a substantial degree of covalency. The way in which the properties of these bonds is affected by the row and column of the periodic table from which the M atom is drawn, and the number and nature of ligands, is elucidated.

Anion⋯anion self-assembly under the control of σ- and π-hole bonds

The electrostatic attraction between charges of opposite signs and the repulsion between charges of the same sign are ubiquitous and influential phenomena in recognition and self-assembly processes. However, it has been recently revealed that specific attractive forces between ions with the same sign are relatively common. These forces can be strong enough to overcome the Coulomb repulsion between ions with the same sign, leading to the formation of stable anion⋯anion and cation⋯cation adducts. Hydroden bonds (HBs) are probably the best-known interaction that can effectively direct these counterintuitive assembly processes. In this review we discuss how σ-hole and π-hole bonds can break the paradigm of electrostatic repulsion between like-charges and effectively drive the self-assembly of anions into discrete as well as one-, two-, or three-dimensional adducts. σ-Hole and π-hole bonds are the attractive forces between regions of excess electron density in molecular entities (e.g., lone pairs or π bond orbitals) and regions of depleted electron density that are localized at the outer surface of bonded atoms opposite to the σ covalent bonds formed by atoms (σ-holes) and above and below the planar portions of molecular entities (π-holes). σ- and π-holes can be present on many different elements of the p and d block of the periodic table and the self-assembly processes driven by their presence can thus involve a wide diversity of mono- and di-anions. The formed homomeric and heteromeric adducts are typically stable in the solid phase and in polar solvents but metastable or unstable in the gas phase. The pivotal role of σ- and π-hole bonds in controlling anion⋯anion self-assembly is described in key biopharmacological systems and in molecular materials endowed with useful functional properties.

Many-body Effects on Electronic Transport in Molecular Junctions: A Quantum Perspective

This concept delves into quantum particle transport at the nanoscale, with a particular focus on how electrons move through molecular circuits. The thriving field of single molecular electronics benefits from the unique electrical and other properties of nanostructures. It concentrates on single molecular junctions that serve as bridges between electrodes. In this context, the electronic correlation-induced many-body effect gives rise to resonant states. These states, along with conductance, depend on electron spin. Thus, the field acts as a bridge between quantum and macroscopic worlds, unveiling unique behaviors of electrons. Additionally, external factors, such as magnetic fields and voltages, offer means to control the electron correlation in these junctions.

Halogen Bond via an Electrophilic π-Hole on Halogen in Molecules: Does It Exist?

This study reveals a new non-covalent interaction called a π-hole halogen bond, which is directional and potentially non-linear compared to its sister analog (σ-hole halogen bond). A π-hole is shown here to be observed on the surface of halogen in halogenated molecules, which can be tempered to display the aptness to form a π-hole halogen bond with a series of electron density-rich sites (Lewis bases) hosted individually by 32 other partner molecules. The [MP2/aug-cc-pVTZ] level characteristics of the π-hole halogen bonds in 33 binary complexes obtained from the charge density approaches (quantum theory of intramolecular atoms, molecular electrostatic surface potential, independent gradient model (IGM-δginter)), intermolecular geometries and energies, and second-order hyperconjugative charge transfer analyses are discussed, which are similar to other non-covalent interactions. That a π-hole can be observed on halogen in halogenated molecules is substantiated by experimentally reported crystals documented in the Cambridge Crystal Structure Database. The importance of the π-hole halogen bond in the design and growth of chemical systems in synthetic chemistry, crystallography, and crystal engineering is yet to be fully explicated.

Conformation-Associated C···dz2-PtII Tetrel Bonding: The Case of Cyclometallated Platinum(II) Complex with 4-Cyanopyridyl Urea Ligand

The nucleophilic addition of 3-(4-cyanopyridin-2-yl)-1,1-dimethylurea (1) to cis-[Pt(CNXyl)2Cl2] (2) gave a new cyclometallated compound 3. It was characterized by NMR spectroscopy (1H, 13C, 195Pt) and high-resolution mass spectrometry, as well as crystallized to obtain two crystalline forms (3 and 3·2MeCN), whose structures were determined by X-ray diffraction. In the crystalline structure of 3, two conformers (3A and 3B) were identified, while the structure 3·2MeCN had only one conformer 3A. The conformers differed by orientation of the N,N-dimethylcarbamoyl moiety relative to the metallacycle plane. In both crystals 3 and 3·2MeCN, the molecules of the Pt(II) complex are associated into supramolecular dimers, either {3A}2 or {3B}2, via stacking interactions between the planes of two metal centers, which are additionally supported by hydrogen bonding. The theoretical consideration, utilizing a number of computational approaches, demonstrates that the C···dz2(Pt) interaction makes a significant contribution in the total stacking forces in the geometrically optimized dimer [3A]2 and reveals the dz2(Pt)→π*(PyCN) charge transfer (CT). The presence of such CT process allowed for marking the C···Pt contact as a new example of a rare studied phenomenon, namely, tetrel bonding, in which the metal site acts as a Lewis base (an acceptor of noncovalent interaction).

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.

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.

Computational Insight into the Nature and Strength of the π-Hole Type Chalcogen∙∙∙Chalcogen Interactions in the XO2∙∙∙CH3YCH3 Complexes (X = S, Se, Te; Y = O, S, Se, Te)

In recent years, the non-covalent interactions between chalcogen centers have aroused substantial research interest because of their potential applications in organocatalysis, materials science, drug design, biological systems, crystal engineering, and molecular recognition. However, studies on π-hole-type chalcogen∙∙∙chalcogen interactions are scarcely reported in the literature. Herein, the π-hole-type intermolecular chalcogen∙∙∙chalcogen interactions in the model complexes formed between XO2 (X = S, Se, Te) and CH3YCH3 (Y = O, S, Se, Te) were systematically studied by using quantum chemical computations. The model complexes are stabilized via one primary X∙∙∙Y chalcogen bond (ChB) and the secondary C-H∙∙∙O hydrogen bonds. The binding energies of the studied complexes are in the range of -21.6~-60.4 kJ/mol. The X∙∙∙Y distances are significantly smaller than the sum of the van der Waals radii of the corresponding two atoms. The X∙∙∙Y ChBs in all the studied complexes except for the SO2∙∙∙CH3OCH3 complex are strong in strength and display a partial covalent character revealed by conducting the quantum theory of atoms in molecules (QTAIM), a non-covalent interaction plot (NCIplot), and natural bond orbital (NBO) analyses. The symmetry-adapted perturbation theory (SAPT) analysis discloses that the X∙∙∙Y ChBs are primarily dominated by the electrostatic component.

Halide Complexes of 5,6-Dicyano-2,1,3-Benzoselenadiazole with 1 : 4 Stoichiometry: Cooperativity between Chalcogen and Hydrogen Bonding

The [M4 -Hal]- (M=the title compound; Hal=Cl, Br, and I) complexes were isolated in the form of salts of [Et4 N]+ cation and characterized by XRD, NMR, UV-Vis, DFT, QTAIM, EDD, and EDA. Their stoichiometry is caused by a cooperative interplay of σ-hole-driven chalcogen (ChB) and hydrogen (HB) bondings. In the crystal, [M4 -Hal]- are connected by the π-hole-driven ChB; overall, each [Hal]- is six-coordinated. In the ChB, the electrostatic interaction dominates over orbital and dispersion interactions. In UV-Vis spectra of the M+[Hal]- solutions, ChB-typical and [Hal]- -dependent charge-transfer bands are present; they reflect orbital interactions and allow identification of the individual [Hal]- . However, the structural situation in the solutions is not entirely clear. Particularly, the UV-Vis spectra of the solutions are different from the solid-state spectra of the [Et4 N]+ [M4 -Hal]- ; very tentatively, species in the solutions are assigned [M-Hal]- . It is supposed that the formation of the [M4 -Hal]- proceeds during the crystallization of the [Et4 N]+ [M4 -Hal]- . Overall, M can be considered as a chromogenic receptor and prototype sensor of [Hal]- . The findings are also useful for crystal engineering and supramolecular chemistry.

Sigma-Hole and Lone-Pair-Hole Site-Based Interactions of Seesaw Tetravalent Chalcogen-Bearing Molecules with Lewis Bases

For the first time, sigma (σ)- and lone-pair (lp)-hole site-based interactions of SF4 and SeF4 molecules in seesaw geometry with NH3 and FH Lewis bases were herein comparatively investigated. The obtained findings from the electrostatic potential analysis outlined the emergence of sundry holes on the molecular entity of the SF4 and SeF4 molecules, dubbed the σ- and lp-holes. The energetic viewpoint announced splendid negative binding energy values for σ-hole site-based interactions succeeded by lp-hole analogues, which were found to be -9.21 and -0.50 kcal/mol, respectively, for SeF4···NH3 complex as a case study. Conspicuously, a proper concurrence between the strength of chalcogen σ-hole site-based interactions and the chalcogen's atomic size was obtained, whereas a reverse pattern was proclaimed for the lp-hole counterparts. Further, a higher preference for the YF4···NH3 complexes with elevated negative binding energy was promulgated over the YF4···FH ones, indicating the eminent role of Lewis basicity. The indications of the quantum theory of atoms in molecules generally asserted the closed-shell nature of all the considered interactions. The observation of symmetry-adapted perturbation theory revealed the substantial contributing role of the electrostatic forces beyond the occurrence of σ-hole site-based interactions. In comparison, the dispersion forces were specified to govern the lp-hole counterparts. Such emerging findings would be a gate for the fruitful forthcoming applications of chalcogen bonding interactions in crystal engineering and biological systems.

Chalcogen Bond as a Factor Stabilizing Ligand Conformation in the Binding Pocket of Carbonic Anhydrase IX Receptor Mimic

It is postulated that the overexpression of Carbonic Anhydrase isozyme IX in some cancers contributes to the acidification of the extracellular matrix. It was proved that this promotes the growth and metastasis of the tumor. These observations have made Carbonic Anhydrase IX an attractive drug target. In the light of the findings and importance of the glycoprotein in the cancer treatment, we have employed quantum-chemical approaches to study non-covalent interactions in the binding pocket. As a ligand, the acetazolamide (AZM) molecule was chosen, being known as a potential inhibitor exhibiting anticancer properties. First-Principles Molecular Dynamics was performed to study the chalcogen and other non-covalent interactions in the AZM ligand and its complexes with amino acids forming the binding site. Based on Density Functional Theory (DFT) and post-Hartree-Fock methods, the metric and electronic structure parameters were described. The Non-Covalent Interaction (NCI) index and Atoms in Molecules (AIM) methods were applied for qualitative/quantitative analyses of the non-covalent interactions. Finally, the AZM-binding pocket interaction energy decomposition was carried out. Chalcogen bonding in the AZM molecule is an important factor stabilizing the preferred conformation. Free energy mapping via metadynamics and Path Integral molecular dynamics confirmed the significance of the chalcogen bond in structuring the conformational flexibility of the systems. The developed models are useful in the design of new inhibitors with desired pharmacological properties.

Recognition in the Domain of Molecular Chirality: From Noncovalent Interactions to Separation of Enantiomers

It is not a coincidence that both chirality and noncovalent interactions are ubiquitous in nature and synthetic molecular systems. Noncovalent interactivity between chiral molecules underlies enantioselective recognition as a fundamental phenomenon regulating life and human activities. Thus, noncovalent interactions represent the narrative thread of a fascinating story which goes across several disciplines of medical, chemical, physical, biological, and other natural sciences. This review has been conceived with the awareness that a modern attitude toward molecular chirality and its consequences needs to be founded on multidisciplinary approaches to disclose the molecular basis of essential enantioselective phenomena in the domain of chemical, physical, and life sciences. With the primary aim of discussing this topic in an integrated way, a comprehensive pool of rational and systematic multidisciplinary information is provided, which concerns the fundamentals of chirality, a description of noncovalent interactions, and their implications in enantioselective processes occurring in different contexts. A specific focus is devoted to enantioselection in chromatography and electromigration techniques because of their unique feature as "multistep" processes. A second motivation for writing this review is to make a clear statement about the state of the art, the tools we have at our disposal, and what is still missing to fully understand the mechanisms underlying enantioselective recognition.

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.

Principles Guiding the Square Bonding Motif Containing a Pair of Chalcogen Bonds between Chalcogenadiazoles

The bonding motif adopted by a dimer of chalcogenadiazole molecules is characterized by a pair of equivalent Ch···N chalcogen bonds. Quantum calculations show that the interaction energy is substantial, varying between 4 kcal/mol for Ch = S and 17 kcal/mol for Te. The interaction is cooperative in that the total bond strength is greater than either chalcogen bond individually. Neither the addition of a phenyl ring nor the addition of a pair of cyano substituents to the diazole ring has much influence on this binding. Removal of one N from the diazole weakens the binding, and addition of two nitrogens has little effect. The largest perturbation arises with three N atoms in each ring, for which the binding energy increases by some 25%. The ring size plays a minor role in most cases, although a near doubling of bond strength occurs if there are two N atoms present on a four-membered ring.

The Bifurcated σ-Hole···σ-Hole Stacking Interactions

The bifurcated σ-hole···σ-hole stacking interactions between organosulfur molecules, which are key components of organic optical and electronic materials, were investigated by using a combined method of the Cambridge Structural Database search and quantum chemical calculation. Due to the geometric constraints, the binding energy of one bifurcated σ-hole···σ-hole stacking interaction is in general smaller than the sum of the binding energies of two free monofurcated σ-hole···σ-hole stacking interactions. The bifurcated σ-hole···σ-hole stacking interactions are still of the dispersion-dominated noncovalent interactions. However, in contrast to the linear monofurcated σ-hole···σ-hole stacking interaction, the contribution of the electrostatic energy to the total attractive interaction energy increases significantly and the dispersion component of the total attractive interaction energy decreases significantly for the bifurcated σ-hole···σ-hole stacking interaction. Another important finding of this study is that the low-cost spin-component scaled zeroth-order symmetry-adapted perturbation theory performs perfectly in the study of the bifurcated σ-hole···σ-hole stacking interactions. This work will provide valuable information for the design and synthesis of novel organic optical and electronic materials.

Experimental and computational evidence for stabilising parallel, offset π[C(O)N(H)NC]⋯π(phenyl) interactions in acetohydrazide derivatives

Stabilising π[C(O)N(H)NC]⋯π(phenyl) interactions are described.

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.

Anatomy of π-hole bonds: Linear systems

The list of σ-hole bonds is long and growing, encompassing both H-bonds and its closely related halogen, chalcogen, etc., sisters. These bonds rely on the asymmetric distribution of electron density, whose depletion along the extension of a covalent bond leaves a positive region of electrostatic potential from which these bonds derive their name. However, the density distributions of other molecules contain analogous positive regions that lie out of the molecular plane known as π-holes, which are likewise capable of engaging in noncovalent bonds. Quantum calculations are applied to study such π-hole bonds that involve linear molecules, whose positive region is a circular belt surrounding the molecule, rather than the more restricted area of a σ-hole. These bonds are examined in terms of their most fundamental elements arising from the spatial dispositions of their relevant molecular orbitals and the π-holes in both the total electron density and the electrostatic potential to which they lead. Systems examined comprise tetrel, chalcogen, aerogen, and triel bonds, as well as those involving group II elements, with atoms drawn from various rows of the Periodic Table. The π-hole bonds established by linear molecules tend to be weaker than those of comparable planar systems.

Yet another perspective on hole interactions

Hole interactions are known by different names depending on the key atom of the bond (halogen bond, chalcogen bond, hydrogen bond, etc.), and the geometry of the interaction (σ if in line, π if perpendicular to the Lewis acid plane). However, its origin starts with the creation of a Lewis acid by an underlying covalent bond, which forms an electrostatic depletion and a virtual antibonding orbital, which can create non-covalent interactions with Lewis bases. In this (maybe subjective) perspective, we will claim that hole interactions must be defined via the molecular orbital origin of the molecule. Under this premise we can better explore the richness of such bonding patterns. For that, we will study old, recent and new systems, trying to pinpoint some misinterpretations that are often associated with them. We will use as exemplars the triel bonds, a couple of metal complexes, a discussion on convergent σ-holes, and many cases of anti-electrostatic hole interactions.