Sigma-hole carbon-bonding interactions in carbon-carbon double bonds: an unnoticed contact

Data and Molecular Fingerprint-Driven Machine Learning Approaches to Halogen Bonding

The ability to predict the strength of halogen bonds and properties of halogen bond (XB) donors has significant utility for medicinal chemistry and materials science. XBs are typically calculated through expensive ab initio methods. Thus, the development of tools and techniques for fast, accurate, and efficient property predictions has become increasingly more important. Herein, we employ three machine learning models to classify the XB donors and complexes by their principal halogen atom as well as predict the values of the maximum point on the electrostatic potential surface (VS,max) and interaction strength of the XB complexes through a molecular fingerprint and data-based analysis. The fingerprint analysis produces a root-mean-square error of ca. 7.5 and ca. 5.5 kcal mol-1 while predicting the VS,max for the halobenzene and haloethynylbenzene systems, respectively. However, the prediction of the binding energy between the XB donors and ammonia acceptor is shown to be within 1 kcal mol-1 of the density functional theory (DFT)-calculated energy. More accurate predictions can be made from the precalculated DFT data when compared to the fingerprint analysis.

Bandgap modification in 0D tellurium iodide perovskite derivatives via incorporation of polyiodide species

Halide perovskites provide a versatile platform for exploring the effect of non-covalent interactions, including halogen bonding, on material properties such as band gap, luminescence, and frontier orbital landscape. Herein we report six new zero-dimensional tellurium iodide perovskite derivatives, consisting of [TeI₆]^2- octahedra charge balanced by one of several X-Py cations (X = H, Cl, Br, I, and Py = pyridinium). These compounds also feature robust halogen bonding between [TeI₆]^2- octahedra and polyiodides in the form of I₂ (1-4), I₃ ^- (5), or adjacent octahedra (4 and 6). These relatively strong non-covalent interactions (NCIs) are modeled by natural bond order (NBO) and second order perturbation theory (SOPT) calculations. NCIs are responsible for reducing the bandgap of these materials (measured via diffuse reflectance spectroscopy) relative to those without polyiodide species. They also affect inner sphere bonding in the metal halide, exacerbating [TeI₆]^2- octahedron asymmetry as compared to previously published compounds, with greater asymmetry correlating with higher van der Waals overlap of halogen-halogen contacts. We also demonstrate the ability of hydrogen and carbon bonding (which dominates in the absence of polyiodides) to affect inner sphere tellurium iodide bonding and octahedral symmetry.

Intermolecular interactions between the heavy-atom analogues of acetylene T2H2 (T = Si, Ge, Sn, Pb) and HCN

METHODS

The intermolecular interactions between the heavy-atom analogues of acetylene T₂H₂ (T = Si, Ge, Sn, Pb) and HCN have been investigated by theoretical calculations at the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVDZ level.

RESULTS

The global energy minimum of T₂H₂ is the butterfly structure A, and another energy minimum is the planar structure B. Both structures A and B exhibit the dual behavior when binding with HCN. The various hydrogen bond (HB), dihydrogen bond (DB) and tetrel bond (TB) complexes can be found according to the MEP maps of T₂H₂. One TB and three HB complexes formed between structure A and HCN can be located for Si₂H₂ and Ge₂H₂. One TB, two HB and one DB complexes formed between structure A and HCN can be located for Sn₂H₂ and Pb₂H₂. Four TB and one HB complexes formed between structure B and HCN can be located for all the T₂H₂. The geometries and binding strengths of the complexes are compared and analyzed.

CONCLUSIONS

The interactions in these complexes are generally weak, and the interaction energies of these complexes range from -0.53 to -8.23 kcal/mol. The interaction energies of the TB complexes are larger than those of the corresponding HB and DB complexes for structure A···HCN systems. The relative binding strength of the four TB complexes exhibits different order for different structure B···HCN systems, which is consistent with the MEP maps of the isolated monomers.

Crystal Structure Survey and Theoretical Analysis of Bifurcated Halogen Bonds

The possibility that two Lewis bases can share a single halogen atom within the context of a bifurcated halogen bond (XB) is explored first by a detailed examination of the CSD. Of the more than 22,000 geometries that fit the definition of an XB (with X = Cl, Br, I), less than 2% are bifurcated. There is a heavy weighting of I in such bifurcated arrangements as opposed to Br, which prefers monofurcated bonds. The conversion from mono to bifurcated is associated with a smaller number of short contact distances, as well as a trend toward lesser linearity. The two XBs within a bifurcated system are somewhat symmetrical: the two lengths generally differ by less than 0.05 Å, and the two XB angles are within several degrees of one another. Quantum calculations of model systems reflect the patterns observed in crystals and reinforce the idea that the negative cooperativity within a bifurcated XB weakens and lengthens each individual bond.

Insight on noncovalent interactions and orbital constructs in low-dimensional antimony halide perovskites

Reported is a series of eight antimony halide perovskite derivatives synthesized from acidic aqueous solutions of antimony oxide and halogen substituted pyridines. These materials feature anionic one-dimensional antimony halide (SbX; X = Cl, Br, I) chains or ribbons charge-balanced by organic para-halopyridinium cations (XPy; X = H, Cl, Br) which assemble into three-dimensional networks via halogen and hydrogen noncovalent interactions (NCIs) between ion pairs. Computational density functional theory (DFT) based natural bonding orbital (NBO) and density of state (DOS) methods were utilized to map the band structure and quantify and categorize noncovalent interaction strength and type. Moreover, we determined the presence of hybridized intermediate bands which are responsible for the small bandgap energies within this family and arise from mixing of the halide p-states and the Sb s-states. We note that the degree of hybridization, and thus optical properties, is influenced primarily by changes about inner sphere bonding and independent of second sphere interactions. This report is the first to specifically monitor the evolution of haloantimonate(III) hybrid perovskite atomic and molecular orbitals involved in optical behavior as a function of inner and outer sphere effects.

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.

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.

Intermolecular interactions between the heavy alkenes H2Si = TH2 (T = C, Si, Ge, Sn, Pb) and acetylene

The intermolecular interactions between the heavy alkenes H₂Si = TH₂ (T = C, Si, Ge, Sn, Pb) and C₂H₂ have been calculated at the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVDZ level, and the nature of these complexes has been investigated by natural bond orbital. The four types (type-A, type-B, type-C and type-D) of complexes can be located for H₂Si = TH₂···C₂H₂ system. The complexes involving H₂Si = TH₂···C₂F₂ and H₂Si = TH₂···C₂(CN)₂ have also been examined to explore the substituent effects. Some complexes which are stable for H₂Si = TH₂···C₂H₂ system become unstable for H₂Si = TH₂···C₂F₂ or H₂Si = TH₂···C₂(CN)₂ system, while other complexes which are unstable for H₂Si = TH₂···C₂H₂ system become stable for H₂Si = TH₂···C₂F₂ or H₂Si = TH₂···C₂(CN)₂ system.

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.

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.

Intermolecular Interactions Involving Heavy Alkenes H2Si=TH2 (T = C, Si, Ge, Sn, Pb) with H2O and HCl: Tetrel Bond and Hydrogen Bond

The intermolecular interactions between the heavy alkenes H₂Si=TH₂ (T = C, Si, Ge, Sn, Pb) and H₂O or HCl have been explored at the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVDZ level. The various hydrogen bond (HB) and tetrel bond (TB) complexes can be located on the basis of molecular electrostatic potential maps of the isolated monomers. The competition between TB and HB interactions has been investigated through the relaxed potential energy surface scan. The results indicate that the HB complexes become more and more unstable relative to the TB complexes with the increase of the T atomic number, and cannot even retain as a minimum in some cases, for H₂Si=TH2···H₂O systems. In contrast, the HB complexes are generally more stable than TB complexes, and the TB complexes exhibit rather weak binding strength, for H₂Si=TH₂···HCl systems. The majority of the TB complexes formed between H₂Si=TH₂ and H₂O possesses very strong binding strength with covalent characteristics. The noncovalent TB complexes can be divided into two types on the basis of the orbital interactions: π-hole complexes, with binding angles ranging from 91 to 111°, and hybrid σ/π-hole complexes, with binding angles ranging from 130 to 165°. The interplay between different molecular interactions has been explored, and an interesting result is that the covalent TB interaction is significantly abated and becomes noncovalent because of the competitive effect.

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.

Theoretical Description of R-X⋯NH3 Halogen Bond Complexes: Effect of the R Group on the Complex Stability and Sigma-Hole Electron Depletion

In the present work, a number of R–X⋯NH₃ (X = Cl, Br, and I) halogen bonded systems were theoretical studied by means of DFT calculations performed at the ωB97XD/6-31+G(d,p) level of theory in order to get insights on the effect of the electron-donating or electron-withdrawing character of the different R substituent groups (R = halogen, methyl, partially fluorinated methyl, perfluoro-methyl, ethyl, vinyl, and acetyl) on the stability of the halogen bond. The results indicate that the relative stability of the halogen bond follows the Cl < Br < I trend considering the same R substituent whereas the more electron-withdrawing character of the R substituent the more stable the halogen bond. Refinement of the latter results, performed at the MP2/6-31+G(d,p) level showed that the DFT and the MP2 binding energies correlate remarkably well, suggesting that the Grimme’s type dispersion-corrected functional produces reasonable structural and energetic features of halogen bond systems. DFT results were also observed to agree with more refined calculations performed at the CCSD(T) level. In a further stage, a more thorough analysis of the R–Br⋯NH₃ complexes was performed by means of a novel electron localization/delocalization tool, defined in terms of an Information Theory, IT, based quantity obtained from the conditional pair density. For the latter, our in-house developed C++/CUDA program, called KLD (acronym of Kullback–Leibler divergence), was employed. KLD results mapped onto the one-electron density plotted at a 0.04 a.u. isovalue, showed that (i) as expected, the localized electron depletion of the Br sigma-hole is largely affected by the electron-withdrawing character of the R substituent group and (ii) the R–X bond is significantly polarized due to the presence of the NH₃ molecule in the complexes. The afore-mentioned constitutes a clear indication of the dominant character of electrostatics on the stabilization of halogen bonds in agreement with a number of studies reported in the main literature. Finally, the cooperative effects on the [Br—CN]_n system (n = 1–8) was evaluated at the MP2/6-31+G(d,p) level, where it was observed that an increase of about ~14.2% on the complex stability is obtained when going from n = 2 to n = 8. The latter results were corroborated by the analysis of the changes on the Fermi-hole localization pattern on the halogen bond zones, which suggests an also important contribution of the electron correlation in the stabilization of these systems.

A Million Crystal Structures: The Whole Is Greater than the Sum of Its Parts

The founding in 1965 of what is now called the Cambridge Structural Database (CSD) has reaped dividends in numerous and diverse areas of chemical research. Each of the million or so crystal structures in the database was solved for its own particular reason, but collected together, the structures can be reused to address a multitude of new problems. In this Review, which is focused mainly on the last 10 years, we chronicle the contribution of the CSD to research into molecular geometries, molecular interactions, and molecular assemblies and demonstrate its value in the design of biologically active molecules and the solid forms in which they are delivered. Its potential in other commercially relevant areas is described, including gas storage and delivery, thin films, and (opto)electronics. The CSD also aids the solution of new crystal structures. Because no scientific instrument is without shortcomings, the limitations of CSD research are assessed. We emphasize the importance of maintaining database quality: notwithstanding the arrival of big data and machine learning, it remains perilous to ignore the principle of garbage in, garbage out. Finally, we explain why the CSD must evolve with the world around it to ensure it remains fit for purpose in the years ahead.

Tetrel Bond between 6-OTX₃-Fulvene and NH₃: Substituents and Aromaticity

Carbon bonding is a weak interaction, particularly when a neutral molecule acts as an electron donor. Thus, there is an interesting question of how to enhance carbon bonding. In this paper, we found that the –OCH₃ group at the exocyclic carbon of fulvene can form a moderate carbon bond with NH₃ with an interaction energy of about −10 kJ/mol. The –OSiH₃ group engages in a stronger tetrel bond than does the –OGeH₃ group, while a reverse result is found for both –OSiF₃ and –OGeF₃ groups. The abnormal order in the former is mainly due to the stronger orbital interaction in the –OSiH₃ complex, which has a larger deformation energy. The cyano groups adjoined to the fulvene ring not only cause a change in the interaction type, from vdW interactions in the unsubstituted system of –OCF₃ to carbon bonding, but also greatly strengthen tetrel bonding. The formation of tetrel bonding has an enhancing effect on the aromaticity of the fulvene ring.

Quantum-mechanical investigation of tetrel bond characteristics based on the point-of-charge (PoC) approach

The point-of-charge (PoC) approach was employed to investigate the characteristics of the tetrel bond from an electrostatic perspective. W-T-XYZ···B nomenclature was suggested where T is a tetrel atom, W is the atom along the σ-hole extension, B is a Lewis base, and X, Y, and Z are three atoms on the same side of the σ-hole. Quantum-mechanical calculations were carried out on F-T-F₃ systems (where T = C, Si, Ge, or Sn) at the MP2/aug-cc-pVTZ level of theory, with PP functions for Ge and Sn atoms. The tetrel bond strength was estimated via the molecular stabilization energy. Tetrel bond strength was found to increase with increasing PoC negativity (i.e., Lewis basicity) and the electronegativity of the W atom. Moreover, the effects of the T···PoC distance, the W-T···PoC angle, and the aqueous medium on the tetrel bond strength were also investigated. Correlations between tetrel bond strength and several atomic and molecular descriptors such as the natural charge on the tetrel atom, E_HOMO, and the p-orbital contribution to W-T bond hybridization were observed. Contrary to expectations, the tetrel bond strength in F-C-X₃ increased as the electronegativity of X decreased. The σ-node criteria for the studied molecules were also introduced and discussed. The ability of these molecules to simultaneously form more than one tetrel bond was examined via the σⁿ-hole test. In conclusion, the tetrel bond strength was found to be governed by the strengths of (i) the attractive electrostatic interaction of the Lewis base with the σ-hole, (ii) the attractive/repulsive interaction between the Lewis base and the X, Y, and Z atoms, and (iii) the van der Waals interaction between the Lewis base and the X, Y, and Z atoms. Graphical Abstract Characterization of tetrel bond using the Point-of-Charge (PoC) approach.

On the σ, π and δ hole interactions: a molecular orbital overview

With molecular orbital theory it is possible to distinguish and design σ, π and the elusive δ electrostatic holes.