Interaction and Polarization Energy Relationships in σ-Hole and π-Hole Bonding

Perfluoroaromatic Bisselanes: From Molecular Design to Supramolecular Architecture Through Tandem σ/π-hole Interactions

The molecular design of a series of perfluoroarylbisselanes (30-68 %) o-, m- and p-(ArFSe)2C6F4 and (ArFSe)2C12F8 (ArF=C6F5 and p-C6F4CF3) were achieved through the reaction of ArFSeCu with diiodoperfluoroarenes bearing phenyl and biphenyl rings. Analysis of the X-ray diffraction (XRD) data for the resulting perfluoroaromatic bisselanes 5-12 demonstrated their significant potential for constructing supramolecular architectures through tandem noncovalent interactions, including chalcogen bonding (ChB) and πhole-π interactions. 1,2-Bis(pentafluorophenylseleno)tetrafluorobenzene 5 was cocrystallized with dibenzyl ether, yielding the adduct 52⋅Bn2O, which exhibited a triad structural motif. Its XRD data provided structural insights into the ChB-based catalysis mechanism of Friedel-Crafts type reaction involving benzyl ether derivatives. Comprehensive density functional theory studies: energy decomposition analysis (EDA), molecular electrostatic potential (MEP) assessments, van der Waals potential evaluations, electrostatic potential and energy density (ED/ESP) plots, as well as natural bond orbital (NBO) analysis - revealed that Se⋅⋅⋅O chalcogen bonding (10.1 kcal/mol) and πhole-π interactions (12.6 kcal/mol) contribute comparably to the overall energetics, thus playing a significant role in guiding molecular assembly.

An orbital-overlap complement to σ-hole electrostatic potentials

A σ-hole is an electron-deficient region of positive electrostatic potential (ESP) opposite from a half-filled p orbital involved in forming a covalent bond. The σ-hole concept helps rationalize directional noncovalent interactions, known as σ-hole bonds, between covalently bonded group V-VII atoms and electron-pair donors. The magnitude and orientation of σ-holes are correlated with the strength and geometry of halogen bonds. However, ESP computed for isolated σ-holes are not always predictive of interaction energies. For example, the σ-holes of isolated CHFBr2 and isolated CH2FI have identical ESP on the molecule surface, but halogen bonds to these molecules generally have different strengths. Here we show that the compact/diffuse nature of the orbitals involved plays an important role. Our orbital overlap distance quantifies the compact/diffuse nature of the "test orbital" that best overlaps with a systems orbitals at each point. The overlap distance captures the response properties of σ-holes: diffuse σ-holes with large overlap distance are typically "softer" and more polarizable. This aids visualization and interpretation. A linear fit to overlap distance and ESP is predictive of the halogen bond strengths of CH3X and CF3X (X = Cl, Br and I). We suggest that the overlap distance will be a useful partner to ESP for characterizing σ-holes.

Radial Behavior of Electrostatic Potentials of Atoms and Ions Revisited: Isotropy and Anisotropy

In this paper we revisit earlier work relating to monoatomic atoms and ions published by pioneers in the area of electrostatic potentials. We include plots of the radial distributions of the electrostatic potentials for spherically symmetric atoms and cations, and for singly, doubly and triply negative anions. For atoms with anisotropy in their densities and electrostatic potentials, such as the halonium cations, it is shown how the molecular surface approach for plotting electrostatic potentials complements that achieved by directional radial distributions.

A comprehensive electron wavefunction analysis toolbox for chemists, Multiwfn

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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.

The Formation of σ-Hole Bonds: A Physical Interpretation

This paper discusses two quite different computational experiments relating to the formation of σ-hole bonds A···B. The first involves looking at the complex at equilibrium and finding the contour X of the electronic density which allows the iso-density envelopes of A and B to be nearly touching. This contour increases, becoming closer to the nuclei, as the strength of the interaction increases. The second experiment involves allowing A and B to approach each other, with the aim of finding the distance at which their 0.001 a.u. iso-density envelopes are nearly merging into one envelope. What is found in the second experiment may be somewhat surprising, in that the ratio of the distance between interacting atoms at this nearly merging point-divided by the sum of the van der Waals radii of these atoms-covers a narrow range, typically between 1.2 and 1.3. It is intriguing to note that for the dataset presented, approaching molecules attracted to each other appear to do so unknowing of the strength of their ultimate interaction. This second experiment also supports the notion that one should expect favorable interactions, in some instances, to have close contacts significantly greater than the sums of the van der Waals radii.

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.

N-X⋅⋅⋅O-N Halogen Bonds in Complexes of N-Haloimides and Pyridine-N-oxides: A Large Data Set Study

N-X⋅⋅⋅- O-N+ halogen-bonded systems formed by 27 pyridine N-oxides (PyNOs) as halogen-bond (XB) acceptors and two N-halosuccinimides, two N-halophthalimides, and two N-halosaccharins as XB donors are studied in silico, in solution, and in the solid state. This large set of data (132 DFT optimized structures, 75 crystal structures, and 168 1 H NMR titrations) provides a unique view to structural and bonding properties. In the computational part, a simple electrostatic model (SiElMo) for predicting XB energies using only the properties of halogen donors and oxygen acceptors is developed. The SiElMo energies are in perfect accord with energies calculated from XB complexes optimized with two high-level DFT approaches. Data from in silico bond energies and single-crystal X-ray structures correlate; however, data from solution do not. The polydentate bonding characteristic of the PyNOs' oxygen atom in solution, as revealed by solid-state structures, is attributed to the lack of correlation between DFT/solid-state and solution data. XB strength is only slightly affected by the PyNO oxygen properties [(atomic charge (Q), ionization energy (Is,min ) and local negative minima (Vs,min )], as the σ-hole (Vs,max ) of the donor halogen is the key determinant leading to the sequence N-halosaccharin>N-halosuccinimide>N-halophthalimide on the XB strength.

Anomalous π-backbonding in complexes between B(SiR3)3 and N2: catalytic activation and breaking of scaling relations

Chemical transformations of molecular nitrogen (N2), including the nitrogen reduction reaction (NRR), are difficult to catalyze because of the weak Lewis basicity of N2. In this study, it is shown that Lewis acids of the types B(SiR3)3 and B(GeR3)3 bind N2 and CO with anomalously short and strong B-N or B-C bonds. B(SiH3)3·N2 has a B-N bond length of 1.48 Å and a complexation enthalpy of -15.9 kcal mol-1 at the M06-2X/jun-cc-pVTZ level. The selective binding enhancement of N2 and CO is due to π-backbonding from Lewis acid to Lewis base, as demonstrated by orbital analysis and density difference plots. The π-backbonding is found to be a consequence of constructive orbital interactions between the diffuse and highly polarizable B-Si and B-Ge bond regions and the π and π* orbitals of N2. This interaction is strengthened by electron donating substituents on Si or Ge. The π-backbonding interaction is predicted to activate N2 for chemical transformation and reduction, as it decreases the electron density and increases the length of the N-N bond. The binding of N2 and CO by the B(SiR3)3 and B(GeR3)3 types of Lewis acids also has a strong σ-bonding contribution. The relatively high σ-bond strength is connected to the highly positive surface electrostatic potential [VS(r)] above the B atom in the tetragonal binding conformation, but the σ-bonding also has a significant coordinate covalent (dative) contribution. Electron withdrawing substituents increase the potential and the σ-bond strength, but favor the binding of regular Lewis acids, such as NH3 and F-, more strongly than binding of N2 and CO. Molecules of the types B(SiR3)3 and B(GeR3)3 are chemically labile and difficult to synthesize. Heterogenous catalysts with the wanted B(Si-)3 or B(Ge-)3 bonding motif may be prepared by boron doping of nanostructured silicon or germanium compounds. B-doped and hydrogenated silicene is found to have promising properties as catalyst for the electrochemical NRR.

Methylammonium Tetrel Halide Perovskite Ion Pairs and Their Dimers: The Interplay between the Hydrogen-, Pnictogen- and Tetrel-Bonding Interactions

The structural stability of the extensively studied organic-inorganic hybrid methylammonium tetrel halide perovskite semiconductors, MATtX₃ (MA = CH₃NH₃⁺; Tt = Ge, Sn, Pb; X = Cl, Br, I), arises as a result of non-covalent interactions between an organic cation (CH₃NH₃⁺) and an inorganic anion (TtX₃^-). However, the basic understanding of the underlying chemical bonding interactions in these systems that link the ionic moieties together in complex configurations is still limited. In this study, ion pair models constituting the organic and inorganic ions were regarded as the repeating units of periodic crystal systems and density functional theory simulations were performed to elucidate the nature of the non-covalent interactions between them. It is demonstrated that not only the charge-assisted N-H···X and C-H···X hydrogen bonds but also the C-N···X pnictogen bonds interact to stabilize the ion pairs and to define their geometries in the gas phase. Similar interactions are also responsible for the formation of crystalline MATtX₃ in the low-temperature phase, some of which have been delineated in previous studies. In contrast, the Tt···X tetrel bonding interactions, which are hidden as coordinate bonds in the crystals, play a vital role in holding the inorganic anionic moieties (TtX₃^-) together. We have demonstrated that each Tt in each [CH₃NH₃⁺•TtX₃^-] ion pair has the capacity to donate three tetrel (σ-hole) bonds to the halides of three nearest neighbor TtX₃^- units, thus causing the emergence of an infinite array of 3D TtX₆^4- octahedra in the crystalline phase. The TtX₄^4- octahedra are corner-shared to form cage-like inorganic frameworks that host the organic cation, leading to the formation of functional tetrel halide perovskite materials that have outstanding optoelectronic properties in the solid state. We harnessed the results using the quantum theory of atoms in molecules, natural bond orbital, molecular electrostatic surface potential and independent gradient models to validate these conclusions.

Gauging the Strength of the Molecular Halogen Bond via Experimental Electron Density and Spectroscopy

Strong and weak halogen bonds (XBs) in discrete aggregates involving the same acceptor are addressed by experiments in solution and in the solid state. Unsubstituted and perfluorinated iodobenzenes act as halogen donors of tunable strength; in all cases, quinuclidine represents the acceptor. NMR titrations reliably identify the strong intermolecular interactions in solution, with experimental binding energies of approx. 7 kJ/mol. Interaction of the σ hole at the halogen donor iodine leads to a redshift in the symmetric C-I stretching vibration; this shift reflects the interaction energy in the halogen-bonded adducts and may be assessed by Raman spectroscopy in condensed phase even for weak XBs. An experimental picture of the electronic density for the XBs is achieved by high-resolution X-ray diffraction on suitable crystals. Quantum theory of atoms in molecules (QTAIM) analysis affords the electron densities and energy densities in the bond critical points of the halogen bonds and confirms stronger interaction for the shorter contacts. For the first time, the experimental electron density shows a significant effect on the atomic volumes and Bader charges of the quinuclidine N atoms, the halogen-bond acceptor: strong and weak XBs are reflected in the nature of their acceptor atom. Our experimental findings at the acceptor atom match the discussed effects of halogen bonding and thus the proposed concepts in XB activated organocatalysis.

"Noncovalent Interaction": A Chemical Misnomer That Inhibits Proper Understanding of Hydrogen Bonding, Rotation Barriers, and Other Topics

We discuss the problematic terminology of "noncovalent interactions" as commonly applied to hydrogen bonds, rotation barriers, steric repulsions, and other stereoelectronic phenomena. Although categorization as "noncovalent" seems to justify classical-type pedagogical rationalizations, we show that these phenomena are irreducible corollaries of the same orbital-level conceptions of electronic covalency and resonance that govern all chemical bonding phenomena. Retention of such nomenclature is pedagogically misleading in supporting superficial dipole-dipole and related "simple, neat, and wrong" conceptions as well as perpetuating inappropriate bifurcation of the introductory chemistry curriculum into distinct "covalent" vs. "noncovalent" modules. If retained at all, the line of dichotomization between "covalent" and "noncovalent" interaction should be re-drawn beyond the range of quantal exchange effects (roughly, at the contact boundary of empirical van der Waals radii) to better unify the pedagogy of molecular and supramolecular bonding phenomena.

Halogen bonds with carbenes acting as Lewis base units: complexes of imidazol-2-ylidene: theoretical analysis and experimental evidence

ωB97XD/aug-cc-pVDZ and ωB97XD/aug-cc-pVTZ calculations were performed on complexes of imidazol-2-ylidene that are linked by halogen bonds. This singlet carbene acts as the Lewis base through a lone electron pair located at the carbon centre. The XCCH, XCN and X₂ units were chosen here as those that interact through the X Lewis acid halogen centre (X = Cl, Br and I); if X = F the complexes are linked by interactions which are not classified as halogen bonds. The properties of interactions that occur in complexes are analyzed using the results of DFT calculations which are supported by parameters derived from the Quantum Theory of Atoms in Molecules, QTAIM, and the Natural Bond Orbital, NBO, approaches. The energy decomposition analysis, EDA, applied here provided additional characteristics of interactions linking complexes analyzed. The majority of complexes are linked by the medium in strength and strong halogen bonds which often possess characteristics typical for covalent bonds. Searches through the Cambridge Structural Database were also performed and structures analogues to complexes analyzed theoretically were found, and these structures are also discussed in this study.

Shedding Light on the Vibrational Signatures in Halogen-Bonded Graphitic Carbon Nitride Building Blocks

The relative contributions of halogen and hydrogen bonding to the interaction between graphitic carbon nitride monomers and halogen bond (XB) donors containing C-X and C≡C bonds were evaluated using computational vibrational spectroscopy. Conventional probes into select vibrational stretching frequencies can often lead to disconnected results. To elucidate this behavior, local mode analyses were performed on the XB donors and complexes identified previously at the M06-2X/aVDZ-PP level of theory. Due to coupling between low and high energy C-X vibrations, the C≡C stretch is deemed a better candidate when analyzing XB complex properties or detecting XB formation. The local force constants support this conclusion, as the C≡C values correlate much better with the σ-hole magnitude than their C-X counterparts. The intermolecular local stretching force constants were also assessed, and it was found that attractive forces other than halogen bonding play a supporting role in complex formation.

Unexpected Strengthening of the H-Bond Complexes in a Polar Solvent Due to a More Efficient Solvation of the Complex Compared to Isolated Monomers

It is generally assumed that hydrogen-bonded complexes are less stable in solvents than in the gas phase and that their stability decreases with increasing solvent polarity. This assumption is based on the size of the area available to the solvent, which is always smaller in the complex compared to the subsystems, thereby reducing the solvation energy. This reduction prevails over the amplification of the electrostatic hydrogen bond by the polar solvent. In this work, we show, using experimental IR spectroscopy and DFT calculations, that there are hydrogen-bonded complexes whose stability becomes greater with increasing solvent polarity. The explanation for this surprising stabilization is based on the analysis of the charge redistribution in the complex leading to increase of its dipole moment and solvation energy. Constrained DFT calculations have shown a dominant role of charge transfer over polarization effects for dipole moment and solvation energy.

Noncovalent interactions between benzochalcogenadiazoles and nitrogen bases

A theoretical study has been carried out on the intermolecular interactions between tetrafluoro-benzochalcogenadiazoles (chalcogen = S, Se, Te) and a series of nitrogen bases (FCN, ClCN, NP, trans-N₂H₂, pyridine, pyrazole, imidazole) at the B97-D3/def2-TZVP level, to obtain a better insight into the nature and strength of Ch···N chalcogen bond and secondary interaction in the binary and 1:2 ternary complexes. The dispersion force plays a prominent role on the stability of the sulfur complexes, and the electrostatic effect enhanced for the heavier chalcogen complexes. Most of intermolecular bonds display the characters of closed-shell and noncovalent interaction. For the complexes involving pyridine and imidazole, chalcogen bond is stronger than hydrogen bond, while the strength of chalcogen bond is equivalent to the secondary interaction for other complexes. With the addition of nitrogen base in the 1:2 complexes, chalcogen bond is weakened, while the secondary interaction remains unchanged. In the 1:2 complexes formed by pyridine and imidazole, stronger chalcogen bond results in larger negative cooperativity than that of other complexes.

A bibliographic survey of the supramolecular architectures sustained by delocalised C–I⋯π(arene) interactions in metal-organic crystals

A survey of the crystallographic literature of metal-organic crystal structures for the presence of C–I···π(arene) interactions where the iodide atom occupies a position close to plumb to the ring centroid, corresponding to a delocalised interaction, and is within the assumed sum of the van der Waals radii, i.e. 3.88 Å, has been undertaken. The majority of the 26 identified examples feature supramolecular chains of varying topology whereby C–I···π(arene) contacts are readily identified and apparently operating independently of other obvious supramolecular synthons. The next most prevalent supramolecular aggregate was zero-dimensional, containing up to a maximum of three molecules. While there were three examples of two-dimensional arrays among a series of isostructural crystal structures, no examples of three-dimensional structures largely sustained by C–I···π(arene) interactions were noted. This distribution of supramolecular aggregation patterns matched that noted for all-organic systems. In terms of the overall adoption rate, delocalised C–I···π(arene) interactions were found in 3% of crystals of metal-organic species where they could form, a percentage lower than 4% noted for all-organic crystals.

Periodate anions as a halogen bond donor: formation of anion⋯anion dimers and other adducts

Single crystal X-ray analyses show that iodine in pyridinium periodates acts as a halogen bond (HaB) donor forming short and almost linear contacts with neutral and anionic electron donors. A combination of QTAIM and NCIplot computational tools proves the attractive nature of these contacts.

Domination of H-Bond Interactions in the Solvent-Triggering Gelation Process

Gels prepared with the solvent-triggering method are attractive for their easy and fast preparation; however, the role of solvents in this process remains unclear, which hinders the efficient and accurate control of desired gel properties. In this study, the role of solvents in the solvent-triggering gelation process is studied using 9-fluorenylmethoxycarbonyl (Fmoc)-protected diphenylalanine (Fmoc-FF) as the gelator. Density functional theory (DFT)-based calculations and corresponding wavefunction analyses are conducted to identify the H-bonding interaction sites between the molecules. The calculation results clearly annotate the activating role of DMF and the triggering role of H₂O in the gelation process. The solvation of Fmoc-FF by DMF can activate the H-bonding sites on the peptide chain, showing a conformation reversal and higher electrostatic potentials. Then, the H-bonding between Fmoc-FF and H₂O is facilitated to trigger gelation. The physical Fmoc-FF/DMF/H₂O gels show easily tuned mechanical strengths (G' of 10²-10⁵ Pa), injectable potentials (general yield strain < 100%), and stable recoverability (80-98% within 100 s). The regulation of these properties depends on not only the gelator concentration but also the H-bonding interactions with solvent molecules, which have seldom been studied in detail before. By understanding the effect of solvents, low-molecular-weight gelator-based gels can be designed, prepared, and tuned efficiently for potential applications.

Rational Computational Design of Systems Exhibiting Strong Halogen Bonding Involving Fluorine in Bicyclic Diamine Derivatives

Perhaps the most controversial and rare aspect of the halogen bonding interaction is the potential of fluorine in compounds to serve as a halogen bond donor. In this note, we provide clear and convincing examples of hypothetical molecules in which fluorine is strongly halogen bonding in a metastable state. Of particular note is a polycyclic system inspired by Selectfluor, which has been controversially proposed to engage in halogen bonding.

Altering singlet fission pathways in perylene-dimers; perylene-diimide versus perylene-monoimide

We used a systematic approach to shed light on the inherent differences in perylenes, namely monoimides versus diimides, including coplanarity and dipole moment, and their impact on singlet fission (SF) by designing, synthesizing, and probing a full fledged series of phenylene- and naphthalene-linked dimers. Next to changing the functionality of the perylene core, we probed the effect of the spacers and their varying degrees of rotational freedom, molecular electrostatic potentials, and intramolecular interactions on the SF-mechanism and -efficiencies. An arsenal of spectroscopic techniques revealed that for perylene-monoimides, a strong charge-transfer mixing with the singlet and triplet excited states restricts SF and yields low triplet quantum yields. This is accompanied by an up-conversion channel that includes geminate triplet-triplet recombination. Using perylene-diimides alters the SF-mechanism by populating a charge-separated-state intermediate, which either favors or shuts-down SF. Napthylene-spacers bring about higher triplet quantum yields and overall better SF-performance for all perylene-monoimides and perylene-diimides. The key to better SF-performance is rotational freedom because it facilitates the overall excited-state polarization and amplifies intramolecular interactions between chromophores.

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.

Noble-gas compounds: A general procedure of bonding analysis

This paper accounts for a general procedure of bonding analysis that is, expectedly, adequate to describe any type of interaction involving the noble-gas (Ng) atoms. Building on our recently proposed classification of the Ng-X bonds (X = binding partner) [New J. Chem. 44, 15536 (2020)], these contacts are first distinguished into three types, namely, A, B, or C, based on the topology of the electron energy density H(r) and on the shape of its plotted form. Bonds of type B or C are, then, further assigned as B-loose (B^l) or B-tight (B^t) and C-loose (C^l) or C-tight (C^t) depending on the sign that H(r) takes along the Ng-X bond path located from the topological analysis of ρ(r), particularly at around the bond critical point (BCP). Any bond of type A, B^l/B^t, or C^l/C^t is, finally, assayed in terms of contribution of covalency. This is accomplished by studying the maximum, minimum, and average value of H(r) over the volume enclosed by the low-density reduced density gradient (RDG) isosurface associated with the bond (typically, the RDG isosurface including the BCP) and the average ρ(r) over the same volume. The bond assignment is also corroborated by calculating the values of quantitative indices specifically defined for the various types of interactions (A, B, or C). The generality of our taken approach should encourage its wide application to the study of Ng compounds.

The use of electrostatic potential at nuclei in the analysis of halogen bonding

Molecular electrostatic potential data at interacting nuclei provide strong evidence of bond formation in many intermolecular halogen bonded complexes.

Electric fields and potentials in condensed phases

The electric fields and potentials inside and at the interface of matter are relevant to many branches of physics, chemistry, and biology. Accurate quantification of these fields and/or potentials is essential to control and exploit chemical and physical transformations. Before we understand the response of matter to external fields, it is first important to understand the intrinsic interior and interfacial fields and potentials, both classically and quantum mechanically, as well as how they are probed experimentally. Here we compare and contrast, beginning with the hydrogen atom in vacuum and ending with concentrated aqueous NaCl electrolyte, both classical and quantum mechanical electric potentials and fields. We make contact with experimental vibrational Stark, electrochemical, X-ray, and electron spectroscopic probes of these potentials and fields, outline relevant conceptual difficulties, and underscore the advantage of electron holography as a basis to better understand electrostatics in matter.

The π-hole revisited

It follows from the Schrödinger equation that the forces operating within molecules and molecular complexes are Coulombic, which necessarily entails both electrostatics and polarization. A common and important class of molecular complexes is due to π-holes. These are molecular regions of low electronic density that are perpendicular to planar portions of the molecular frameworks. π-Holes often have positive electrostatic potentials associated with them, which result in mutually polarizing attractive forces with negative sites such as lone pairs, π electrons or anions. In many molecules, π-holes correspond to a flattening of the electronic density surface but in benzene derivatives and in polyazines the π-holes are craters above and below the rings. The interaction energies of π-hole complexes can be expressed quite well in terms of regression relationships that account for both the electrostatics and the polarization. There is a marked gradation in the interaction energies, from quite weak (about -2 kcal mol-1) to relatively strong (about -40 kcal mol-1). Gradations are also evident in the ratios of the intermolecular separations to the sums of the respective van der Waals radii and in the gradual transition of the π-hole atoms from trigonal to quasi-tetrahedral configurations. These trends are consistent with the concept that chemical interactions form a continuum, from very weak to very strong.

Concerning the Role of σ-Hole in Non-Covalent Interactions: Insights from the Study of the Complexes of ArBeO with Simple Ligands

The structure, stability, and bonding character of some exemplary LAr and L-ArBeO (L = He, Ne, Ar, N₂, CO, F₂, Cl₂, ClF, HF, HCl, NH₃) were investigated by MP2 and coupled-cluster calculations, and by symmetry-adapted perturbation theory. The nature of the stabilizing interactions was also assayed by the method recently proposed by the authors to classify the chemical bonds in noble-gas compounds. The comparative analysis of the LAr and L-ArBeO unraveled geometric and bonding effects peculiarly related to the σ-hole at the Ar atom of ArBeO, including the major stabilizing/destabilizing role of the electrostatic interactionensuing from the negative/positive molecular electrostatic potential of L at the contact zone with ArBeO. The role of the inductive and dispersive components was also assayed, making it possible to discern the factors governing the transition from the (mainly) dispersive domain of the LAr, to the σ-hole domain of the L-ArBeO. Our conclusions could be valid for various types of non-covalent interactions, especially those involving σ-holes of respectable strength such as those occurring in ArBeO.

Hydrogen-Bonded and Halogen-Bonded: Orthogonal Interactions for the Chloride Anion of a Pyrazolium Salt

In the hydrochloride of a pyrazolyl-substituted acetylacetone, the chloride anion is hydrogen-bonded to the protonated pyrazolyl moiety. Equimolar co-crystallization with tetrafluorodiiodobenzene (TFDIB) leads to a supramolecular aggregate in which TFDIB is situated on a crystallographic center of inversion. The iodine atom in the asymmetric unit acts as halogen bond donor, and the chloride acceptor approaches the σ-hole of this TFDIB iodine subtending an almost linear halogen bond, with Cl···I = 3.1653(11) Å and Cl···I-C = 179.32(6)°. This contact is roughly orthogonal to the N-H···Cl hydrogen bond. An analysis of the electron density according to Bader's Quantum Theory of Atoms in Molecules confirms bond critical points (bcps) for both short contacts, with ρbcp = 0.129 for the halogen and 0.321eÅ-3 for the hydrogen bond. Our halogen-bonded adduct represents the prototype for a future class of co-crystals with tunable electron density distribution about the σ-hole contact.

Can Counter-Intuitive Halogen Bonding Be Coulombic?

We use the term "counter-intuitive" to describe an intermolecular interaction in which the electrostatic potentials of the interacting regions of the ground-state molecules have the same sign, both positive or both negative. In the present work, we consider counter-intuitive halogen bonding with nitrogen bases, in which both the halogen σ-hole and the nitrogen lone pair have negative potentials on their molecular surfaces. We show that these interactions can be treated as Coulombic despite the apparent repulsion between the ground-state molecules, provided that both electrostatics and polarization are explicitly taken into account. We demonstrate first that the energies of 20 counter-intuitive interactions with four nitrogen bases can be expressed very well in terms of just two molecular properties: the electrostatic potential of the halogen σ-hole and the average polarizability of the nitrogen base. Then we show that the same two properties can also represent the energies of an expanded data base that includes the 20 counter-intuitive plus an additional 20 weak and moderately-strong intuitive halogen bonding interactions (in which the σ-hole potentials are now positive).

Comparative Structural Study of Three Tetrahalophthalic Anhydrides: Recognition of X···O(anhydride) Halogen Bond and πh···O(anhydride) Interaction

Structures of three tetrahalophthalic anhydrides (TXPA: halogen = Cl (TCPA), Br (TBPA), I (TIPA)) were studied by X-ray diffraction, and several types of halogen bonds (HaB) and lone pair···π-hole (lp···πh) contacts were revealed in their structures. HaBs involving the central oxygen atom of anhydride group (further X···O(anhydride) were recognized in the structures of TCPA and TBPA. In contrast, for the O(anhydride) atom of TIPA, only interactions with the π system (π-hole) of the anhydride ring (further lp(O)···πh) were observed. Computational studies by a number of theoretical methods (molecular electrostatic potentials, the quantum theory of atoms in molecules, the independent gradient model, natural bond orbital analyses, the electron density difference, and symmetry-adapted perturbation theory) demonstrated that the X···O(anhydride) contacts in TCPA and TBPA and lp(O)···πh in TIPA are caused by the packing effect. The supramolecular architecture of isostructural TCPA and TBPA was mainly affected by X···O(acyl) and X···X HaBs, and, for TIPA, the main contribution provided I···I HaBs.

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

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

"Anti-electrostatic" halogen bonding in solution

Halogen-bonded (XB) complexes between halide anions and a cyclopropenylium-based anionic XB donor were characterized in solution for the first time. Spontaneous formation of such complexes confirms that halogen bonding is sufficiently strong to overcome electrostatic repulsion between two anions. The formation constants of such "anti-electrostatic" associations are comparable to those formed by halides with neutral halogenated electrophiles. However, while the latter usually show charge-transfer absorption bands, the UV-Vis spectra of the anion-anion complexes examined herein are determined by the electronic excitations within the XB donor. The identification of XB anion-anion complexes substantially extends the range of the feasible XB systems, and it provides vital information for the discussion of the nature of this interaction.

Noncovalent Bonds through Sigma and Pi-Hole Located on the Same Molecule. Guiding Principles and Comparisons

Over the last years, scientific interest in noncovalent interactions based on the presence of electron-depleted regions called σ-holes or π-holes has markedly accelerated. Their high directionality and strength, comparable to hydrogen bonds, has been documented in many fields of modern chemistry. The current review gathers and digests recent results concerning these bonds, with a focus on those systems where both σ and π-holes are present on the same molecule. The underlying principles guiding the bonding in both sorts of interactions are discussed, and the trends that emerge from recent work offer a guide as to how one might design systems that allow multiple noncovalent bonds to occur simultaneously, or that prefer one bond type over another.

Nitrogen as a pnicogen?: evidence for π-hole driven novel pnicogen bonding interactions in nitromethane-ammonia aggregates using matrix isolation infrared spectroscopy and ab initio computations

The role of nitrogen, the first member of the pnicogen group, as an electron donor in hypervalent non-covalent interactions has been established long ago, while observation of its electron accepting capability is still elusive experimentally, and remains quite intriguing, conceptually. In the light of minimal computational exploration of this novel class of pnicogen bonding so far, the present work provides experimental proof with unprecedented clarity, for the existence of N(acceptor)N(donor) interaction using the model nitromethane (NM) molecule with ammonia (AM) as a Lewis base in NM-AM aggregates. The NM-AM dimer, in which the nitrogen atom of NM (as a unique pnicogen) accepts electrons from AM (the traditional electron donor), was synthesized at low temperatures under isolated conditions within inert gas matrixes and was characterized using infrared spectroscopy. The experimental generation of the NM-AM dimer stabilized via NN interaction has strong corroboration from ab initio calculations. Furthermore, confirmation regarding the directional prevalence of this NN interaction over C-HN and N-HO hydrogen bonding is elucidated quantitatively by quantum theory of atoms in molecules (QTAIM), electrostatic potential mapping (ESP), natural bond orbital (NBO), non-covalent interaction (NCI) and energy decomposition (ED) analyses. The present study also allows the extension of σ-hole/π-hole driven interactions to the atoms of the second period, in spite of their low polarizability.

Weak yet Decisive: Molecular Halogen Bond and Competing Weak Interactions of Iodobenzene and Quinuclidine

The halogen bonded adduct between the commonly used constituents quinuclidine and iodobenzene is based on a single weak nitrogen-iodine contact, and the isolation of this adduct was initially unexpected. Iodobenzene does not contain any electron-withdrawing group and therefore represents an unconventional halogen bond donor. Based on excellent diffraction data of high resolution, an electron density study was successfully accomplished and confirmed one of the longest N···I molecular halogen bonds with a distance of 2.9301(4) Å. The topological analysis identified the XB as a directional but weak σ hole interaction and revealed secondary contacts between peripheral regions of opposite charge. These additional contacts and their competition with a nitrogen-based interaction were confirmed by NOESY experiments in solution. Integration enabled us to determine the relative NOE ratios and provided insight regarding the existing interactions.

Influence of halogen atom substitution and neutral HCN/anion CN- Lewis base on the triel-bonding interactions

Triel-bonding interactions composed of Lewis acid TrOHH₂/TrOH₂X/TrOHX₂ (Tr = B, Al, Ga; X = F, Cl, Br) molecule and Lewis base neutral HCN or anionic CN^- molecule are of research significance in bond properties, which has been investigated at MP2/aug-cc-pVTZ theory level. It is also feasible to study the halogen atom substituent effect and influence of different Lewis bases on the formation of triel bond. AIM analyses reveal that Tr (Tr = B, Al, Ga)···N bond critical point (BCP) exists in all studied triel bond. In the formation of triel bonding, compared with Lewis base HCN molecule, Lewis base anionic CN^- can participate in a stronger triel bond. Specifically, the structural change, deformation energy, and charge transfer of CN^- complexes are all larger than that of HCN complexes. In addition, halogen atom substitution effect is also discussed. MEP value and binding energy of HCN and CN^- complexes all increase after replacing one or two hydrogen atoms by halogen atoms (F, Cl, Br) in Lewis acid. Especially, replacing two hydrogen atoms by halogen atoms in Lewis acid has more remarkable enhancement in MEP value and binding energy than that of replacing only one hydrogen atom. After replacement, binding energy can be increased by 21.77 kcal/mol. The neutral and anionic triel-bonded complexes composed by Lewis acid TrOHH₂/TrOH₂X/TrOHX₂ (Tr = B, Al, Ga; X = F, Cl, Br) with Lewis base HCN and CN^- are systematically investigated at MP2/aug-cc-pVTZ level. The neutral (HCN) triel bonding is weaker than the anionic (CN^-) triel bonding due to the smaller MEP value of the neutral HCN molecule. The replacement of hydrogens (-H) in Lewis acid by electron-withdrawing groups (-F, -Cl, -Br) has a prominent enhancement effect on the MEP value of π-hole and triel-bonding strength.

Concentration-dependent adsorption of organic contaminants by graphene nanosheets: quantum-mechanical models

Adsorption is the key process in the expression of environmentally relevant physicochemical and toxicological properties of carbon nanomaterials. However, the adsorption of organic contaminants on to nanomaterials is a highly complex phenomenon, owing to the heterogeneity of adsorption sites, for example, on graphene surface as well as due to multiple factors operative during the adsorption, particularly, at the quantum-mechanical level. For predicting the concentration-dependent adsorption coefficients of organic contaminants by carbon nanomaterials, one option has been to rely on the existing linear-solvation energy relationship (LSER) models. The present work on the adsorption of aromatic and aliphatic organic contaminants by graphene nanosheets reveals that the existing LSER models are prone to failure when tested for internal and external validation using an external prediction set of compounds unknown to the model. As an alternative to the LSERs, the present work reports pure quantum-mechanical models developed using computational only quantum-mechanical descriptors. The reliability of the quantum-mechanical models was tested using state-of-the-art validation procedures employing an external prediction set of compounds. The proposed quantum-mechanical models reveal mean polarizability, zero-point vibrational energy, and its electron-correlation contribution to be the key descriptors in the prediction of adsorption coefficients of organic contaminants by graphene nanosheets.

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

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

Supramolecular architectures sustained by delocalised C–I⋯π(arene) interactions in molecular crystals and the propensity of their formation

A survey of delocalised C–I⋯π(chelate ring) interactions is presented.

5-Iodo-1-Arylpyrazoles as Potential Benchmarks for Investigating the Tuning of the Halogen Bonding

5-Iodo-1-arylpyrazoles are interesting templates for investigating the halogen bond propensity in small molecules other than the already well-known halogenated molecules such as tetrafluorodiiodobenzene. Herein, we present six compounds with different substitution on the aryl ring attached at position 1 of the pyrazoles and investigate them in the solid state in order to elucidate the halogen bonding significance to the crystallographic landscape of such molecules. The substituents on the aryl ring are generally combinations of halogen atoms (Br, Cl) and various alkyl groups. Observed halogen bonding types spanned by these six 5-iodopyrazoles included a wide variety, namely, C–I⋯O, C–I⋯π, C–I⋯Br, C–I⋯N and C–Br⋯O interactions. By single crystal X-ray diffraction analysis combined with the descriptive Hirshfeld analysis, we discuss the role and influence of the halogen bonds among the intermolecular interactions.

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

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

"Anti-Electrostatic" Halogen Bonding

Halogen bonding is often described as being driven predominantly by electrostatics, and thus adducts between anionic halogen bond (XB) donors (halogen-based Lewis acids) and anions seem counterintuitive. Such "anti-electrostatic" XBs have been predicted theoretically but for organic XB donors, there are currently no experimental examples except for a few cases of self-association. Reported herein is the synthesis of two negatively charged organoiodine derivatives that form anti-electrostatic XBs with anions. Even though the electrostatic potential is universally negative across the surface of both compounds, DFT calculations indicate kinetic stabilization of their halide complexes in the gas phase and particularly in solution. Experimentally, self-association of the anionic XB donors was observed in solid-state structures, resulting in dimers, trimers, and infinite chains. In addition, co-crystals with halides were obtained, representing the first cases of halogen bonding between an organic anionic XB donor and a different anion. The bond lengths of all observed interactions are 14-21 % shorter than the sum of the van der Waals radii.

New Crystal Forms for Biologically Active Compounds. Part 2: Anastrozole as N-Substituted 1,2,4-Triazole in Halogen Bonding and Lp-π Interactions with 1,4-Diiodotetrafluorobenzene

For an active pharmaceutical ingredient, it is important to stabilize its specific crystal polymorph. If the potential interconversion of various polymorphs is not carefully controlled, it may lead to deterioration of the drug’s physicochemical profile and, ultimately, its therapeutic efficacy. The desired polymorph stabilization can be achieved via co-crystallization with appropriate crystallophoric excipients. In this work, we identified an opportunity for co-crystallization of anastrozole (ASZ), a well-known aromatase inhibitor useful in second-line therapy of estrogen-dependent breast cancer, with a classical XB donor, 1,2,4,5-tetrafluoro-3,6-diiodobenzene (1,4-FIB). In the X-ray structures of ASZ·1.5 (1,4-FIB) co-crystal, different non-covalent interactions involving hydrogen and halogen atoms were detected and studied by quantum chemical calculations and QTAIM analysis at the ωB97XD/DZP-DKH level of theory.