Electrostatics and Polarization in σ‐ and π‐Hole Noncovalent Interactions: An Overview

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.

Unraveling pnicogen bonding cooperativity: Insights from molecular electrostatic potential analysis

A theoretical investigation on the cooperativity of a series of binary, ternary, and quaternary complexes interconnected by pnicogen bonds has been conducted using calculations at the M06-2X/aug-cc-pVTZ level of density functional theory. By measuring changes in the molecular electrostatic potential (MESP) at the nucleus of interacting atoms in all of the complexes, it is possible to quantify the substantial reorganization of the electron density triggered by the formation of pnicogen bonds. The positive change in MESP, indicating a loss of electron density from the donor molecule in a dimer, facilitates the acceptance of electron density from a third molecule, resulting in the formation of a ternary complex with a stronger pnicogen bond compared to the one present in the binary complex. Similarly, the acceptor molecule in a dimer with a negative change in MESP showed an enhanced tendency to donate electron density to an electron-deficient third molecule. The MESP analysis provided valuable insights into the donor/acceptor characteristics of pnicogen bonds within the quaternary complexes. The proposed MESP hypotheses are consistent with the positive cooperativity observed in the pnicogen-bonded clusters. To quantify the changes in MESP, both at the donor atom (ΔVdonor ) and the acceptor atom (ΔVacceptor ), for all pnicogen bonds in the cluster, the total change in MESP (ΔΔVn ) was measured as ΔΔVn  = ∑(ΔVdonor )-∑(ΔVacceptor ). Remarkably, ΔΔVn exhibited a strong linear relationship with the sum of the bond energies of the pnicogen bonds in the cluster. This establishes the MESP analysis as a robust approach for understanding the strength and cooperative behavior of pnicogen-bonded clusters. Additionally, the MESP features provided clear evidence of pnicogen bond formation, further supporting the reliability of this approach.

Wolfium bonds in homodimers of MX4Y (M = Mo, W; X = F, Cl, Br; Y = O, S, Se)

The term "wolfium bond" has been recently introduced to describe the noncovalent attraction between an atom of group 6 and a nucleophile via a σ-hole binding site. Crystal structures commonly contain a motif wherein two MX4Y units are arranged in close proximity, where M represents either Mo or W, and X and Y refer to halogen and chalcogen atoms respectively. DFT calculations were thus applied to a wide range of homodimers of these molecules so as to assess their preferred arrangements, and to characterize the types of bonding that are present in each in a systematic manner. The most stable Dual-X configuration is symmetric and contains a pair of equivalent M⋯X bonds. The interaction energies range from -8 to -29 kcal mol-1, and are largest for X = F, Y = O, and M = W. The X electron donor is replaced by Y, and the two wolfium bonds are reduced to one, in the less stable Mono-Y structure, with interaction energies between -2 and -10 kcal mol-1. There is some question as to whether the weaker bonds of this type constitute true wolfium bonds.

Chalcogen Bonding Catalysis: Tellurium, the Last Frontier?

Chalcogen bonding (ChB) is the non-covalent interaction occurring between chalcogen atoms as Lewis acid sites and atoms or groups of atoms able to behave as Lewis bases through their lone pair or π electrons. Analogously to its sister halogen bonding, the high directionality of this interaction was implemented for precise structural organizations in the solid state and in solution. Regarding catalysis, ChB is now accepted as a new mode of activation as demonstrated by the increased number of examples in the last five years. In the family of ChB catalysts, those based on tellurium rapidly appeared to overcome their lighter sulfur and selenium counterparts. In this review, we highlight the Lewis acid properties of tellurium-based derivatives in solution and summarize the start-of-the-art of their applications in catalysis.

Intermolecular Covalent Interactions: Nature and Directionality

Quantum chemical methods were employed to analyze the nature and the origin of the directionality of pnictogen (PnB), chalcogen (ChB), and halogen bonds (XB) in archetypal F_m Z⋅⋅⋅F^- complexes (Z=Pn, Ch, X), using relativistic density functional theory (DFT) at ZORA-M06/QZ4P. Quantitative Kohn-Sham MO and energy decomposition analyses (EDA) show that all these intermolecular interactions have in common that covalence, that is, HOMO-LUMO interactions, provide a crucial contribution to the bond energy, besides electrostatic attraction. Strikingly, all these bonds are directional (i.e., F-Z⋅⋅⋅F^- is approximately linear) despite, and not because of, the electrostatic interactions which, in fact, favor bending. This constitutes a breakdown of the σ-hole model. It was shown how the σ-hole model fails by neglecting both, the essential physics behind the electrostatic interaction and that behind the directionality of electron-rich intermolecular interactions. Our findings are general and extend to the neutral, weaker ClI⋅⋅⋅NH₃ , HClTe⋅⋅⋅NH₃ , and H₂ ClSb⋅⋅⋅NH₃ complexes.

Chalcogen Bonds: How to Characterize Them in Solution?

Chalcogen bonds (ChBs) occur between molecules containing Lewis acidic chalcogen substituents and Lewis bases. Recently, ChB emerged as a pivotal interaction in solution-based applications such as anion recognition, anion transport and catalysis. However, before moving to applications, the involvement of ChB must be established in solution. In this Concept article, we provide a brief review of the currently available experimental investigations of ChB in solution.

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.

Effects of fluorine bonding and nonbonding interactions on 19F chemical shifts

19F-NMR signals are sensitive to local electrostatic fields and are useful in probing protein structures and dynamics. Here, we used chemically identical ortho-F nuclei in N-phenyl γ-lactams to investigate the relationship between 19F NMR chemical shifts and local environments. By varying the structures at the C5- and C7-substituents, we demonstrated that 19F shifts and Hammett coefficients in Hammett plots follow typical relationships in bonding interactions, while manifesting reverse correlations in nonbonding contacts. Quantum mechanics calculations revealed that one of the ortho-F nuclei engages in n → π* orbital delocalization between F lone pair electrons (n) and a C[double bond, length as m-dash]O/Ar[double bond, length as m-dash]N antibonding orbital (π*), and the other ortho-F nucleus exhibits n ↔ σ orbital polarization between the n electrons and the C-H σ bonding orbital. As 19F NMR spectroscopy find increasing use in molecular sensors and biological sciences, our findings are valuable for designing sensitive probes, elucidating molecular structures, and quantifying analytes.

Water: new aspect of hydrogen bonding in the solid state

All water-water contacts in the crystal structures from the Cambridge Structural Database with d _OO ≤ 4.0 Å have been found. These contacts were analysed on the basis of their geometries and interaction energies from CCSD(T)/CBS calculations. The results show 6729 attractive water-water contacts, of which 4717 are classical hydrogen bonds (d _OH ≤ 3.0 Å and α ≥ 120°) with most being stronger than -3.3 kcal mol^-1. Beyond the region of these hydrogen bonds, there is a large number of attractive interactions (2062). The majority are antiparallel dipolar interactions, where the O-H bonds of two water molecules lying in parallel planes are oriented antiparallel to each other. Developing geometric criteria for these antiparallel dipoles (β₁, β₂ ≥ 160°, 80 ≤ α ≤ 140° and T _HOHO > 40°) yielded 1282 attractive contacts. The interaction energies of these antiparallel oriented water molecules are up to -4.7 kcal mol^-1, while most of the contacts have interaction energies in the range -0.9 to -2.1 kcal mol^-1. This study suggests that the geometric criteria for defining attractive water-water interactions should be broader than the classical hydrogen-bonding criteria, a change that may reveal undiscovered and unappreciated interactions controlling molecular structure and chemistry.

The roles of charge transfer and polarization in non-covalent interactions: a perspective from ab initio valence bond methods

Noncovalent interactions are ubiquitous and have been well recognized in chemistry, biology and material science. Yet, there are still recurring controversies over their natures, due to the wide range of noncovalent interaction terms. In this Essay, we employed the Valence Bond (VB) methods to address two types of interactions which recently have drawn intensive attention, i.e., the halogen bonding and the CH‧‧‧HC dihydrogen bonding. The VB methods have the advantage of interpreting molecular structures and properties in the term of electron-localized Lewis (resonance) states (structures), which thereby shed specific light on the alteration of the bonding patterns. Due to the electron localization nature of Lewis states, it is possible to define individually and measure both polarization and charge transfer effects which have different physical origins. We demonstrated that both the ab initio VB method and the block-localized wavefunction (BLW) method can provide consistent pictures for halogen bonding systems, where strong Lewis bases NH₃, H₂O and NMe₃ partake as the halogen bond acceptors, and the halogen bond donors include dihalogen molecules and XNO₂ (X = Cl, Br, I). Based on the structural, spectral, and energetic changes, we confirm the remarkable roles of charge transfer in these halogen bonding complexes. Although the weak C-H∙∙∙H-C interactions in alkane dimers and graphene sheets are thought to involve dispersion only, we show that this term embeds delicate yet important charge transfer, bond reorganization and polarization interactions.

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.

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.

Transition Metal Catalysis Controlled by Hydrogen Bonding in the Second Coordination Sphere

Transition metal catalysis is of utmost importance for the development of sustainable processes in academia and industry. The activity and selectivity of metal complexes are typically the result of the interplay between ligand and metal properties. As the ligand can be chemically altered, a large research focus has been on ligand development. More recently, it has been recognized that further control over activity and selectivity can be achieved by using the "second coordination sphere", which can be seen as the region beyond the direct coordination sphere of the metal center. Hydrogen bonds appear to be very useful interactions in this context as they typically have sufficient strength and directionality to exert control of the second coordination sphere, yet hydrogen bonds are typically very dynamic, allowing fast turnover. In this review we have highlighted several key features of hydrogen bonding interactions and have summarized the use of hydrogen bonding to program the second coordination sphere. Such control can be achieved by bridging two ligands that are coordinated to a metal center to effectively lead to supramolecular bidentate ligands. In addition, hydrogen bonding can be used to preorganize a substrate that is coordinated to the metal center. Both strategies lead to catalysts with superior properties in a variety of metal catalyzed transformations, including (asymmetric) hydrogenation, hydroformylation, C-H activation, oxidation, radical-type transformations, and photochemical reactions.

Theoretical investigation on the nature of substituted benzene⋯AuX interactions: covalent or noncovalent?

The nature of interactions between AuX (X = F, Cl, Br, CN, NO2, CH3) and aromatic moieties with different electronic properties has been investigated for possible tuning of coinage–metal bonds by varying the substituents.

Expanding the toolbox of coinage bond: Adducts involving new gold(III) derivatives and bioactive molecules

X-ray analyses of a small library of adducts between AuX3 (X=Cl, Br) and several pyridine derivatives indicate the systematic presence of quite short π -holes coinage bonds; computational studies reveal...

Chalcogen-bonded donor–acceptor complexes of 5,6-dicyano[1,2,5]selenadiazolo[3,4-b]pyrazine with halide ions

With halides X− (X = Cl, Br, I) 5,6-dicyano-[1,2,5]selenadiazolo[3,4-b]pyrazine 1 forms chalcogen-bonded complexes [1–X]− structurally defined by XRD. UV/Vis spectra of [1–X]− feature red-shifted charge-transfer bands in the Vis part.

Inorganic–Organic {dz2-MIIS4}···π-Hole Stacking in Reverse Sandwich Structures. The Case of Cocrystals of Group 10 Metal Dithiocarbamates with Electron-deficient Arenes

Cocrystallization of the dithiocarbamate complexes [M(S2CNEt2)2] (M = Ni 1, Pd 2, Pt 3) and X-substituted perfluoroarenes (X = I, Br; 1,2-dibromoperfluorobenzene FBrB and 1,2-diiodoperfluorobenzene FIB) gives isomorphous cocrystals of...

An emerging deep eutectic solvent based on halogen-bond

A new deep eutectic solvents (DES) driven by halogen-bond was exploited. A family of eutectic mixtures in liquid state were obtained by combination of quaternary ammonium salts and dihalogens. The...

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.

"Anti-electrostatic" Halogen Bonding between Ions of Like Charge

Halogen bonding occurs between molecules featuring Lewis acidic halogen substituents and Lewis bases. It is often rationalized as a predominantly electrostatic interaction and thus interactions between ions of like charge (e. g., of anionic halogen bond donors with halides) seem counter-intuitive. Herein, we provide an overview on such complexes. First, theoretical studies are described and their findings are compared. Next, experimental evidences are presented in the form of crystal structure database analyses, recent examples of strong "anti-electrostatic" halogen bonding in crystals, and the observation of such interactions also in solution. We then compare these complexes to select examples of "counter-intuitive" adducts formed by other interactions, like hydrogen bonding. Finally, we comment on key differences between charge-transfer and electrostatic polarization.

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.

5-HT2 Receptor Subfamily and the Halogen Bond Promise

The binding of C-4-halogenated 1-(4-X-2,5-dimethoxyphenyl)-2-aminopropane (DOX) serotonin agonist psychedelics at all three 5-HT₂ receptor subtypes is up to two orders of magnitude stronger for X = Cl, Br, or I (but not F) than when C-4 bears a hydrogen atom and more than expected from their hydrophobicities. Our docking and molecular dynamics simulations agree with the fact that increasing the polarizability of halogens results in halogen-oxygen distances to specific backbone C═O groups, and C-X···O angles, in ranges expected for halogen bonds (XBs), which could contribute to the high affinities observed. Good linear correlations are found for each receptor type, indicating that the binding pocket-ligand affinity is enhanced as the XB interaction becomes stronger (i.e., I ≈ Br > Cl > F). It is also striking to note how the linear equations unveil that the receptor's response on the strength of the XB interaction is quite similar among 5-HT_2A and 5-HT_2C, whereas the 5-HT_2B's sensitivity is less. The calculated dipole polarizabilities in the binding pocket of the receptors reflect the experimental affinity values, indicating that less-polarizable and harder binding sites are more prone to XB formation.

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

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

The 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.

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.

Theoretical study on the noncovalent interactions involving triplet diphenylcarbene

The properties of some types of noncovalent interactions formed by triplet diphenylcarbene (DPC³) have been investigated by means of density functional theory (DFT) calculations and quantum theory of atoms in molecule (QTAIM) studies. The DPC³···LA (LA = AlF₃, SiF₄, PF₅, SF₂, ClF) complexes have been analyzed from their equilibrium geometries, binding energies, and properties of electron density. The triel bond in the DPC³···AlF₃ complex exhibits a partially covalent nature, with the binding energy - 65.7 kJ/mol. The tetrel bond, pnicogen bond, chalcogen bond, and halogen bond in the DPC³···LA (LA = SiF₄, PF₅, SF₂, ClF) complexes show the character of a weak closed-shell noncovalent interaction. Polarization plays an important role in the formation of the studied complexes. The strength of intermolecular interaction decreases in the order LA = AlF₃ > ClF > SF₂ > SiF₄ > PF₅. The electron spin density transfers from the radical DPC³ to ClF and SF₂ in the formation of halogen bond and chalcogen bond, but for the DPC³···AlF₃/SiF₄/PF₅ complexes, the transfer of electron spin density is minimal.

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).

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.

The competition and cooperativity of hydrogen/halogen bond and π-hole bond involving the heteronuclear ethylene analogues

The noncovalent interactions involving heteronuclear ethylene analogues H₂ CEH₂ (E = Si, Ge and Sn) have been studied by the Møller-Plesset perturbation theory to investigate the competition and cooperativity between the hydrogen/halogen bond and π-hole bond. H₂ CEH₂ has a dual role of being a Lewis base and acid with the region of π-electron accumulation above the carbon atom and the region of π-electron depletion (π-hole) above the E atom to participate in the NCX···CE (X = H and Cl) hydrogen/halogen bond and CE···NCY (Y = H, Cl, Li and Na) π-hole bond, respectively. When HCN/ClCN interacts with H₂ CEH₂ by two sites, the strength of hydrogen bond/halogen bond is stronger than that of π-hole bond. The π-hole bond becomes obviously stronger when the metal substituent of YCN (Y = Li and Na) interacting with H₂ CEH₂ , showing the character of partial covalent, its strength is much greater than that of hydrogen/halogen bond. In the ternary complexes, both hydrogen/halogen bond and π-hole bond are simultaneously strengthened compared to those in the binary complexes, especially in the systems containing alkali metal.

Assessing the Orbital Contribution in the "Spodium Bond" by Natural Orbital for Chemical Valence-Charge Displacement Analysis

The term "spodium bond" (SpB) has been recently proposed to describe the noncoordinative interaction that can be established between a polarized group 12 metal and a mild Lewis base (LB). Most of the systems showing short metal-donor distances compatible with SpB are characterized by the coexistence of multiple weak interactions, including hydrogen and halogen bonding, making the assessment of real importance of SpB difficult. Here, we show that the relative importance of each contribution can be probed by dissecting the orbital component of the interaction through the extended transition state-natural orbital for chemical valence-charge displacement analysis (ETS-NOCV-CD). The latter gives useful information about relative energies and electrons involved, for model systems ([(thiourea)₂MX₂]···LB; M = Zn, Cd, and Hg; X = Cl and I; and LB = CH₂S, CH₂O, CH₃CN, and CO) and a variety of structures extracted from experimentally characterized adducts, allowing us to demonstrate the lack of a direct correlation between a favorable metal-base distance and the presence of an orbital contribution for the SpB.

Role of Charge Transfer in Halogen Bonding

Halogen bonding has received intensive attention recently for its applications in the construction of supramolecular assemblies and crystal engineering and its implications and potentials in chemical and biological processes and rational drug design. Peculiarly, in intermolecular interactions, halogen atoms are known as electron-donating groups carrying partial negative charges in molecules due to its high electronegativity, but they can counterintuitively act as Lewis acids and bind with Lewis bases in the form of a halogen bond. The unsettling issue regarding the nature of the halogen bonding is whether the electrostatics or charge transfer interaction dominates. The recently proposed σ-hole concept nicely reinforces the role of electrostatic attraction. Also, good correlations between the halogen bonding strength and the interaction energy from the simple point-charge model have been found. This leads to the claim that there is no need to invoke the charge transfer concept in the halogen bond. But there is alternative evidence supporting the importance of charge transfer interaction. Here, we visited a series of prominent halogen bonded complexes of the types Y₃C-X···Z (X = Br, I; Y = F, Cl, Br; Z = F^-, Cl^-, Br^-, I^-, NMe₃) with the block-localized wave function (BLW) method at the M06-2X-D3/6-311+G(d,p) (def2-SVP for iodine) level of theory. As the simplest variant of ab initio valence bond (VB) theory, the BLW method is unique in the strict localization of electrons within interacting moieties, allowing for quantitative evaluation of the charge transfer effect on geometries, spectral properties, and energetics in halogen bonding complexes. By comparing the halogen bonding complexes with and without the charge transfer interaction, we proved that the charge transfer interaction significantly shortens the X···Z bonding distance and stretches the C-X bonds. But the shortening of the halogen bonding results in the less favorable steric effect, which is composed of Pauli repulsion, electrostatics, and electron correlation. There are approximate linear correlations between the charge transfer effect and binding energy and between bonding distance and binding energy. These correlations may lead to the illusion that the charge transfer interaction is unimportant or irrelevant, but further analyses showed that the inclusion of charge transfer is critical for the proper description of the halogen bonding, as considering only electrostatics and polarization leads to only about 45-60% of the binding strengths and much elongated bonding distances.

Nature of the Hydrogen Bond Enhanced Halogen Bond

The factors responsible for the enhancement of the halogen bond by an adjacent hydrogen bond have been quantitatively explored by means of state-of-the-art computational methods. It is found that the strength of a halogen bond is enhanced by ca. 3 kcal/mol when the halogen donor simultaneously operates as a halogen bond donor and a hydrogen bond acceptor. This enhancement is the result of both stronger electrostatic and orbital interactions between the XB donor and the XB acceptor, which indicates a significant degree of covalency in these halogen bonds. In addition, the halogen bond strength can be easily tuned by modifying the electron density of the aryl group of the XB donor as well as the acidity of the hydrogen atoms responsible for the hydrogen bond.

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.

Ternary Cocrystals with Large Soft Cavities: A 1,4-diiodotetrafluorobenzene (DITFB)⋅4-Biphenylpyridine N-oxide (BPNO) Host Assembled by Inclusion of Planar Aromatic Guests

A large soft-cavity host composed of 1,4-diiodotetrafluorobenzene (DITFB) and 4-biphenylpyridine N-oxide (BPNO) is assembled under the mediation of a planar aromatic guest molecule (pyrene or perylene) through C-I⋅⋅⋅^- O-N⁺ halogen bonds and π-hole⋅⋅⋅π bonds. Single-crystal X-ray diffraction reveals that guest molecules can be completely encapsulated in the four-layer host cavity to assemble ternary host-guest cocrystals; namely, Pyr@DITFB ⋅ BPNO and Per@DITFB ⋅ BPNO. The luminescence of these ternary cocrystals originates from their discrete guest molecules, which exhibit pure-blue and yellow emissions, respectively, that are localized at 425 nm and in the range of 485 to 578 nm, respectively. In addition, the contribution of different fragments to the stabilization of the crystal structure is estimated by computational chemistry. These cocrystals have significant potential for use in optical applications or materials, such as photonics or organic light-emitting diodes, respectively, that require to avoid the aggregation between luminophores.

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.

DFT and IsoStar Analyses to Assess the Utility of σ- and π-Hole Interactions for Crystal Engineering

The interpretation of 36 charge neutral 'contact pairs' from the IsoStar database was supported by DFT calculations of model molecules 1-12, and bimolecular adducts thereof. The 'central groups' are σ-hole donors (H2 O and aromatic C-I), π-hole donors (R-C(O)Me, R-NO2 and R-C6 F5 ) and for comparison R-C6 H5 (R=any group or atom). The 'contact groups' are hydrogen bond donors X-H (X=N, O, S, or R2 C, or R3 C) and lone-pair containing fragments (R3 C-F, R-C≡N and R2 C=O). Nearly all the IsoStar distributions follow expectations based on the electrostatic potential of the 'central-' and 'contact group'. Interaction energies (ΔEBSSE ) are dominated by electrostatics (particularly between two polarized molecules) or dispersion (especially in case of large contact area). Orbital interactions never dominate, but could be significant (∼30 %) and of the n/π→σ*/π* kind. The largest degree of directionality in the IsoStar plots was typically observed for adducts more stable than ΔEBSSE ≈-4 kcal⋅mol-1 , which can be seen as a benchmark-value for the utility of an interaction in crystal engineering. This benchmark could be met with all the σ- and π-hole donors studied.

Theoretical and experimental study of guar gum sulfation

The synthesis of guar gum sulfates by a complex of sulfur trioxide with 1,4-dioxane was studied. The influence of temperature, process duration, and the volume of chlorosulfonic acid on the degree of substitution of guar gum sulfates was studied. The sulfation process has been optimized using the Box-Behnken design. It was shown that the optimal conditions for sulfation of guar gum with a complex of sulfur trioxide-1.4-dioxane: temperature 60 °C, duration 2.9 h, and a volume of chlorosulfonic acid of 3.1 ml. Sulfate groups embedding into the structure of guar gum was confirmed by elemental analysis and FTIR. The initial and sulfated guar gum were also characterized by methods: X-ray diffraction, scanning electron microscopy, and gel permeation chromatography. Using X-ray diffraction, it was shown that amorphization of guar gum occurs during sulfation. Using scanning electron microscopy, it was shown that the morphology of guar gum changes in the process of sulfation. Using gel permeation chromatography, it was shown in the process of guar gum sulfation by a complex of sulfur trioxide with 1,4-dioxane, the molecular weight decreases from 600 to 176 kDa. The geometric parameters of all complexes were carried out by using the DFT/B3PW91 method with a 6-31 + G (d,p) basis set. These structures are optimized to predict the important properties of a theme. MEP with contour map has been performed to obtain the electronic properties. Frontier molecular orbital HOMO-LUMO orbital diagram has been obtained for different energy levels and their band gap energies have been computed.

Design and DFT study of nitrogen-rich donor systems for improved photovoltaic performance in dye-sensitized solar cells

Donor modifications, especially through N-annulation, for enhancing the structure–performance relationship of D–π–A systems for DSSC applications.

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.

The σ-hole⋯σ-hole stacking interaction: An unrecognized type of noncovalent interaction

The σ-hole⋯σ-hole stacking interaction, an unrecognized type of noncovalent interaction, has been found to be present in large quantities in the Cambridge Structural Database. In the σ-hole⋯σ-hole stacking interaction, each of the two interacting σ-holes has the dual electron donor/electron acceptor character; when one σ-hole acts as an electron donor, the other σ-hole acts as an electron acceptor, and vice versa. The σ-hole⋯σ-hole stacking interaction is clearly different from the σ-hole bond in which the charge transfer occurs mainly from the electron donor to the σ-hole. Energy component analysis shows that the σ-hole⋯σ-hole stacking interaction is dominated by the dispersion energy, which is similar to the nature of the aromatic stacking interaction between unsaturated molecules or the σ⋯σ stacking interaction between saturated molecules.

Dissecting the electric quadrupolar and polarization effects operating in halogen bonding through electron density analysis with a focus on bromine

The form of the electron density change (or difference) is usable as a kind of fingerprint of the electronic structural origin or mechanism that gives rise to intermolecular interactions. Here, this method is applied to halogen-bonding brominated systems to dissect the electric quadrupolar effect (arising from the anisotropic distribution of the valence electrons and intrinsic to the s²p_x ²p_y ²p_z electronic configuration) and the polarization effect (induced by a partial negative charge of the halogen-bond accepting atom). It is shown that a suitable location of the "extra point" for placing a partial positive charge to represent the former is crucial and is clearly found from the electron density difference from the spherically isotropic Br^- ion, while the latter consists of the dipolar polarization of the Br atom and the delocalized polarization of the whole molecule. A practical way for application to molecular dynamics simulations, etc., to represent these two factors is discussed.

Halogen bonds and other noncovalent interactions in the crystal structures of trans-1,2-diiodo alkenes: an ab initio and QTAIM study

A series of interatomic interactions interpretable as halogen bonds involving I…I, I…O, and I…C(π), as well as the noncovalent interactions I…H and O…O, were observed in the crystal structures of trans-1,2-diiodoolefins dimers according to ab initio calculations and the quantum theory of "atoms in molecules" (QTAIM) method. The interplay between each type of halogen bond and other noncovalent interactions was studied systematically in terms of bond length, electrostatic potential, and interaction energy, which are calculated via ab initio methods at the B3LYP-D3/6-311++G(d,p) and B3LYP-D3/def2-TZVP levels of theory. Characteristics and nature of the halogen bonds and other noncovalent interactions, including the topological properties of the electron density, the charge transfer, and their strengthening or weakening, were analyzed by means of both QTAIM and "natural bond order" (NBO). These computational methods provide additional insight into observed intermolecular interactions and are utilized to explain the differences seen in the crystal structures. Graphical abstract The contour map presents the regions of electronic concentration and depletion along each bond in one dimer. The blue points denote the BCPs. The blue lines denote positive Laplacian of electron density, which indicate the ionic interactions, van der Waals or intermolecular interactions, and the red lines denote negative Laplacian of electron density which indicate the covalent bonds.