Electrostatics and polarization determine the strength of the halogen bond: a red card for charge transfer

Anisotropies in electronic densities and electrostatic potentials of Halonium Ions: focus on Chlorine, Bromine and Iodine

CONTEXT

Why are the halonium cations so effective in forming strongly-bound complexes? We directed our research to address this question and we present electrostatic potential data for the valence-state halogen atoms X and halonium cations X+, where X = Cl, Br, I. The electron densities and electrostatic potentials of the halonium cations show considerably greater anisotropy than do the valence state halogens. The distances from the electrostatic potential surface maxima to the halogen nuclei are about 0.5 Å smaller than the distances from the electrostatic potential surface minima to the nuclei, giving the halonium cations each a more disk-like shape than the corresponding neutral valence state halogens. Their surface electrostatic potentials are totally consistent with the directionalities of halonium cations in complexes and the strengths of their interactions. To add perspective to this brief report, we have included calculations of the isotropic cation K+ and noble gas Kr.

METHODS

The calculations of the electrostatic potentials of the valence states of the halogen atoms Cl, Br and I and the halonium cations Cl+, Br+ and I+, as well as K+ and Kr, on 0.001 au contours of their electronic densities were carried out with Gaussian O9 and the Wave Function Analysis - Surface Analysis Suite (WFA-SAS) at the M06-2X/6-31 + G(d,p) and M06-2X/3-21G* levels.

Catalytic activation via π-backbonding in halogen bonds

The role of halogen bonding (XB) in chemical catalysis has largely involved using XB donors as Lewis acid activators to modulate the reactivity of partner Lewis bases. We explore a more uncommon scenario, where a Lewis base modulates reactivity via a spectator halogen bond interaction. Our computational studies reveal that spectator halogen bonds may play an important role in modulating the rate of SN2 reactions. Most notably, π acceptors such as PF3 significantly decrease the barrier to substitution by decreasing electron density in the very electron rich transition state. Such π-backbonding represents an example of a heretofore unexplored situation in halogen bonding: the combination of both σ-donation and π-backdonation in this "non-covalent" interaction. The broader implications of this observation are discussed.

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.

How deeply should we analyze non-covalent interactions?

CONTEXT

Just how much effort and detail should we invest in analyzing interactions of the order of 5 kcal mol^-1? This comment attempts to provide a conciliatory overview of what is often a contentious field and to pose some questions that I hope will eventually lead at least to some consensus.

METHODS

This is an opinion article without calculations or data.

Synthesis, substitution kinetics, DNA/BSA binding and cytotoxicity of tridentate N^E^N (E = NH, O, S) pyrazolyl palladium(II) complexes

The pincer complexes, [Pd(L₁)Cl]BF₄ (PdL₁), [Pd(L₂)Cl]BF₄ (PdL₂), [Pd(L₃)Cl]BF₄ (PdL₃), [Pd(L₄)Cl]BF₄ (PdL₄) were prepared by reacting the corresponding ligands, 2,6-bis[(1H-pyrazol-1-yl)methyl]pyridine (L₁), bis[2-(1H-pyrazol-1-yl)ethyl]amine (L₂), bis[2-(1H-pyrazol-1-yl)ethyl]ether (L₃), and bis[2-(1H-prazol-1-yl)ethyl]sulphide (L₄) with [PdCl₂(NCMe)]₂ in the presence NaBF₄. The solid-state structures of complexes PdL₁-PdL₄ confirmed a tridentate coordination mode, with one chloro ligand completing the coordination sphere to afford square-planar complexes. Chemical behaviour of the complexes in solution confirms their stability in both aqueous and DMSO stock media. The electrochemical properties of the compounds showed irreversible two-electron reduction process. Kinetic reactivity of Pd complexes with the biological nucleophiles viz, thiourea (Tu), L-methionine (L-Met) and guanosine 5'-diphosphate disodium salt (5'-GMP) followed the order: PdL₂ < PdL₃ < PdL₄, and PdL₂ < PdL₁. The kinetic reactivity is subject to the electronic effects of the spectator ligand(s), and the trend was supported by the DFT computed results. The palladium complexes PdL₁-PdL₄ bind to calf thymus (CT-DNA) via intercalation mode. In addition, the bovine serum albumin (BSA) showed good binding affinity to the complexes. The mode of quenching mechanism of the intrinsic fluorescence of CT-DNA and BSA by the complexes was found to be static. The order of interactions of the complexes with DNA and BSA was in tandem with the rate of substitution kinetics. The complexes, however, displayed relatively low cytotoxicity (IC₅₀ > 100 µM) when tested against the human cervical adenocarcinoma (HeLa) cell line and the transformed human lung fibroblast cell line (MRC-5 SV2).

Enhancing Effects of the Cyano Group on the C-X∙∙∙N Hydrogen or Halogen Bond in Complexes of X-Cyanomethanes with Trimethyl Amine: CH3−n(CN)nX∙∙∙NMe3, (n = 0–3; X = H, Cl, Br, I)

In this paper, density functional theory and wave function theory calculations are carried out to investigate the strength and nature of the intermolecular C-X∙∙∙N bond interaction as a function of the number of cyano groups, CN, in the X-bond donor while maintaining the X-bond acceptor as fixed. Specifically, complexes of X-cyanomethanes with trimethyl amine CH_3−n(CN)_nX∙∙∙NMe₃ (n = 0–3; X = H, Cl, Br, I) are used as model systems. Geometrical parameters and vibrational C-X-stretching frequencies as well as interaction energies are used as relevant indicators to gauge hydrogen or halogen bond strength in the complexes. Additional characteristics of interactions that link these complexes, i.e., hydrogen or halogen bonds, are calculated with the use of the following theoretical tools: the atoms in molecules (AIM) approach, the natural bond orbital (NBO) method, and energy decomposition analysis (EDA). The results show that, for the specified X-center, the strength of C-X∙∙∙N interaction increases significantly and in a non-additive fashion with the number of CN groups. Moreover, the nature (noncovalent or partly covalent) of the interactions is revealed via the AIM approach.

The Importance of Electrostatics and Polarization for Noncovalent Interactions: Ionic Hydrogen Bonds vs Ionic Halogen Bonds

A series of 26 hydrogen-bonded complexes between Br⁻ and halogen, oxygen and sulfur hydrogen-bond (HB) donors is investigated at the M06-2X/6–311 + G(2df,2p) level of theory. Analysis using a model in which Br⁻ is replaced by a point charge shows that the interaction energy (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{Int}$$\end{document}ΔEInt) of the complexes is accurately reproduced by the scaled interaction energy with the point charge (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{Int}^{PC}$$\end{document}ΔEIntPC).This is demonstrated by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{Int}=0.86{\Delta E}_{Int}^{PC}$$\end{document}ΔEInt=0.86ΔEIntPC with a correlation coefficient, R² =0.999. The only outlier is (Br-H-Br)⁻, which generally is classified as a strong charge-transfer complex with covalent character rather than a HB complex. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{Int}^{PC}$$\end{document}ΔEIntPC can be divided rigorously into an electrostatic contribution (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{ES}^{PC}$$\end{document}ΔEESPC) and a polarization contribution (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{Pol}^{PC}$$\end{document}ΔEPolPC).Within the set of HB complexes investigated, the former varies between -7.2 and -32.7 kcal mol⁻¹, whereas the latter varies between -1.6 and -11.5 kcal mol⁻¹. Compared to our previous study of halogen-bonded (XB) complexes between Br⁻ and C–Br XB donors, the electrostatic contribution is generally stronger and the polarization contribution is generally weaker in the HB complexes. However, for both types of bonding, the variation in interaction strength can be reproduced accurately without invoking a charge-transfer term. For the Br⁻···HF complex, the importance of charge penetration on the variation of the interaction energy with intermolecular distance is investigated. It is shown that the repulsive character of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{Int}$$\end{document}ΔEInt at short distances in this complex to a large extent can be attributed to charge penetration.

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.

Assessing the effects of covalent, dative and halogen bonds on the electronic structure of selenoamides

The C–NMe2 bond rotation of a selenoamide is proposed as an experimental probe to compare different chemical interactions.

"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.

Yet another perspective on hole interactions

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

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.

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).

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.

Thermal hysteresis induced by external pressure in a 3D Hofmann-type SCO-MOF

Two 3D Hofmann-type compounds [Fe^II(dbdpe)M^II(CN)₄]·4H₂O have been synthesized. The application of pressure on compound 1 shifted the transition temperature from 185 K to 298 K and led to a hysteresis loop of 13–25 K.

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.

Resonance-assisted/impaired anion-π interaction: towards the design of novel anion receptors

Substituents alter the electron density distribution in benzene in various ways, depending on their electron withdrawing and donating capabilities, as summarized by the empirical Hammett equation. The change of the π electron density distribution subsequently impacts the interaction of substituted benzenes or other cyclic conjugated rings with anions. Currently the design and synthesis of conjugated cyclic receptors capable of binding anions is an active field due to their applications in the sensing and removal of environmental contaminants and molecular recognition. By using the block-localized wavefunction (BLW) method, which is a variant of ab initio valence bond (VB) theory and can derive the reference resonance-free state self-consistently, we quantified the resonance-assisted (RA) or resonance-impaired (RI) phenomena in anion–π interactions from both structural and energetic perspectives. The frozen interaction, in which the electrostatic attraction is involved, has been shown to be the governing factor for the RA or RI interactions with anions. Energy analyses based on the empirical point charge (EPC) model indicated that the anion–π interactions can be simplified as the attraction between a negative point charge (anion) and a group of local dipoles, affected by the enriched or diminished π-cloud due to the resonance between the substituents and the conjugated ring. Hence, two strategies for the design of novel anion receptors can be envisioned. One is the enhancement of the magnitudes and/or numbers of local dipoles (polarized σ bonds), and the other is the reduction of π electron density in conjugated rings. For cases with the RI characteristics, “curved” aromatic molecules are preferred to be anion receptors. Indeed, extremely strong binding was found in complexes formed with fluorinated corannulene (F-CDD) and fluorinated [5]cycloparaphenylene (F-[5]CPP). Inspired by the RA phenomenon, complexes of p-, o- and m-benzoquinones with halides were revisited.

Substituents alter the electron density distribution in benzene in various ways, depending on their electron withdrawing and donating capabilities, as summarized by the empirical Hammett equation.

Not Only Hydrogen Bonds: Other Noncovalent Interactions

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

Does Chlorine in CH3Cl Behave as a Genuine Halogen Bond Donor?

The CH3Cl molecule has been used in several studies as an example purportedly to demonstrate that while Cl is weakly negative, a positive potential can be induced on its axial surface by the electric field of a reasonably strong Lewis base (such as O=CH2). The induced positive potential then has the ability to attract the negative site of the Lewis base, thus explaining the importance of polarization leading to the formation of the H3C–Cl···O=CH2 complex. By examining the nature of the chlorine’s surface in CH3Cl using the molecular electrostatic surface potential (MESP) approach, with MP2/aug-cc-pVTZ, we show that this view is not correct. The results of our calculations demonstrate that the local potential associated with the axial surface of the Cl atom is inherently positive. Therefore, it should be able to inherently act as a halogen bond donor. This is shown to be the case by examining several halogen-bonded complexes of CH3Cl with a series of negative sites. In addition, it is also shown that the lateral portions of Cl in CH3Cl features a belt of negative electrostatic potential that can participate in forming halogen-, chalcogen-, and hydrogen-bonded interactions. The results of the theoretical models used, viz. the quantum theory of atoms in molecules; the reduced density gradient noncovalent index; the natural bond orbital analysis; and the symmetry adapted perturbation theory show that Cl-centered intermolecular bonding interactions revealed in a series of 18 binary complexes do not involve a polarization-induced potential on the Cl atom.

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

We demonstrate that a wide range of σ- and π-hole interaction energies can be related to (a) the electrostatic potentials and electric fields of the σ- and π-hole molecules at the approximate positions of the negative sites and (b) the electrostatic potentials and polarizabilities of the latter. This is consistent with the Coulombic nature of these interactions, which should be understood to include both electrostatics and polarization. The energies associated with polarization were estimated and were shown to overall be greater for the stronger interactions; no new factors need be introduced to account for these. All of the interactions can be treated in the same manner.

Charge Displacement Analysis-A Tool to Theoretically Characterize the Charge Transfer Contribution of Halogen Bonds

Theoretical bonding analysis is of prime importance for the deep understanding of the various chemical interactions, covalent or not. Among the various methods that have been developed in the last decades, the analysis of the Charge Displacement function (CD) demonstrated to be useful to reveal the charge transfer effects in many contexts, from weak hydrogen bonds, to the characterization of σ hole interactions, as halogen, chalcogen and pnictogen bonding or even in the decomposition of the metal-ligand bond. Quite often, the CD analysis has also been coupled with experimental techniques, in order to give a complete description of the system under study. In this review, we focus on the use of CD analysis on halogen bonded systems, describing the most relevant literature examples about gas phase and condensed phase systems. Chemical insights will be drawn about the nature of halogen bond, its cooperativity and its influence on metal-ligand bond components.

An Overview of Strengths and Directionalities of Noncovalent Interactions: σ-Holes and π-Holes

Quantum mechanics, through the Hellmann–Feynman theorem and the Schrödinger equation, show that noncovalent interactions are classically Coulombic in nature, which includes polarization as well as electrostatics. In the great majority of these interactions, the positive electrostatic potentials result from regions of low electronic density. These regions are of two types, designated as σ-holes and π-holes. They differ in directionality; in general, σ-holes are along the extensions of covalent bonds to atoms (or occasionally between such extensions), while π-holes are perpendicular to planar portions of molecules. The magnitudes and locations of the most positive electrostatic potentials associated with σ-holes and π-holes are often approximate guides to the strengths and directions of interactions with negative sites but should be used cautiously for this purpose since polarization is not being taken into account. Since these maximum positive potentials may not be in the immediate proximities of atoms, interatomic close contacts are not always reliable indicators of noncovalent interactions. This is demonstrated for some heterocyclic rings and cyclic polyketones. We briefly mention some problems associated with using Periodic Table Groups to label interactions resulting from σ-holes and π-holes; for example, the labels do not distinguish between these two possibilities with differing directionalities.