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.

Participation of transition metal atoms in noncovalent bonds

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

Dichlorine-pyridine N-oxide halogen-bonded complexes

A new Cl-Cl···-O-N+ halogen-bonded paradigm has been demonstrated, using dichlorine as a halogen bond (XB) donor and N-oxide as an XB acceptor. Their crystalline complexes were formed during the warm-up process from -196 °C to -80 °C for X-ray diffraction analysis. They exhibit high instability in the crystalline state, even at these low temperatures, leading to rapid decomposition and the formation of Cl⋯H-O-N hydrogen-bonded complexes. The normalized XB interaction ratio (R XB) of Cl⋯O interactions in the solid-state demonstrates affinity comparable to traditional I⋯O interactions observed in I-I···-O-N+ halogen-bonded systems. The Cl-Cl⋯O XB angles vary from 172° to 177°, manifesting the structure-guiding influence of the electronegative chlorine atom's σ-hole on these XB interactions.

Functionally Modified Polymer Electrolyte Based on Noncovalent Interaction for Stable Lithium Metal Batteries

The charge transfer efficiency of the solid electrolyte depends on the number of lithium ions that can be effectively transported and participate in the electrode reaction. However, limited by the strong coupling relationship between Li+ and Lewis basic sites on the polymer chain, the Li+ transference number (tLi+) of the solid polymer electrolyte (SPE) based dual-ion conductor is typically low, resulting in excessive anion aggregation at the electrode side and inducing concentration polarization. In this study, we present a functionalized modified polymer electrolyte (FMPE) with selective cation transport, which was synthesized by embedding 4-(trifluoromethyl)styrene (TFS) functionalized groups onto the poly(diethylene glycol diacrylate) polymer chain. The TFS group formed noncovalent couplings with TFSI- anions through hydrogen bondings and dipole-dipole interactions, which effectively limited the migration of the anions and contributed to the elevated tLi+ of the FMPEs to 0.595 and 0.699 at 25 and 60 °C, respectively. Density functional theory (DFT) calculations were performed to verify the increased anion migration barriers for different noncovalent interactions and revealed that the conjugated system formed by the delocalized π electrons of the benzene ring and the C═O groups helped to disperse the electron distribution of the polymer chains. Consequently, the decrease in the degree of Li+ immobilization promotes the decoupling and migration of Li+ between the polymer chains. Benefiting from optimized Li+ transport behavior, the lithium metal batteries (LMBs) assembled by FMPEs and LiFePO4 exhibit excellent rate performance (discharge specific capacity of 88.8 mAh g-1 at 5 C) and stable long-term cycle performance (capacity decay rate of only 0.064% per cycle for 500 cycles at 25 °C and 0.5 C).

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.

Ortho-Substituent Effects on Halogen Bond Geometry for N-Haloimide⋯2-Substituted Pyridine Complexes

The nature of (imide)N-X⋯N(pyridine) halogen-bonded complexes formed by six N-haloimides and sixteen 2-substituted pyridines are studied using X-ray crystallography (68 crystal structures), Density Functional Theory (DFT) (86 complexation energies), and NMR spectroscopy (90 association constants). Strong halogen bond (XB) donors such as N-iodosuccinimide form only 1:1 haloimide:pyridine crystalline complexes, but even stronger N-iodosaccharin forms 1:1 haloimide:pyridine and three other distinct complexes. In 1:1 haloimide:pyridine crystalline complexes, the haloimide's N─X bond exhibits an unusual bond bending feature that is larger for stronger N-haloimides. DFT complexation energies (ΔEXB ) for iodoimide-pyridine complexes range from -44 to -99 kJ mol-1 , while for N-bromoimide-pyridine, they are between -31 and -77 kJ mol-1 . The ΔEXB of I⋯N XBs in 1:1 iodosaccharin:pyridine complexes are the largest of their kind, but they are substantially smaller than those in [bis(saccharinato)iodine(I)]pyridinium salts (-576 kJ mol-1 ), formed by N-iodosaccharin and pyridines. The NMR association constants and ΔEXB energies of 1:1 haloimide:pyridine complexes do not correlate as these complexes in solution are heavily influenced by secondary interactions, which DFT studies do not account for. Association constants follow the σ-hole strengths of N-haloimides, which agree with DFT and crystallography data. The haloimide:2-(N,N-dimethylamino)pyridine complex undergoes a halogenation reaction resulting in 5-iodo-2-dimethylaminopyridine.

Building a new reasonable molecular theory⊗

CONTEXT

This article intends to show a new way to setup and solve chemical bonds which can be incorporated into molecules. The new approach is analytical and purely based on simple math and science. We need analytical methods in our molecular theory which can be used to obtain results with our eyes open to the process. The utilization of computer software is fine as long as the user understands what the software is exactly doing. An analytical molecular theory can be utilized in different areas of science including chemistry. It can be also an asset in classrooms to better train our future generations, making them better "thinkers" and ready to tackle the complicated issues in our changing world. This article first introduces a new analytical approach to study chemical bonds and then goes through several examples of chemical bonds to show the applicability of the suggested approach.

METHODS

All of the calculations and figures presented in this article are done by the use of Microsoft excel spreadsheet. The presented approach does not need any sophisticated software and/or heavy computations.

Benchmarking Swaths of Intermolecular Interaction Components with Symmetry-Adapted Perturbation Theory

A benchmark database for interaction energy components of various noncovalent interactions (NCIs) along their dissociation curve is one of the essential needs in theoretical chemistry, especially for the development of force fields and machine-learning methods. We utilize DFT-SAPT or SAPT(DFT) as one of the most accurate methods to generate an extensive stock of the energy components, including dispersion energies extrapolated to the complete basis set limit (CBS). Precise analyses of the created data, and benchmarking the total interaction energies against the best available CCSD(T)/CBS values, reveal different aspects of the methodology and the nature of NCIs. For example, error cancellation effects between the S2 approximation and nonexact xc-potentials occur, and large charge transfer energies in some systems, including heavy atoms, can explain the lower accuracy of DFT-SAPT. This method is perfect for neutral complexes containing light nonmetals, while other systems with heavier atoms should be treated carefully. In the last part, a representative data set for all NCIs is extracted from the original data.

Exploring the role of halogen bonding in iodonium ylides: insights into unexpected reactivity and reaction control

Halogen bonding is commonly found with iodine-containing molecules, and it arises when Lewis bases interact with iodine's σ-holes. Halogen bonding and σ-holes have been encountered in numerous monovalent and hypervalent iodine-containing compounds, and in 2022 σ-holes were computationally confirmed and quantified in the iodonium ylide subset of hypervalent iodine compounds. In light of this new discovery, this article provides an overview of the reactions of iodonium ylides in which halogen bonding has been invoked. Herein, we summarize key discoveries and mechanistic proposals from the early iodonium ylide literature that invoked halogen bonding-type mechanisms, as well as recent reports of reactions between iodonium ylides and Lewis basic nucleophiles in which halogen bonding has been specifically invoked. The reactions discussed herein are organized to enable the reader to build an understanding of how halogen bonding might impact yield and chemoselectivity outcomes in reactions of iodonium ylides. Areas of focus include nucleophile σ-hole selectivity, and how ylide structural modifications and intramolecular halogen bonding (e.g., the ortho-effect) can improve ylide stability or solubility, and alter reaction outcomes.

"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.

Effects of Lewis Basicity and Acidity on σ-Hole Interactions in Carbon-Bearing Complexes: A Comparative Ab Initio Study

The effects of Lewis basicity and acidity on σ-hole interactions were investigated using two sets of carbon-containing complexes. In Set I, the effect of Lewis basicity was studied by substituting the X3/X atom(s) of the NC-C6H2-X3 and NCX Lewis bases (LB) with F, Cl, Br, or I. In Set II, the W-C-F3 and F-C-X3 (where X and W = F, Cl, Br, and I) molecules were utilized as Lewis acid (LA) centers. Concerning the Lewis basicity effect, higher negative interaction energies (Eint) were observed for the F-C-F3∙∙∙NC-C6H2-X3 complexes compared with the F-C-F3∙∙∙NCX analogs. Moreover, significant Eint was recorded for Set I complexes, along with decreasing the electron-withdrawing power of the X3/X atom(s). Among Set I complexes, the highest negative Eint was ascribed to the F-C-F3∙∙∙NC-C6H2-I3 complex with a value of -1.23 kcal/mol. For Set II complexes, Eint values of F-C-X3 bearing complexes were noted within the -1.05 to -2.08 kcal/mol scope, while they ranged from -0.82 to -1.20 kcal/mol for the W-C-F3 analogs. However, Vs,max quantities exhibited higher values in the case of W-C-F3 molecules compared with F-C-X3; preferable negative Eint were ascribed to the F-C-X3 bearing complexes. These findings were delineated as a consequence of the promoted contributions of the X3 substituents. Dispersion forces (Edisp) were identified as the dominant forces for these interactions. The obtained results provide a foundation for fields such as crystal engineering and supramolecular chemistry studies that focus on understanding the characteristics of carbon-bearing complexes.

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.

Simulating chalcogen bonding using molecular mechanics: a pseudoatom approach to model ebselen

The organoselenium compound ebselen has recently been investigated as a treatment for COVID-19; however, efforts to model ebselen in silico have been hampered by the lack of an efficient and accurate method to assess its binding to biological macromolecules. We present here a Generalized Amber Force Field modification which incorporates classical parameters for the selenium atom in ebselen, as well as a positively charged pseudoatom to simulate the σ-hole, a quantum mechanical phenomenon that dominates the chemistry of ebselen. Our approach is justified using an energy decomposition analysis of a number of density functional theory–optimized structures, which shows that the σ-hole interaction is primarily electrostatic in origin. Finally, our model is verified by conducting molecular dynamics simulations on a number of simple complexes, as well as the clinically relevant enzyme SOD1 (superoxide dismutase), which is known to bind to ebselen.

Graphical Abstract

"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.

Iodine(III)-Based Halogen Bond Donors: Properties and Applications

Halogen bonding, the non-covalent interaction of Lewis bases with an electron-deficient region of halogen substituents, received increased attention recently. Consequently, the design and evaluation of numerous halogen-containing species as halogen bond donors have been subject to intense research. More recently, organoiodine compounds at the iodine(III) state have been receiving growing attention in the field. Due to their electronic and structural properties, they provide access to unique binding modes. For this reason, our groups have been involved in the development of such compounds, in the quantification of their halogen bonding strength (through the evaluation of their Lewis acidities), as well as in the evaluation of their activities as catalysts in several model reactions. This account will describe these contributions.

The Electrophilicities of XCF3 and XCl (X=H, Cl, Br, I) and the Propensity of These Molecules To Form Hydrogen and Halogen Bonds with Lewis Bases: An Ab Initio Study

Equilibrium dissociation energies, De , of four series of halogen- and hydrogen-bonded complexes B⋅⋅⋅XCF3 (X=H, Cl, Br and I) are calculated ab initio at the CCSD(T)(F12c)/cc-pVDZ-F12 level. The Lewis bases B involved are N2 , CO, PH3 , C2 H2 , C2 H4 , H2 S, HCN, H2 O and NH3 . Plots of De versus NB , where the NB are the nucleophilicities assigned to the Lewis bases previously, are good straight lines through the origin, as are those for the corresponding set of complexes B⋅⋅⋅XCl. The gradients of the De versus NB plots define the electrophilicities EXCF3 and EXCl of the various Lewis acids. The determined values are: EXCF3 =2.58(22), 1.40(9), 2.15(2) and 3.04(9) for X=H, Cl, Br and I, respectively, and EXCl =4.48(22), 2.31(9), 4.37(27) and 6.06(37) for the same order of X. Thus, it is found that, for a given X, the ratio EXCl / EXCF3 is 2 within the assessed errors, and therefore appears to be independent of the atom X and of the type of non-covalent interaction (hydrogen bond or different varieties of halogen bond) in which it is involved. Consideration of the molecular electrostatic surface potentials shows that De and the maximum positive electrostatic potential σmax (the most electrophilic region of XCF3 and XCl, which lies on the symmetry axes of these molecules, near to the atom X) are strongly correlated.

CHAL336 Benchmark Set: How Well Do Quantum-Chemical Methods Describe Chalcogen-Bonding Interactions?

We present the CHAL336 benchmark set-the most comprehensive database for the assessment of chalcogen-bonding (CB) interactions. After careful selection of suitable systems and identification of three high-level reference methods, the set comprises 336 dimers each consisting of up to 49 atoms and covers both σ- and π-hole interactions across four categories: chalcogen-chalcogen, chalcogen-π, chalcogen-halogen, and chalcogen-nitrogen interactions. In a subsequent study of DFT methods, we re-emphasize the need for using proper London dispersion corrections when treating noncovalent interactions. We also point out that the deterioration of results and systematic overestimation of interaction energies for some dispersion-corrected DFT methods does not hint at problems with the chosen dispersion correction but is a consequence of large density-driven errors. We conclude this work by performing the most detailed DFT benchmark study for CB interactions to date. We assess 109 variations of dispersion-corrected and dispersion-uncorrected DFT methods and carry out a detailed analysis of 80 of them. Double-hybrid functionals are the most reliable approaches for CB interactions, and they should be used whenever computationally feasible. The best three double hybrids are SOS0-PBE0-2-D3(BJ), revDSD-PBEP86-D3(BJ), and B2NCPLYP-D3(BJ). The best hybrids in this study are ωB97M-V, PW6B95-D3(0), and PW6B95-D3(BJ). We do not recommend using the popular B3LYP functional nor the MP2 approach, which have both been frequently used to describe CB interactions in the past. We hope to inspire a change in computational protocols surrounding CB interactions that leads away from the commonly used, popular methods to the more robust and accurate ones recommended herein. We would also like to encourage method developers to use our set for the investigation and reduction of density-driven errors in new density functional approximations.

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.

Components of the interaction energy of the odd-electron halogen bond: an ab initio study

In the realm of non-covalent interactions (NCI), the odd-electron halogen bond offers a fertile ground to explore the nature of such weak interactions. Here, an ab initio study of odd-electron halogen bonding (XB) is reported. The interactions of five radicals with several freons and interhalogens are studied using the Møller-Plesset (MP2) method. The regioselectivity, interaction energy and the components of the interaction energy of odd-electron XB were tuned by judicial selection of donor-acceptor pairs as revealed by scrutinizing the conceptual DFT parameters, NCI plot and LED-DLPNO-CCSD(T) analysis. The contribution from dispersion interaction is rather high for all XB bonded complexes and it increases when the interacting atom of the XB donor is highly polarizable. Additionally, the polarisation and intermolecular charge-transfer also contribute significantly when both the donor and acceptor atoms are soft species, resulting in a soft-soft interaction. We believe that our finding will not only shed new light on non-covalent interaction of odd-electron XB but will also be able to capture the pnictogen, chalcogen and tetrel bonding interactions. The ability of conceptual DFT parameters to predict the interaction energy and its components shown in this study will be helpful for tuning of substrates for desired products, modelling bio/macromolecules and crystal engineering.

On the reciprocal relationship between σ-hole bonding and (anti)aromaticity gain in ketocyclopolyenes

σ-Hole bonding interactions (e.g., tetrel, pnictogen, chalcogen, and halogen bonding) can polarize π-electrons to enhance cyclic [4n] π-electron delocalization (i.e., antiaromaticity gain) or cyclic [4n + 2] π-electron delocalization (i.e., aromaticity gain). Examples based on the ketocyclopolyenes: cyclopentadienone, tropone, and planar cyclononatetraenone are presented. Recognizing this relationship has implications, for example, for tuning the electronic properties of fulvene-based π-conjugated systems such as 9-fluorenone.

Models of necessity

The way chemists represent chemical structures as two-dimensional sketches made up of atoms and bonds, simplifying the complex three-dimensional molecules comprising nuclei and electrons of the quantum mechanical description, is the everyday language of chemistry. This language uses models, particularly of bonding, that are not contained in the quantum mechanical description of chemical systems, but has been used to derive machine-readable formats for storing and manipulating chemical structures in digital computers. This language is fuzzy and varies from chemist to chemist but has been astonishingly successful and perhaps contributes with its fuzziness to the success of chemistry. It is this creative imagination of chemical structures that has been fundamental to the cognition of chemistry and has allowed thought experiments to take place. Within the everyday language, the model nature of these concepts is not always clear to practicing chemists, so that controversial discussions about the merits of alternative models often arise. However, the extensive use of artificial intelligence (AI) and machine learning (ML) in chemistry, with the aim of being able to make reliable predictions, will require that these models be extended to cover all relevant properties and characteristics of chemical systems. This, in turn, imposes conditions such as completeness, compactness, computational efficiency and non-redundancy on the extensions to the almost universal Lewis and VSEPR bonding models. Thus, AI and ML are likely to be important in rationalizing, extending and standardizing chemical bonding models. This will not affect the everyday language of chemistry but may help to understand the unique basis of chemical language.

"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.

The Molpro quantum chemistry package

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

Is There a Single Ideal Parameter for Halogen-Bonding-Based Lewis Acidity?

Halogen-bond donors (halogen-based Lewis acids) have now found various applications in diverse fields of chemistry. The goal of this study was to identify a parameter obtainable from a single DFT calculation that reliably describes halogen-bonding strength (Lewis acidity). First, several DFT methods were benchmarked against the CCSD(T) CBS binding data of complexes of 17 carbon-based halogen-bond donors with chloride and ammonia as representative Lewis bases, which revealed M05-2X with a partially augmented def2-TZVP(D) basis set as the best model chemistry. The best single parameter to predict halogen-bonding strengths was the static σ-hole depth, but it still provided inaccurate predictions for a series of compounds. Thus, a more reliable parameter, Ωσ* , has been developed through the linear combination of the σ-hole depth and the σ*(C-I) energy, which was further validated against neutral, cationic, halogen- and nitrogen-based halogen-bond donors with very good performance.

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.

On the Interplay between Charge-Shift Bonding and Halogen Bonding

The nature of halogen-bond interactions has been analysed from the perspective of the astatine element, which is potentially the strongest halogen-bond donor. Relativistic quantum calculations on complexes formed between halide anions and a series of Y₃ C-X (Y=F to X, X=I, At) halogen-bond donors disclosed unexpected trends, e. g., At₃ C-At revealing a weaker donating ability than I₃ C-I despite a stronger polarizability. All the observed peculiarities have their origin in a specific component of C-Y bonds: the charge-shift bonding. Descriptors of the Quantum Chemical Topology show that the halogen-bond strength can be quantitatively anticipated from the magnitude of charge-shift bonding operating in Y₃ C-X. The charge-shift mechanism weakens the ability of the halogen atom X to engage in halogen bonds. This outcome provides rationales for outlier halogen-bond complexes, which are at variance with the consensus that the halogen-bond strength scales with the polarizability of the halogen atom.

The Structure of CCl5- in the Gas Phase

The first experimental evidence of the structure of the CCl₅^- gas-phase anion complex is presented in conjunction with results from high-level theoretical calculations. The photoelectron spectrum of the system shows a single peak with a maximum at 4.22 eV. Coupled cluster single double (triple) detachment energies of two stable C_3v ion-molecule complexes of the form Cl^-···CCl₄ were also determined. The first complex found features the Cl^- bound linearly in a Cl^-···Cl-C bonding arrangement, while the second, less stable minimum has the Cl^- positioned at the face of the CCl₄ molecule, midway between three chlorine atoms. The calculated detachment energy for the first complex was found to be in excellent agreement with experiment, allowing the structure of CCl₅^- in the gas phase to be postulated as a noncovalent Cl^-···CCl₄ anion complex, with the Cl^- anion tethered by a typical halogen bond.

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.

Theoretical and conceptual DFT study of pnicogen- and halogen-bonded complexes of PH2X---BrCl

The pnicogen and halogen bonding interactions in the PH₂X---BrCl(X = H, F, OH, OCH₃ and CH₃) complexes have been studied at the MP2/aug-cc-pVTZ level. Analysis of interaction energies shows that the pnicogen-bonded structures are less stable than the corresponding halogen-bonded structures. The pnicogen and halogen bonds were also studied by conceptual DFT reactivity indices. Noncovalent interaction (NCI) and SAPT analysis reveals that the dispersion interactions dominate the pnicogen-bonded complexes of PH₂X---BrCl in nature, while the halogen-bonded complexes are dominantly electrostatic energy. Graphical abstract It is found that the local softness s⁺ or s^-on the basic center P of PH₂X is related to the interaction energies (ΔE^CP) of halogen- or pnicogen-bonded complexes.

The chalcogen bond in F2P(S)N⋅⋅⋅SX2, F2PNS⋅⋅⋅SX2, F2PSN⋅⋅⋅SX2 (X = F, Cl, Br, OH, CH3, NH2) complexes

As a kind of intermolecular noncovalent interaction, chalcogen bonding plays a critical role in the fields of chemistry and biology. In this paper, S⋅⋅⋅S chalcogen bonds in three groups of complexes, F₂P(S)N⋅⋅⋅SX₂, F₂PNS⋅⋅⋅SX₂, and F₂PSN⋅⋅⋅SX₂ (X = F, Cl, Br, OH, CH₃, NH₂), were investigated at the MP2/aug-cc-pVTZ level of theory. The calculated results show that the formation of S⋅⋅⋅S chalcogen bond is in the manner of attraction between the positive molecular electrostatic potential (V_S,max) of chalcogen bond donator and the negative V_S,min of chalcogen bond acceptor. It is found that a good correlation exists between the S⋅⋅⋅S bond length and the interaction energy. The energy decomposition indicates the electrostatic energy and polarization energy are closely correlated with the total interaction energy. NBO analysis reveals that the charge transfer is rather closely correlated with the polarization, and the charge transfer has a similar behavior as the polarization in the formation of complex. Our results provide a new example for interpreting the noncovalent interaction based on the σ-hole concept. Graphical abstract The chalcogen bonds in the studied binary complexes are Coulombic in nature, and the charge transfer has a similar behavior as the polarization in the formation of the complex.

Tetrel bonding interaction: an analysis with the block-localized wavefunction (BLW) approach

In this study, fifty-one iconic tetrel bonding complexes were studied using the block localized wave function (BLW) method which can derive the self-consistent wavefunction for an electron-localized (diabatic) state where charge transfer is strictly deactivated.

Halogen bonding in differently charged complexes: basic profile, essential interaction terms and intrinsic σ-hole

Studies on halogen bonds (XB) between organohalogens and their acceptors in crystal structures revealed that the XB donor and acceptor could be differently charged, making it difficult to understand the nature of the interaction, especially the negatively charged donor's electrophilicity and positively charged acceptor's nucleophilicity. In this paper, 9 XB systems mimicking all possibly charged halogen bonding interactions were designed and explored computationally. The results revealed that all XBs could be stable, with binding energies after removing background interaction as strong as -1.2, -3.4, and -8.3 kcal mol-1 for Cl, Br, and I involved XBs respectively. Orbital and dispersion interactions are found to be always attractive while unidirectional intermolecular electron transfer from a XB acceptor to a XB donor occurs in all XB complexes. These observations could be attributed to the intrinsic σ-hole of the XB donor and the intrinsic electronic properties of the XB acceptor regardless of their charge states. Intramolecular charge redistribution inside both the donor and the acceptor is found to be system-dependent but always leads to a more stable XB. Accordingly, this study demonstrates that the orbital-based origin of halogen bonds could successfully interpret the complicated behaviour of differently charged XB complexes, while electrostatic interaction may dramatically change the overall bonding strength. The results should further promote the application of halogens in all related areas.

A perspective on quantum mechanics and chemical concepts in describing noncovalent interactions

Since quantum mechanical calculations do not typically lend themselves to chemical interpretation, analyses of bonding interactions depend largely upon models (the octet rule, resonance theory, charge transfer, etc.). This sometimes leads to a blurring of the distinction between mathematical modelling and physical reality. The issue of polarization vs. charge transfer is an example; energy decomposition analysis is another. The Hellmann-Feynman theorem at least partially bridges the gap between quantum mechanics and conceptual chemistry. It proceeds rigorously from the Schrödinger equation to demonstrating that the forces exerted upon the nuclei in molecules, complexes, etc., are entirely classically coulombic attractions with the electrons and repulsions with the other nuclei. In this paper, we discuss these issues in the context of noncovalent interactions. These can be fully explained in coulombic terms, electrostatics and polarization (which include electronic correlation and dispersion).