A look at bonds and bonding

Chemical bonding and electronic properties along Group 13 metal oxides

CONTEXT

The present work provides a systematic theoretical analysis of the nature of the chemical bond in Al2O3, Ga2O3, and In2O3 group 13 cubic crystal structure metal oxides. The influence of the functional in the resulting band gap is assessed. The topological analysis of the electron density provides unambiguous information about the degree of ionicity along the group which is linearly correlated with the band gap values and with the cost of forming a single oxygen vacancy. Overall, this study offers a comprehensive insight into the electronic structure of metal oxides and their interrelations. This will help researchers to harness information effectively, boosting the development of novel metal oxide catalysts or innovative methodologies for their preparation.

METHODS

Periodic density functional theory was used to predict the atomic structure of the materials of interest. Structure optimization was carried out using the PBE functional, using a plane wave basis set and the PAW representation of the atomic cores, using the VASP code. Next, the electronic properties were computed by carrying out single point calculations employing PBE, PBE + U functionals using VASP and also with PBE and the hybrid HSE06 functionals using the FHI-AIMS software. For the hybrid HSE06, the impact of the screening parameter, ω, and mixing parameter, α, on the calculated band gap has also been assessed.

Probing intramolecular interactions using molecular electrostatic potentials: changing electron density contours to unveil both attractive and repulsive interactions

We focus on intramolecular interactions, using the electrostatic potential plotted on iso-density surfaces to lead the way. We show that plotting the electrostatic potential on varying iso-density envelopes much closer to the nuclei than the commonly used 0.001 a.u. contour can reveal the driving forces for such interactions, whether they be stabilizing or destabilizing. Our approach involves optimizing the structures of molecules exhibiting intramolecular interactions and then finding the contour of the electronic density which allows the interacting atoms to be separated; we call this the nearly-touching contour. The electrostatic potential allows then to identify the intramolecular interactions as either attractive or repulsive. The discussed 1,5- and 1,6-intramolecular interactions in o-bromophenol and o-nitrophenol are attractive, while the interactions between terminal methyl hydrogens in diethyl disulfides (as shown recently) and those between the closest hydrogens in planar biphenyl and phenanthrene are clearly repulsive in nature. For the attractive 1,4-interactions in trinitromethane and chlorotrinitromethane, and the 1,3-S⋯N and the 1,4-Si⋯N interactions in the ClH2Si(CH2)nNH2 series, the lack of (3,-1) bond critical points has often been cited as reason to not identify such interactions as attractive in nature. Here, by looking at the nearly-touching contours we see that bond critical points are neither necessary nor sufficient for attractive interactions, as others have pointed out, and in some instances also pointing to repulsive interactions, as the examples of planar biphenyl and phenanthrene discussed in this work show.

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.

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.

Intramolecular Repulsion Visible Through the Electrostatic Potential in Disulfides: Analysis via Varying Iso-density Envelopes

For a series of diethyl disulfide conformations, the nearly touching contours of the electrostatic potential plotted on iso-density molecular surfaces allow the assessment of intramolecular repulsion. The electrostatic potential is plotted on varying iso-density envelopes to find the nearly touching contours for which (a) the surface electrostatic potential does not show overlap between atoms or functional groups and (b) the typical features are visible (σ-hole, lone pair, hydrogen VS,max). When these nearly touching contours X are closer to the nuclei, the more electron density is excluded from the iso-density envelopes and the smaller are the volumes corresponding to these envelopes. Both the contours X and the corresponding volumes are found to correlate with relative conformational energy, reflecting the degree of intramolecular repulsion present in the various diethyl disulfides. Quantitative estimates of intramolecular repulsion can be made based on relationships between the nearly touching contour X vs relative energy and volume (of the nearly touching contour X) vs relative energy, obtained for series of diethyl disulfide conformers. These relations were used to analyze intramolecular repulsion in a set of disulfides broader than diethyl disulfide conformers. We have shown that the approach of varying electronic density contours can be used in the study of repulsive intramolecular interactions, hereby extending earlier work involving attractive intermolecular interactions.

"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.

Analysis of Bonding by Quantum Chemistry─Resolving Delocalization Stabilization in a Mechanistic Basis and New Hückel Model

No general and unique understanding of the mechanism of covalent bonding in physical terms is provided by current computational methods or by a consensus among experts. Bonding is studied by energy decomposition analysis but may also be related to the interatomic motion of valence electrons within the molecule. This dynamical view of the mechanism of bonding is not widely appreciated. The aim here is to make it accessible by translation into a corresponding form of quantum chemical energy analysis. The interatomic electron motion is directly related to the delocalization taking place when atomic basis functions are combined into molecular orbitals. A "tribasis method" is introduced, allowing an atomic basis set to form subsets of (1) strictly localized atomic functions and (2) interatomic bridge functions which allow delocalization. Calculations can then identify ground states without (no bridge functions) and with delocalization. The scheme is based on exact quantum mechanics but demonstrated by a minimal basis treatment of H₂⁺ and H₂ in Hartree-Fock and valence bond approximations which show that the bond energy is a sum of repulsive localization and more strongly attractive delocalization energies. The tribasis method is used to reconstruct the Hückel theory of π-electron delocalization in planar hydrocarbon molecules to account for the "overlap problem". In its empirically fitted form, the new theory can accurately resolve both π → π* transition energy and aromatic stabilization energy. The picture of covalent bonding emerging from both hydrogenic and Hückel calculations is that there is a presence of a Pauli repulsion of localization which is overcome by a roughly twice as strong delocalization stabilization to form the bond.

Can We Merge the Weak and Strong Tetrel Bonds? Electronic Features of Tetrahedral Molecules Interacted with Halide Anions

Using the orbital-free quantum crystallography approach, we have disclosed the quantitative trends in electronic features for bonds of different strengths formed by tetrel (Tt) atoms in stable molecular complexes consisting of electrically neutral tetrahedral molecules and halide anions. We have revealed the role of the electrostatic and exchange-correlation components of the total one-electron static potential that are determined by the equilibrium atomic structure and by kinetic Pauli potential, which reflects the spin-dependent electron motion features of the weak and strong bonds. The gap between the extreme positions in the electrostatic and total static potentials along the line linking the Tt atom and halide anion is wide for weak bonds and narrow for strong ones. It is in very good agreement with the number of minima in the Pauli potential between the bounded atoms. This gap exponentially correlates with the exchange-correlation potential in various series with a fixed nucleophilic fragment. A criterion for categorizing the noncovalent tetrel bonds (TtB) based on the potential features is suggested.

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.

From the gas phase to the solid state: The chemical bonding in the superheavy element flerovium

As early as 1975, Pitzer suggested that copernicium, flerovium and oganesson are volatile substances behaving noble-gas like because of their closed-shell configurations and accompanying relativistic effects. It is, however, precarious to predict the chemical bonding and physical behavior of a solid by knowledge of the atomic or molecular properties only. Copernicium and oganesson have been analyzed very recently by our group. Both are predicted to be semi-conductors and volatile substances with rather low melting and boiling points, which may justify a comparison with the noble gas elements. Here we study closed-shell flerovium in detail to predict solid-state properties including the melting point from a decomposition of the total energy into many-body forces derived from relativistic coupled-cluster and from density functional theory. The convergence of such a decomposition for flerovium is critically analyzed, and the problem of using density functional theory is highlighted. We predict that flerovium is in many ways not behaving like a typical noble gas element despite its closed-shell 7$p_{1/2}^2$ configuration and resulting weak interactions. Unlike for the noble gases, the many-body expansion in terms of the interaction energy is not converging smoothly. This makes the accurate prediction of phase transitions very difficult. Nevertheless, a first prediction by Monte-Carlo simulation estimates the melting point at $284\pm 50$ K. Furthermore, calculations for the electronic band gap suggests that flerovium is a semi-conductor similar to copernicium

From the Electron Density Gradient to the Quantitative Reactivity Indicators: Local Softness and the Fukui Function

Important reactivity measures such as the local softness, the Fukui function, and the global hardness have been calculated directly from first principles with the use of the electron density function, beyond the finite difference approximation. Our recently derived density gradient theorem and the principle of nearsightedness of the electronic matter have been instrumental in obtaining the original, albeit approximate, result on the local softness of an atom. By integration of the local softness s(r), we obtain the global softness S and the Fukui function f(r) = s(r)/S. Local and global softness values have also been calculated analytically for the basic hydrogenic orbitals; the general relation to the atomic number S = σZ ^-2 has been demonstrated, with constants σ characteristic for each orbital type. Global hardness η = 1/S calculated for atoms and ions has been favorably tested against its conventional measure given by the finite difference approximation: (I - A). Calculated test results for atoms and ions in rows 1-4 of the periodic table have been presented.

Interpreting the Variations in the Kinetic and Potential Energies in the Formation of a Covalent Bond

We address the long-standing controversy as to the physical origin of covalent bonding, whether it involves a lowering of the potential energy or a lowering of the kinetic energy. We...

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.

Quantifying bond strengths via a Coulombic force model: application to the impact sensitivity of nitrobenzene, nitrogen-rich nitroazole, and non-aromatic nitramine molecules

The quantification of bond strengths is a useful and general concept in chemistry. In this work, a Coulombic force model based on atomic electric charges computed using the accurate distributed multipole analysis (DMA) partition of the molecular charge density was employed to quantify the weakest N-NO₂ and C-NO₂ bond strengths of 19 nitrobenzene, 11 nitroazole, and 10 nitramine molecules. These bonds are known as trigger linkages because they are usually related to the initiation of an explosive. The three families of explosives combine different types of molecular properties and structures ranging from essentially aromatic molecules (nitrobenzenes) to others with moderate aromaticity (nitroazoles) and non-aromatic molecules with cyclic and acyclic skeletons (nitramines). We used the results to investigate the impact sensitivity of the corresponding explosives employing the trigger linkage concept. For this purpose, the computed Coulombic bond strength of the trigger linkages was used to build four sensitivity models that lead to an overall good agreement between the predicted values and available experimental sensitivity values even when the model included the three chemical families simultaneously. We discussed the role of the trigger linkages for determining the sensitivity of the explosives and rationalized eventual discrepancies in the models by examining alternative decomposition mechanisms and features of the molecular structures.

Cospatial σ-Hole and Lone Pair Interactions of Square-Pyramidal Pentavalent Halogen Compounds with π-Systems: A Quantum Mechanical Study

In the spirit of the mounting interest in noncovalent interactions, the present study was conducted to scrutinize a special type that simultaneously involved both σ-hole and lone pair (lp) interactions with aromatic π-systems. Square-pyramidal pentavalent halogen-containing molecules, including X-Cl-F4, F-Y-F4, and F-I-X4 compounds (where X = F, Cl, Br, and I and Y = Cl, Br, and I) were employed as σ-hole/lp donors. On the other hand, benzene (BZN) and hexafluorobenzene (HFB) were chosen as electron-rich and electron-deficient aromatic π-systems, respectively. The investigation relied upon a variety of quantum chemical calculations that complement each other. The results showed that (i) the binding energy of the X-Y-F4···BZN complexes increased (i.e., more negative) as the Y atom had a larger magnitude of σ-hole, contrary to the pattern of X-Y-F4···HFB complexes; (ii) the interaction energies of X-Y-F4···BZN complexes were dominated by both dispersion and electrostatic contributions, while dispersive interactions dominated X-Y-F4···HFB complexes; and (iii) the X4 atoms in F-I-X4···π-system complexes governed the interaction energy pattern: the larger the X4 atoms were, the greater the interaction energies were, for the same π-system. The results had illuminating facets in regard to the rarely addressed cases of the σ-hole/lp contradictory scene.

Halogen bonding interactions in the XC5H4N···YCF3 (X = CH3, H, Cl, CN, NO2; Y = Cl, Br, I) complexes

The noncovalent interactions between the σ-hole region outside the halogen atom and the nitrogen atom of pyridine and its para-substituted derivatives are the focus of this work. Based on the analyses of the electrostatic potentials, YCF₃ (Y = Cl, Br, I) act as halogen bond donors, XC₅H₄N (X = CH₃, H, Cl, CN, NO₂) act as halogen bond acceptors, and the binary halogen-bonded complexes XC₅H₄N···YCF₃ have been designed and investigated by B3LYP-D3/aug-cc-pVDZ calculations together with the aug-cc-pVDZ-PP basis set for iodine. When the halogen bond acceptor remains unchanged, the interactions between C₅H₅N and YCF₃ (Y = Cl, Br, I) increase with the order of Y = Cl, Br, and I. When the halogen donor ICF₃ is fixed, the halogen bonding interactions decrease along the sequence of X = CH₃, H, Cl, CN, NO₂. Therefore, the halogen bond of the CH₃C₅H₄N···ICF₃ complex is the strongest. The interactions between Lewis acid YCF₃ (Y = Cl, Br, I) and pyridine and para-substituted pyridine are closed-shell and noncovalent interactions. On the one hand, when the halogen bond acceptor XC₅H₄N is fixed, with the increase of halogen atomic number, the strength of halogen bond increases; on the other hand, when the halogen bond donor ICF₃ is fixed, as the electron-withdrawing ability of the electron-withdrawing group (X) increases, the halogen bond gradually weakens.

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.

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.

The Connectivity Matrix: A Toolbox for Monitoring Bonded Atoms and Bonds

The concept of a connectivity matrix, essential for the reaction fragility (RF) spectra technique for monitoring electron density evolution in a chemical reaction, has been supported with a novel formulation for the diagonal matrix elements; their direct link to the electron density function ρ(r) has been demonstrated. By combining the concept with the atomization energy of a system, the separation of the potential energy into atomic and/or bond contributions has been achieved. The energy derivative diagrams for atoms and bonds that are variable along a reaction path provide new insight into the reaction mechanism. Diagonalization of the connectivity matrix resulted in the eigenvectors that provide information on a role of individual atoms in the development of structural changes along a reaction path.

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.

Bond Softening Indices Studied by the Fragility Spectra for Proton Migration in Formamide and Related Structures

Computational scheme to obtain bond softening index λ, defined within the conceptual DFT, has been obtained with the use of the reaction fragility (RF) concept. Numerical results were obtained with the RF spectra for the proton transfer reaction in formamide molecule (H₂NCHO) and the water assisted proton migration in H₂NCHO·H₂O complex. Double proton transfer reaction in the formamide dimer, (H₂NCHO)₂, and its analogues, (H₂NCHS)₂ and (H₂NCHO)·(H₂NCHS), have also been studied. The atomic and bond RF spectra clearly describe the density reorganization in the backbone of each molecule, resulting from proton displacement in the systems. The obtained softening indices have been calculated for hydrogen atoms in the reactant state (RS) and product state (PS) configuration. These indices provide fine characteristics for the local sensitivity of the reacting system to a disturbance of the position of a chosen atom.

Identifying intermolecular atom⋯atom interactions that are not just bonding but also competitive

This highlight criticises the QTAIM method and discusses algorithms for identifying intermolecular interactions that are both bonding and competitive.