The Neglected Nuclei

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

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

Halogen Bond via an Electrophilic π-Hole on Halogen in Molecules: Does It Exist?

This study reveals a new non-covalent interaction called a π-hole halogen bond, which is directional and potentially non-linear compared to its sister analog (σ-hole halogen bond). A π-hole is shown here to be observed on the surface of halogen in halogenated molecules, which can be tempered to display the aptness to form a π-hole halogen bond with a series of electron density-rich sites (Lewis bases) hosted individually by 32 other partner molecules. The [MP2/aug-cc-pVTZ] level characteristics of the π-hole halogen bonds in 33 binary complexes obtained from the charge density approaches (quantum theory of intramolecular atoms, molecular electrostatic surface potential, independent gradient model (IGM-δginter)), intermolecular geometries and energies, and second-order hyperconjugative charge transfer analyses are discussed, which are similar to other non-covalent interactions. That a π-hole can be observed on halogen in halogenated molecules is substantiated by experimentally reported crystals documented in the Cambridge Crystal Structure Database. The importance of the π-hole halogen bond in the design and growth of chemical systems in synthetic chemistry, crystallography, and crystal engineering is yet to be fully explicated.

Unraveling pnicogen bonding cooperativity: Insights from molecular electrostatic potential analysis

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

Structure, stability, reactivity and bonding in noble gas compounds

Noble gases (Ngs) are recognized as the least reactive elements due to their fully filled valence electronic configuration. Their reluctance to engage in chemical bond formation necessitates extreme conditions such as low temperatures, high pressures, and reagents with high reactivity. In this Perspective, we discuss our endeavours in the theoretical prediction of viable Ng complexes, emphasizing the pursuit of synthesizing them under nearly ambient conditions. Our research encompasses various bonding categories of Ng complexes and our primary aim is to comprehend the bonding mechanisms within these complexes, utilizing state-of-the-art theoretical tools such as natural bond orbital, energy decomposition, and electron density analyses. These complex types manifest distinct bonding scenarios. In the non-insertion type, the donor-acceptor interaction strength hinges on the polarizing ability of the binding atom, drawing the electron density of the Ng towards itself. In certain instances, especially with heavier Ng elements, this interaction reaches a magnitude where it can be considered a covalent bond. Conversely, in most insertion cases, the Ng prefers to share electrons to form a covalent bond on one side while interacting electrostatically on the other side. In rare cases, both bonds may be portrayed as electron-shared covalent bonds. Furthermore, a host cage serves as an excellent platform to explore the limits of achieving Ng-Ng bonds (even for helium), under high pressure.

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.

The Formation of σ-Hole Bonds: A Physical Interpretation

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

A Theoretical Investigation of Novel Sila- and Germa-Spirocyclic Imines and Their Relevance for Electron-Transporting Materials and Drug Discovery

A new class of spirocyclic imines (SCIs) has been theoretically investigated by applying a variety of quantum chemical methods and basis sets. The uniqueness of these compounds is depicted by various peculiarities, e.g., the incidence of planar six-membered rings each with two imine groups (two π bonds) and the incorporation of the isosteres carbon, silicon, or germanium spiro centers. Additional peculiarities of these novel SCIs are mirrored by their three-dimensionality, the simultaneous occurrence of nucleophilic and electrophilic centers, and the cross-hyperconjugative (spiro-conjugation) interactions, which provoke charge mobility along the spirocyclic scaffold. Substitution of SCIs with strong electron-withdrawing substituents, like the cyano group or fluorine, enhances their docking capability and impacts their reactivity and charge mobility. To gain thorough knowledge about the molecular properties of these SCIs, their structures have been optimized and various quantum chemical concepts and models were applied, e.g., full NBO analysis and the frontier molecular orbitals (FMOs) theory (HOMO-LUMO energy gap) and the chemical reactivity descriptors derived from them. For the assessment of the charge density distribution along the SCI framework, additional complementary quantum chemical methods were used, e.g., molecular electrostatic potential (MESP) and Bader's QTAIM. Additionally, using the aromaticity index NICS (nuclear independent chemical shift) and other criteria, it could be shown that the investigated cross-hyperconjugated sila and germa SCIs are spiro-aromatics of the Heilbronner Craig-type Möbius aromaticity.

Polycyclic Aromatic Hydrocarbons as Anode Materials in Lithium-Ion Batteries: A DFT Study

The structure and energetics of the interactive behavior of Li⁺ and Li with polycyclic aromatic hydrocarbons (PAHs) have been studied at the wB97XD/6-311G(d,p) level of DFT. The electron distribution in the PAHs, analyzed using the topology of the molecular electrostatic potential (MESP), led to the categorization of their aromatic rings into five types, viz R_s, R_n, R_d, R_b, and R_e. Among the different rings, sextet-type R_s and naphthalene-type R_n rings showed the highest interaction with Li⁺. The change in MESP at the nucleus of Li⁺ (ΔV_Li⁺) due to the formation of the complex Li⁺...PAH is found to be proportional to the adsorption energy (E₁). In Li...PAH, the spin density on Li is close to zero, suggesting the formation of Li⁺...PAH^•- due to the electron transfer from Li to PAH. The adsorption energy (E₂) for Li...PAH does not correlate with the change in MESP at the nucleus of Li, whereas the dissociation energy (E₃) of Li⁺...PAH^•- to yield Li⁺ and PAH^•- correlates well with the MESP data, ΔV_Li. The study confirms that the change in MESP at the nucleus of Li⁺ due to complex formation gives a quantitative measure of the electronic effect of the cation-π binding. The cell potential (V_cell) is predicted for the lithium ion battery (LIB) using the Li⁺...PAH and Li...PAH adsorption energies. On the basis of the V_cell data, "carbon nanoflake"-type systems, viz coronene, circumbiphenyl, C₄₂H₁₆, and C₅₀H₁₈ are suggested as good anode materials for LIBs.

Hydration patterns of rings in drugs and relationship to lipophilicity: A DFT study

Rings are one of the major scaffold components of drugs in medicinal chemistry, due to their unique electronic distribution, scaffold rigidity, and three-dimensionality while lipophilicity is considered as a vital parameter of rings that can influence the reactivity, metabolic stability, and toxicity. We have analyzed the electronic features, hydration patterns, solvation effect and lipophilicity data for 51 most widely used ring systems in drugs. Molecular electrostatic potential (MESP) topology analysis has been used to assess the electronic distribution in rings which provided an easy interpretation of the most suitable hydration patterns of the ring with H₂ O molecule. Further, the global minimum of ring…H₂ O complex has been utilized to predict lipophilicity (logP) with the incorporation of implicit solvation effect. Classification of ring systems based on their molecular weight into four categories, viz. small ring 'sr', medium ring 'mr', large ring 'lr' and extra large ring 'xlr' systems has led to the finding of strong correlations between logP and hydration energy with R = 0.942, 0.933, 0.968 and 0.933, respectively. The micro solvation model is found to be useful for locating the hydrophobic-hydrophilic border for each category of rings in terms of hydration energy whereas the implicit solvation model used for two solvents, n-octanol and water on the most stable hydrated structure led to a global correlation between logP and solvation energy ratio. This correlation predicts a limiting logP value -7.03 for the most hydrophilic ring system and also suggests a clear partitioning of the ring molecules into hydrophobic and hydrophilic classes. The MESP topology-guided approach to understand the electronic features and hydration patterns of rings in drugs lead to powerful predictions on their lipophilicity behavior.

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

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

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.