Two-Factor Rule for Distinguishing the Covalent and Tetrel Bonds.

Understanding and exploring the existence of a recognizable boundary between the noncovalent tetrel bond (TtB) and the coordination or weakened covalent bond are important for the bonding characterization. We have developed a simple methodology for analysing the type of bonds based on comparison of the electrostatic and total static potentials along the bond line. For the typical σ-hole noncovalent bond formed by a Tt atom in a tetrahedral molecule, we have found that the space gap between positions of the maxima of the total static potential and the negative quantity of electrostatic potential is much wider than that for the coordination bonds in a trigonal bipyramid molecular system for the Cl-Tt/Cl⋅⋅⋅Tt and N-Tt/N⋅⋅⋅Tt (Tt=C, Si, Ge) bonds in molecules and molecular complexes.

Elastic and piezoelectric properties of β-glycine - a quantum crystallography view on intermolecular interactions and a high-pressure phase transition.

The effect of hydrostatic compression on the elastic and electronic properties of β-glycine was studied using a quantum crystallography approach. The interrelations between the changes in the microscopic quantum pressure in the electronic continuum, macroscopic compressibility and piezoelectricity were considered. The geometries and energies of hydrogen bonds in the crystal structure of β-glycine were considered as functions of pressure before and after a phase transition into the β'-phase in relation to the mechanism of this phase transition.

Electron delocalization in defect-containing graphene and its influence on tetrel bond formation.

Using the advanced analyses of electron density and fermionic potential, we show how electron delocalization influences the ability of defect-containing graphene to form tetrel bonds. The C atoms of a vacancy defect can produce one nonpolar interaction, alongside a peculiar polar C⋯C bond. The latter stems from the presence of a localized electron pair on a vacancy defect C atom and the local depletion of electron localization on another C atom.

DFT potentials from a chemical perspective: Anatomy of electron (de)localization in molecules and crystals.

We introduce a fermionic potential, , as a comprehensive measure of electron (de)localization in atomic-molecular systems. Unlike other common descriptors as ELF, LOL, etc., it characterizes all physical effects responsible for (de)localization of electrons, namely: an exchange hole depth, its tendency to change, a sensitivity of an exchange correlation hidden in a pair density and kinetic potential to local variations in electron density.

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.

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields.

Intricate behaviour of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Channels of locally enhanced kinetic potential and corresponding saddle Lagrange points were found between chemically bonded atoms. Superposition of electrostatic and kinetic potentials and electron density allowed partitioning any molecules and crystals into atomic - and potential-based -basins; -basins explicitly account for the electron exchange effect, which is missed for -ones.

Keto-enol tautomerism from the electron delocalization perspective.

The equilibrium between keto and enol forms in acetylacetone and its derivatives is studied using electron delocalization indices and delocalization tensor density. We demonstrate how electron delocalization governs the equilibrium between keto and enol forms. The less stable enols have more distinct double and single bond character in the CCC fragment, while electron delocalization in this fragment is more pronounced in more stable enols.

Orbital-Free Quantum Crystallographic View on Noncovalent Bonding: Insights into Hydrogen Bonds, π⋅⋅⋅π and Reverse Electron Lone Pair⋅⋅⋅π Interactions.

A detailed analysis of a complete set of the local potentials that appear in the Euler equation for electron density is carried out for noncovalent interactions in the crystal of a uracil derivative using experimental X-ray charge density. The interplay between the quantum theory of atoms in molecules and crystals and the local potentials and corresponding inner-crystal electronic forces of electrostatic and kinetic origin is explored. Partitioning of crystal space into atomic basins and atomic-like potential basins led us to the definite description of interatomic interaction and charge transfer.

The explicit role of electron exchange in the hydrogen bonded molecular complexes.

We applied a set of advanced bonding descriptors to establish the hidden electron density features and binding energy characteristics of intermolecular DH∙∙∙A hydrogen bonds (OH∙∙∙O, NH∙∙∙O and SH∙∙∙O) in 150 isolated and solvated molecular complexes. The exchange-correlation and Pauli potentials as well as corresponding local one-electron forces allowed us to explicitly ascertain how electron exchange defines the bonding picture in the proximity of the H-bond critical point. The electron density features of DH∙∙∙A interaction are governed by alterations in the electron localization in the H-bond region displaying itself in the exchange hole.

Orbital-free quantum crystallography: view on forces in crystals.

Quantum theory of atoms in molecules and the orbital-free density functional theory (DFT) are combined in this work to study the spatial distribution of electrostatic and quantum electronic forces acting in stable crystals. The electron distribution is determined by electrostatic electron mutual repulsion corrected for exchange and correlation, their attraction to nuclei and by electron kinetic energy. The latter defines the spread of permissible variations in the electron momentum resulting from the de Broglie relationship and uncertainty principle, as far as the limitations of Pauli principle and the presence of atomic nuclei and other electrons allow.

Variations of quantum electronic pressure under the external compression in crystals with halogen bonds assembled in Cl-, Br-, I-synthons.

The inner-crystal quantum electronic pressure was estimated for unstrained CCl, CBr, and CI crystals and for those under external compression simulated from 1 to 20 GPa. The changes in its distribution were analyzed for the main structural elements in considered crystals: for triangles of the typical halogen bonds assembled in Hal-synthons, where Hal = Cl, Br, I; for Hal..

Dynamical properties of enzyme-substrate complexes disclose substrate specificity of the SARS-CoV-2 main protease as characterized by the electron density descriptors.

A dynamical approach is proposed to discriminate between reactive (rES) and nonreactive (nES) enzyme-substrate complexes taking the SARS-CoV-2 main protease (Mpro) as an important example. Molecular dynamics simulations with the quantum mechanics/molecular mechanics potentials (QM(DFT)/MM-MD) followed by the electron density analysis are employed to evaluate geometry and electronic properties of the enzyme with different substrates along MD trajectories. We demonstrate that mapping the Laplacian of the electron density and the electron localization function provides easily visible images of the substrate activation that allow one to distinguish rES and nES.

Revealing electronic features governing hydrolysis of cephalosporins in the active site of the L1 metallo-β-lactamase.

The QM/MM simulations followed by electron density feature analysis are carried out to deepen the understanding of the reaction mechanism of cephalosporin hydrolysis in the active site of the L1 metallo-β-lactamase. The differences in reactivity of ten similar cephalosporin compounds are explained by using an extended set of bonding descriptors. The limiting step of the reaction is characterized by the proton transfer to the nitrogen atom of the cephalosporin thiazine ring accompanied with formation of the C[double bond, length as m-dash]C double bond in its N-C-C fragment.

Quantum pressure focusing in solids: a reconstruction from experimental electron density.

Here an approach is presented for reconstructing the distribution of electronic internal quantum pressure in the electronic continuum of solids from the experimental electron density. Using the formalism of the density functional theory, the spatial inner-crystal map of the quantum pressure is obtained. The results are visualized via the indicator of quantum pressure focusing (IQPF) which reveals the regions where the pressure is concentrated or depleted due to quantum effects.

Electronic criterion for categorizing the chalcogen and halogen bonds: sulfur-iodine interactions in crystals.

Diversity of mutual orientations of Y-S and I-X and covalent bonds in molecular crystals complicate categorizing noncovalent chalcogen and halogen bonds. Here, the different types of S..

Identification of the Tetrel Bonds between Halide Anions and Carbon Atom of Methyl Groups Using Electronic Criterion.

The consideration of the disposition of minima of electron density and electrostatic potential along the line between non-covalently bound atoms in systems with Hal···CH₃⁻Y (Hal = Cl, Br; Y = N, O) fragments allowed to prove that the carbon atom in methyl group serves as an electrophilic site provider. These interactions between halide anion and carbon in methyl group can be categorized as the typical tetrel bonds. Statistics of geometrical parameters for such tetrel bonds in CSD is analyzed.

A comparative view on the potential acting on an electron in a molecule and the electrostatic potential through the typical halogen bonds.

This work considers the features of the electrostatic potential (ESP), and the potential acting on an electron in a molecule (PAEM) for the series of isolated dihalide molecules and for their molecular complexes. The joint analysis of these functions enriches the vision of atomic predispositions to the halogen bond formation and reveals details for their characterization. The account for the exchange-correlation interaction in PAEM retains the specific anisotropy of the ESP, which is commonly used for the halogen bonding explanation within σ-hole concept.

Early days of quantum crystallography: A personal account.

This work summarizes the author's activity in developing quantum crystallography. The approximations based on the intrinsic properties of the one-electron single-determinant density matrix, which allow its reconstructing from the experimentally measured coherent X-ray diffraction structure factors are discussed. The actual results obtained within such an approach are given.

Testing the ability of rhodanine and 2, 4-thiazolidinedione to interact with the human pancreatic alpha-amylase: electron-density descriptors complement molecular docking, QM, and QM/MM dynamics calculations.

A combined molecular docking, QM, and QM/MM dynamics modeling complemented with electron-density based descriptors computed at the B3LYP/6-311G++(d,p) level of theory have been carried out in order to understand the ability of the drugs rhodanine (RD) and 2,4-thiazolidinedione (TZD) in the effective treatment of type 2 diabetes mellitus. The global HOMO/LUMO descriptors provided just a very rough estimate of the chemical reactivity of both molecules, while the features of electron density studied in terms of its Laplacian and electrostatic potential allowed identifying the local electron rich/poor sites which were associated with the regions of electrophilic/nucleophilic attacks in RD and TZD. These results were thoroughly checked using the novel physically-grounded functional descriptors such as the phase-space Fisher information density and the internal kinetic electronic pressure density, which confirmed the information on bonding and lone electron pair details.

Testing the tools for revealing and characterizing the iodine-iodine halogen bond in crystals.

To understand what tools are really suitable to identify and classify the iodine-iodine non-covalent interactions in solid organic polyiodides, we have examined the anisotropy of the electron density within the iodine atomic basin along and across the iodine-iodine halogen bond using the Laplacian of electron density, one-electron potential and electron localization function produced by Kohn-Sham calculations with periodic boundary conditions. The Laplacian of electron density exhibits the smallest anisotropy and yields a vague picture of the outermost electronic shells. The one-electron potential does not show such a deficiency and reveals that the valence electron shell for the halogen-bond acceptor iodine is always wider than that for the halogen-bond donor iodine along its σ-hole direction.

An anatomy of intramolecular atomic interactions in halogen-substituted trinitromethanes.

The intramolecular interactions in substituted trinitromethanes, XC(NO2)3 (X = F, Cl, I, H) are studied and clarified by using a combination of the Quantum Theory of Atoms in Molecules (QTAIM), the non-covalent interaction analysis and the Interacting Quantum Atoms (IQA) methods. The stretching vibration modes are formed by the concerted displacements of atoms involved in the covalent bonds showing the significant multiatomic influence in substituted trinitromethanes. In agreement with that, the arrangement of the local reduced density gradient minima indicates that the electron density favors the non-covalent intramolecular interactions X···O and N···O.

Cl···Cl interactions in molecular crystals: insights from the theoretical charge density analysis.

The structure, IR harmonic frequencies and intensities of normal vibrations of 20 molecular crystals with the X-Cl···Cl-X contacts of different types, where X = C, Cl, and F and the Cl···Cl distance varying from ~3.0 to ~4.0 Å, are computed using the solid-state DFT method.

Quantifying steric effect with experimental electron density.

Using experimental electron densities, the recent effort of quantifying steric effect within the framework of density functional theory is continued. In this work, steric potential, steric field, and steric charge distributions are systematically examines for diamond and boron nitride crystals. Bader's zero-flux condition has been employed to discuss the atomic contributions of these quantities.

The experimental and theoretical QTAIMC study of the atomic and molecular interactions in dinitrogen tetroxide.

The atomic and molecular interactions in a crystal of dinitrogen tetraoxide, alpha-N2O4, have been studied in terms of the quantum topological theory of molecular structure using high-resolution, low-temperature X-ray diffraction data. The experimental electron density and electrostatic potential have been reconstructed with the Hansen-Coppens multipole model. In addition, the three-dimensional periodic electron density of crystalline alpha-N2O4 has been calculated at the B3LYP/cc-pVDZ level of theory with and without the geometry optimization.

Binding entropy and its application to solids.

The concept of binding entropy is introduced and information theoretical approach is combined with orbital-free density functional theory. It is shown that binding entropy expresses the deviation of the molecular electron density from the promolecular density and the deviation of the molecular kinetic energy density from the promolecular kinetic energy density. The change of the kinetic energy density during the chemical bond formation explicitly appears in the binding entropy expression.