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.

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.

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.

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.

Proton dynamics in strong (short) intramolecular H-bond. DFT study of the KH maleate crystal.

The structure, harmonic frequencies, and infrared intensities of the fundamental transitions of potassium hydrogen/deuterium maleate crystals have been computed by the density functional theory with periodic boundary conditions. Different functionals with all-electron Gaussian-type orbital (GTO) basis set have been used. It was found that BLYP/GTO approximation provides the best results for the structural parameters of the KH maleate crystal.

Determination of covalent bond orders and atomic valence indices using topological features of the experimental electron density.

We present an approach for the determination of covalent bond orders from the experimental electron density and its derivatives at the bond critical points. An application of this method to a series of organic compounds has shown that it provides a bonding quantification that is in reasonable agreement with that obtained by orbital theory. The 'experimental' atomic valence indices are also defined and their significance for the characterization of chemical problems is discussed.

Atoms-in-molecules study of intra- and intermolecular bonding in the pentaerythritol tetranitrate crystal.

Chemical bonding in the pentaerythritol tetranitrate crystal based on the experimental electron density obtained from X-ray diffraction data at 100 K and theoretical calculations at the experimental molecular geometry have been analyzed in terms of the Quantum Theory of Atoms in Molecules. Features of the intra- and intermolecular bond critical points and the oxygen atom lone-pair locations are discussed. Numerous intermolecular bonding interactions, including O.

Chemical bonding in pentaerythritol at very low temperature or at high pressure: an experimental and theoretical study.

Chemical bonding in the pentaerythritol crystal based on the experimental electron density at 15 (1) K, and theoretical calculations at the experimental molecular geometries obtained at room and low (15 K) temperatures have been analyzed and compared in terms of the topological analysis. Topological electron-density features corresponding to the high-pressure (1.15 GPa) geometry are also reported.

Atomic interactions in ethylenebis(1-indenyl)zirconium dichloride as derived by experimental electron density analysis.

A topological analysis of the experimental electron density in racemic ethylenebis(1-indenyl)zirconium dichloride, C20H16Cl2Zr, measured at 100 (1) K, has been performed. The atomic charges calculated by the numerical integration of the electron density over the zero-flux atomic basins demonstrate the charge transfer of 2.25 e from the Zr atom to the two indenyl ligands (0.

X-ray diffraction by a crystal in a permanent external electric field: general considerations.

The variations of X-ray diffraction intensities from a crystal in the presence of a permanent external electric field is modeled analytically using a first-order stationary perturbation theory. The change in a crystal, induced by an external electric field, is separated into two contributions. The first one is related to a pure polarization of an electron subsystem, while the second contribution can be reduced to the displacements of the rigid pseudoatoms from their equilibrium positions.

X-ray scattering amplitude of an atom in a permanent external electric field.

Quantum-mechanical description of the X-ray scattering by the many-electron atom in a permanent external electric field is developed in terms of the perturbation theory. Explicit expression for the electric field induced addition to the atomic scattering factor is derived and calculations for some atoms are performed. It was found that the change of the X-ray structure factor due to an electric field is too small to be detected with existing experimental techniques.

The mapping of electronic energy distributions using experimental electron density.

It is demonstrated that the approximate kinetic energy density calculated using the second-order gradient expansion with parameters of the multipole model fitted to experimental structure factors reproduces the main features of this quantity in a molecular or crystal position space. The use of the local virial theorem provides an appropriate derivation of approximate potential energy density and electronic energy density from the experimental (model) electron density and its derivatives. Consideration of these functions is not restricted by the critical points in the electron density and provides a comprehensive characterization of bonding in molecules and crystals.