Elastic and piezoelectric properties of ß-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 ß-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 ß-glycine were considered as functions of pressure before and after a phase transition into the ß'-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 Cg atoms of a vacancy defect can produce one nonpolar interaction, alongside a peculiar polar Cg⋯Cg bond. The latter stems from the presence of a localized electron pair on a vacancy defect Cg atom and the local depletion of electron localization on another Cg atom. This interaction is an example of intralayer tetrel bond. In the presence of an absorbed molecule of bisphenol A diglycidyl ether (DGEBA), graphene is able to form incipient tetrel Cg⋯O bonds with an ether group oxygen. In contrast to an epoxy group oxygen, the disposition of the ether oxygen often causes the orientation of electron-rich π-domains of graphene carbon on the weakly expressed electrophilic region of the oxygen. In the case of graphene with a point Si defect, the Si atom can form quite strong Si⋯C interactions with the DGEBA aryl carbons. In contrast to other noncovalent bonds, this interaction significantly alters the electron (de)localization on the Si atom and in the aryl ring. The reliability of the obtained results is enhanced by the use of multiple 2D periodic models with defects located at different positions along the DGEBA skeleton.

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

We introduce a fermionic potential, v f , 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. Wells in the v f distribution correspond to the domains of maximum electron localization, while the potential's barriers prevent delocalization of electrons through them. It also estimates bond orders and successfully reveals the impact of chemical modifications or environmental effects on the delocalization of electrons in molecules and crystals. The v f components provide a unique opportunity to compare the influence of the mentioned physical effects on electron (de)localization. This merges physical and chemical views of electron delocalization using functions appearing in density functional theory.

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.

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 ϕ e s r and kinetic ϕ k r potentials and electron density ρ r allowed partitioning any molecules and crystals into atomic ρ - and potential-based ϕ -basins; ϕ k -basins explicitly account for the electron exchange effect, which is missed for ϕ e s -ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between zero-flux surfaces of ρ - and ϕ -basins. The gap between ϕ e s - and ρ -basins represents the charge transfer, while the gap between ϕ k - and ρ -basins is a real-space manifestation of sharing the transferred electrons caused by the static exchange and kinetic effects as a response against the electron transfer. The regularity describing relative positions of ρ -, ϕ e s -, and ϕ k - basin boundaries between interacting atoms was proposed. The position of ϕ k -boundary between ϕ e s - and ρ -ones within an electron occupier atom determines the extent of transferred electron sharing. The stronger an H⋅⋅⋅O hydrogen bond is, the deeper hydrogen atom's ϕ k -basin penetrates oxygen atom's ρ -basin, while for covalent bonds a ϕ k -boundary closely approaches a ϕ e s -one indicating almost complete sharing of the transferred electrons. In the case of ionic bonds, the same region corresponds to electron pairing within the ρ -basin of an electron occupier atom.

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. Looking for the origin of such behavior, we considered the one-electron potentials entering the Euler equation for the electron density. We found that electron delocalization is mainly governed by the static exchange potential, which depends on the three-dimensional atomic structure. It, however, does not distinguish differences in electron delocalization in more and less stable enols, the effect arising from the kinetic exchange contribution, which reflects spin-dependent effects in the electron motion. The local depletion of kinetic exchange in the conjugated fragment yields the enhanced electron delocalization along the CCC bonds in more stable enols. Thus, a combination of considered descriptors allowed us to reveal the influence of electron delocalization on the equilibrium between keto and enol forms and showed the significant features of this phenomenon.

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. Novel physically grounded bonding descriptors derived within the orbital-free quantum crystallography provided the detailed examination of π-stacking and intricate C=O⋅⋅⋅π interactions and nonclassical hydrogen bonds present in the crystal. The donor-acceptor character of these interactions is revealed by analysis of Pauli and von Weizsäcker potentials together with well-known functions, e. g., deformation electron density and electron localization function. In this way, our analysis throws light on aspects of these closed-shell interactions hitherto hidden from the description.

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. At that, they do not depend on the variations in the exchange hole mobility. The electrostatic interaction mainly defines the energy of H-bonds of different types, whereas the strengthening/weakening of H-bonds in complexes with varying substituents depends on the barrier height of the exchange potential near the bond critical point. Energy variations between H-bonds in isolated and solvated systems are also caused the electron exchange peculiarities as follows from the corresponding potential and the interacting quantum atom analyses complemented by electron delocalization index calculations. Our approach is based on the bonding descriptors associated with the characteristics of the observable electron density and can be recommended for in-depth studies of non-covalent bonding.

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. All forces are expressed via kinetic and DFT potentials and then defined in terms of the experimental electron density and its derivatives; hence, this approach may be considered as orbital-free quantum crystallography. The net force acting on an electron in a crystal at equilibrium is zero everywhere, presenting a balance of the kinetic Fkin(r) and potential forces F(r). The critical points of both potentials are analyzed and they are recognized as the points at which forces Fkin(r) and F(r) individually are zero (the Lagrange points). The positions of these points in a crystal are described according to Wyckoff notations, while their types depend on the considered scalar field. It was found that F(r) force pushes electrons to the atomic nuclei, while the kinetic force Fkin(r) draws electrons from nuclei. This favors formation of electron concentration bridges between some of the nearest atoms. However, in a crystal at equilibrium, only kinetic potential vkin(r) and corresponding force exhibit the electronic shells and atomic-like zero-flux basins around the nuclear attractors. The force-field approach and quantum topological theory of atoms in molecules are compared and their distinctions are clarified.

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. The computed fractions of reactive enzyme-substrate complexes along MD trajectories well correlate with the findings of recent experimental studies on the substrate specificity of Mpro. The results of our simulations demonstrate the role of the theory level used in QM subsystems for a proper description of the nucleophilic attack of the catalytic cysteine residue in Mpro. The activation of the carbonyl group of a substrate is correctly characterized with the hybrid DFT functional PBE0, whereas the use of a GGA-type PBE functional, that lacks the admixture of the Hartree-Fock exchange fails to describe activation.

Variations of quantum electronic pressure under the external compression in crystals with halogen bonds assembled in Cl3-, Br3-, I3-synthons.

The inner-crystal quantum electronic pressure was estimated for unstrained C6Cl6, C6Br6, and C6I6 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 Hal3-synthons, where Hal = Cl, Br, I; for Hal...Hal stacking interactions, as well as for covalent bonds. Under simulated external compression, the quantum electronic pressure in the intermolecular space reduces as the electron density increases, indicating spatial areas of relatively less crystal resistance to external compression. The most compliant C6Cl6 crystal shows the largest changes of quantum electronic pressure in the centre of Cl3-synthon while the deformation of rigid I3-synthon under external compression depends only on the features of I...I halogen bonds.

Revealing electronic features governing hydrolysis of cephalosporins in the active site of the L1 metallo-ß-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-ß-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 C4[double bond, length as m-dash]C3 double bond in its N-C4-C3 fragment. The temporary N⋯H-Ow hydrogen bond, which is formed in the transition state of the limiting step of the reaction was recognized as a key atomic interaction governing the reactivity of various cephalosporins. Non-local real-space bonding descriptors show that different extent of localization of electron lone pair at N atom in the transition state affect the reactivity of compounds: smaller electron localization is typical for the less reactive species. In particular, the Fermi hole analysis shows how exchange electron correlation in the N⋯H-Ow fragment control electron lone pair localization. Delocalization tensor, linear response kernel and source function indicate that features of electron delocalization in the N-C4-C3 fragment of cephalosporins in the transition state complexes determine the differences in C4-C3 bond for substrates with high and low rate constants. The C4-C3 bond of the N-C4-C3 fragment at the transition state is similar to that of the preceding intermediate for the less reactive species and resembles the features of the enzyme-product complex for more reactive compounds. The power and limitations of the descriptors applied for solving the problem are discussed and the generality of approach is stressed.

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. It is established that the binding energy in molecular complexes with tetrel bonds correlate with the potential acting on an electron in molecule (PAEM). The PAEM barriers for tetrel bonds show a similar behavior for both sets of complexes with Br- and Cl- electron donors.

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...I interactions with short interatomic distances are analysed. The selection of S...I interactions for the categorization of the chalcogen and halogen bonds has been made using angles that determine the mutual orientation of electron lone pairs and σ-holes interacted S and I atoms. In complicated cases of noncovalent interactions with `hole-to-hole' of S and I orientations, distinguishing the chalcogen and halogen bonds is only possible if the atom is uniquely determined, which also provides the electrophilic site. The electronic criterion for chalcogen/halogen bonds categorizing that is based on analysis of dispositions of electron density and electrostatic potential minima along the interatomic lines has been suggested and its effectiveness has been demonstrated.

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. IQPF contains all quantum electron-shell structure-forming contributions resulting from kinetic, exchange and correlation effects, and presents a clear picture of the chemical bond features in crystals with different type of bonding mechanisms.

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. Article critically considers the early works in the field and places them to the present context. © 2017 Wiley Periodicals, Inc.

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. Along the halogen bonds, the curvatures of PAEM and ESP functions are opposite. Being jointly mapped on the closed isosurfaces of the reduced density gradient, placed between bound atoms, they are significantly differed from the side facing the halogen atom and from the side looking at the electron donor atom. © 2017 Wiley Periodicals, Inc.

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. The molecular docking, QM, and QM/MM dynamics analyses revealed the detailed picture of interactions of the drugs with the amino acid residues of the active site of the human pancreatic alpha-amylase protein (hPAA). The main difference in behavior of RD and TZD molecules is related to the hydrogen bond between the NH group of the ligand and Asp197. In hPAA complex with RD the proton from the NH group, which carries large positive charge (~ +0.45 e), spontaneously transfers to the carboxyl group of Asp197 and stays there, while in complex with TZD this proton frequently changes its position with the more preferable formation of covalent bond with the N atom. Upon deprotonation of the ligand, its hydrogen bonds with Arg195 and His299 become stronger. This process influences the binding with the difference of the binding constants of RD and TZD about 200 times with the higher value corresponding to the RD molecule. Thus, the cumulative results lead to the conclusion that rhodanine would have a higher binding affinity than the 2,4-thiazolidinedione molecule in the active site of human pancreatic alpha-amylase.

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. We have concluded that the one-electron potential is the most suitable for classification of the iodine-iodine bonds and interactions in complicated cases, while the electron localization function allows to distinguish the diiodine molecule bonded with the monoiodide anion from the typical triiodide anion.

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. However, the corresponding QTAIM bond paths are not formed; instead, contacts, which we call uncompleted links in this context, are accompanied by "quasi-bonding channels" corresponding to the λ2() ≤ 0 regions on the sign[λ2(r)]ρ(r) contour maps. The intramolecular IQA energy contributions signal the appreciable electron exchange between the pairs of atoms associated with potential atomic interactions or the bond-path-free non-covalent links. The IQA analysis shows that the electrostatic term destabilizes FC(NO2)3 and distinctly stabilizes IC(NO2)3, whereas it is close to neutral in ClC(NO2)3. The exchange energy between the X atom and the NO2 groups, in contrast, stabilizes all the molecules.