Atomic Electron Distribution Research Articles

Current developments and trends in quantum crystallography.

Quantum crystallography is an emerging research field of science that has its origin in the early days of quantum physics and modern crystallography when it was almost immediately envisaged that X-ray radiation could be somehow exploited to determine the electron distribution of atoms and molecules. Today it can be seen as a composite research area at the intersection of crystallography, quantum chemistry, solid-state physics, applied mathematics and computer science, with the goal of investigating quantum problems, phenomena and features of the crystalline state. In this article, the state-of-the-art of quantum crystallography will be described by presenting developments and applications of novel techniques that have been introduced in the last 15 years. The focus will be on advances in the framework of multipole model strategies, wavefunction-/density matrix-based approaches and quantum chemical topological techniques. Finally, possible future improvements and expansions in the field will be discussed, also considering new emerging experimental and computational technologies.

Extracting Quantitative Information at Quantum Mechanical Level from Noncovalent Interaction Index Analyses.

The noncovalent interaction (NCI) index is nowadays a well-known strategy to detect NCIs in molecular systems. Even though it initially provided only qualitative descriptions, the technique has been recently extended to also extract quantitative information. To accomplish this task, integrals of powers of the electron distribution were considered, with the requirement that the overall electron density can be clearly decomposed as sum of distinct fragment contributions to enable the definition of the (noncovalent) integration region. So far, this was done by only exploiting approximate promolecular electron densities, which are given by the sum of spherically averaged atomic electron distributions and thus represent too crude approximations. Therefore, to obtain more quantum mechanically (QM) rigorous results from NCI index analyses, in this work, we propose to use electron densities obtained through the transfer of extremely localized molecular orbitals (ELMOs) or through the recently developed QM/ELMO embedding technique. Although still approximate, the electron distributions resulting from the abovementioned methods are fully QM and, above all, are again partitionable into subunit contributions, which makes them completely suitable for the NCI integral approach. Therefore, we benchmarked the integrals resulting from NCI index analyses (both those based on the promolecular densities and those based on ELMO electron distributions) against interaction energies computed at a high quantum chemical level (in particular, at the coupled cluster level). The performed test calculations have indicated that the NCI integrals based on ELMO electron densities outperform the promolecular ones. Furthermore, it was observed that the novel quantitative NCI-(QM/)ELMO approach can be also profitably exploited both to characterize and evaluate the strength of specific interactions between ligand subunits and protein residues in protein-ligand complexes and to follow the evolution of NCIs along trajectories of molecular dynamics simulations. Although further methodological improvements are still possible, the new quantitative ELMO-based technique could be already exploited in situations in which fast and reliable assessments of NCIs are crucial, such as in computational high-throughput screenings for drug discovery.

A Step toward the Quantification of Noncovalent Interactions in Large Biological Systems: The Independent Gradient Model-Extremely Localized Molecular Orbital Approach.

The independent gradient model (IGM) is a recent electron density-based computational method that enables to detect and quantify covalent and noncovalent interactions. When applied to large systems, the original version of the technique still relies on promolecular electron densities given by the sum of spherically averaged atomic electron distributions, which leads to approximate evaluations of the inter- and intramolecular interactions occurring in systems of biological interest. To overcome this drawback and perform IGM analyses based on quantum mechanically rigorous electron densities also for macromolecular systems, we coupled the IGM approach with the recently constructed libraries of extremely localized molecular orbitals (ELMOs) that allow fast and reliable reconstructions of polypeptide and protein electron densities. The validation tests performed on small polypeptides and peptide dimers have shown that the novel IGM-ELMO strategy provides results that are systematically closer to the fully quantum mechanical ones and outperforms the IGM method based on the crude promolecular approximation, but still keeping a quite low computational cost. The results of the test calculations carried out on proteins have also confirmed the trends observed for the IGM analyses conducted on small systems. This makes us envisage the future application of the novel IGM-ELMO approach to unravel complicated noncovalent interaction networks (e.g., in protein-protein contacts) or to rationally design new drugs through molecular docking calculations and virtual high-throughput screenings.

Analytical Model of Electron Density and Its Machine Learning Inference.

We present an analytical model representation of the electron density ρ(r) in molecules in the form of expansions of a few functions (exponentials and a Gaussian) per atom. Based on a former analytical model of ρ(r) in atoms, we devised its molecular implementation by introducing the anisotropy inherent in the electron distribution of atoms in molecules by means of proper anisotropic functions. The resulting model named A2MD (anisotropic analytical model of density) takes an analytical form highly suitable for obtaining the electron density in large biomolecules as its computational cost scales linearly with the number of atoms. To obtain the parameters of the model, we first devised a fitting procedure to reference electron densities obtained in ab initio correlated quantum calculations. Second, in order to skip costly ab initio calculations, we also developed a machine learning (ML)-based predictor that used neural networks trained on broad molecular datasets to determine the parameters of the model. The resulting ML methodology that we named A2MDnet (A2MD network-trained) was able to provide reliable electron densities as a basis to predict molecular features without requiring quantum calculations. The results presented together with the low computational scaling associated to the A2MD representation of ρ(r) suggest potential applications to obtain reliable electron densities and ρ(r)-based molecular properties in biomacromolecules.

Study of Physical Adsorption for Ethanol Gasoline on Metal Surfaces

Using molecular simulation technology based on classical mechanic methods, the physical adsorption conformation of the representative conventional gasoline molecule, ethanol molecule and its oxidation intermediates, including acetaldehyde and acetic acid, on different metal surfaces was performed. Furthermore, the interaction energy composed of van der Waals and electrostatic between the absorbed molecules and the metal surfaces was calculated to study the influence of ethanol gasoline on the metal materials in comparison with the conventional gasoline. The results concluded that iron is the most likely to make strong physical adsorption with organic molecules than other surfaces, whether it is conventional gasoline molecule or ethanol molecule, or the oxidation intermediates. It may be related to the crystal configuration, coordination, atomic electron distribution and orbitals distribution of iron surface. The most stable among the studied surfaces is copper, followed by aluminum. Acid molecules, due to the presence of carboxyl group, are the most prone to form strong adsorption on the metal surfaces. The functional additives, such as antioxidant, stabilizer, detergent, dispersant or corrosion inhibitor, were critical for ethanol gasoline to avoid the undesirable influences. ESP distribution and the charges of the module molecules were calculated to make further analysis based on quantum theory.

Atomic electron distribution and recoil effects following beta decay of the halo nucleus helium-6

SynopsisFollowing the β decay of a 6He nucleus to form 6Li, the atomic electrons adjust to the sudden change of nuclear charge from 2 to 3. The probabilities for electron shake-up and shake-off are calculated, including recoil effects, by the use of a Stieltjes imaging representation of the final states. The results will be applied to ongoing angular correlation studies in a search for new physics beyond the Standard Model.

Ethynyl and Propynylpyrene Inhibitors of Cytochrome P450

The single-crystal X-ray structures and in vivo activities of three aryl acetylenic inhibitors of cytochromes P450 1A1, 1A2, 2A6, and 2B1 have been determined and are reported herein. These are 1-ethynylpyrene, 1-propy-nylpyrene, and 4-propynylpyrene. To investigate electronic influences on the mechanism of enzyme inhibition, the experimental electron density distribution of 1-ethynylpy-rene has been determined using low-temperature X-ray diffraction measurements, and the resulting net atomic charges compared with various theoretical calculations. A total of 82,390 reflections were measured with Mo Kα radiation to a (sinθ/λ)(max) = 0.985 Å(-1). Averaging symmetry equivalent reflections yielded 8,889 unique reflections. A least squares refinement procedure was used in which multipole parameters were added to describe the distortions of the atomic electron distributions from spherical symmetry. A map of the model electron density distribution of 1-ethynylpyrene was obtained. Net atomic charges calculated from refined monopole population parameters yielded charges that showed that the terminal acetylenic carbon atom (C18) is more negative than the internal carbon (C17). Net atomic charges calculated by ab initio, density functional theory, and semi-empirical methods are consistent with this trend suggesting that the terminal acetylenic carbon atom is more likely to be the site of oxidation. This is consistent with the inhibition mechanism pathway that results in the formation of a reactive ketene intermediate. This is also consistent with assay results that determined that 1-ethynylpyrene acts as a mechanism-based inhibitor of P450s 1A1 and 1A2 and as a reversible inhibitor of P450 2B1. Crystallographic data: 1-ethynylpyrene, C(18)H(10), P2(1)/c, a = 14.571(2) Å, b = 3.9094(5) Å, c = 20.242(3) Å, β = 105.042(2)°, V = 1,113.5(2) Å(3); 1-propynylpyrene, C(19)H(12), P2(1)/n, a = 8.970(2) Å, b = 10.136(1) Å, c = 14.080(3) Å, β = 99.77(2)°, V = 1,261.5(4) Å(3); 4-propynylpyrene, C(19)H(12), Pbca, a = 9.904(1) Å, b = 13.174(2) Å, c = 19.401(1) Å, V = 2,531.4(5) Å(3).

Investigation of the effect of nucleus charge and atomic electron distributions on the processes of polarized bremsstrahlung of electrons in crystals

The process of polarized bremsstrahlung of electrons in crystals has been theoretically investigated with application of the new method taking into account the screening of the Coulomb nucleus field by atomic electrons. Real changes in the cross sections of both polarized and unpolarized bremsstrahlung and the degrees of particle polarization in a silicon crystal are obtained.

Gamma Distribution Model To Provide a Direct Assessment of the Overall Quality of Quantum Monte Carlo-Generated Electron Distributions

Our objective is to assess the accuracy of simulated quantum Monte Carlo electron distributions of atoms and molecules. Our approach is first to model the exact electron distribution by a linear combination of gamma distribution functions, with parameters chosen to exactly reproduce highly accurate literature values for a number of selected moments for the system of interest. In application to the ground-state electron distributions of helium and dihydrogen, a high level of accuracy of the model was confirmed upon comparing its predicted moments, not used in the model's parametrization, to those calculated from high-level theory. Next, we generated electron-electron and electron-nucleus distributions for dihydrogen from electron positions outputted from a variety of quantum Monte Carlo algorithms. Upon juxtaposition of the simulated distributions with the putatively exact one that we derived from the model, we quantified the error in simulated distributions. The most accurate distributions were obtained from no-compromise reptation quantum Monte Carlo, a recently developed algorithm designed to ameliorate the distributions' time-step bias. Marginally less accurate distributions were generated from fixed-node diffusion Monte Carlo with descendant counting and detailed balance.

An experimental charge density study of mesulergine hydrochloride, a dopamine agonist

Carefully measured high-resolution X-ray diffraction measurements at 120(2) K have been used to map the electron deformation density of mesulergine hydrochloride, a dopamine agonist. A total of 52,508 intensities were measured with MoKα radiation to a sinθ/λ)max = 0.84~A−1. Averaging symmetry equivalent reflections yielded 9,418 unique reflections. A least squares refinement procedure was used in which multipole parameters were added to describe the distortions of the atomic electron distributions from spherical symmetry. Maps of the model electron deformation density distribution show the distribution of electron density in mesulergine hydrochloride. Molecular electrostatic potentials have been calculated from the electron densities determined in the least-squares multipole refinement. A region of negative electrostatic potential near N23 in the NHSO2N(CH3)2 substituent suggests that the nitrogen atom would be reactive toward electrophilic attack. Net atomic charges calculated from refined monopole population parameters yielded charges of +0.17 for the NHSO2N(CH3)2 substituent and +0.37 for the ergoline fused ring system. There does not seem to be an area of the molecule that, based on the results of this study, is more electron rich or electron deficient than others. Crystallographic data: C18H26N4O2S⋅HCl, P21, a = 12.1281(3) A, b = 6.1357(4) A, c = 13.5935(4) A, β = 105.14(5)∘, V = 974.14(5) A3, Z = 2.

Molecular mechanics analysis of drug-resistant mutants of HIV protease.

Drug-resistant mutants of HIV-1 protease limit the long-term effectiveness of current anti-viral therapy. In order to study drug resistance, the wild-type HIV-1 protease and the mutants R8Q, V32I, M46I, V82A, V82I, V82F, I84V, V32I/I84V and M46I/I84V were modeled with the inhibitors saquinavir and indinavir using the program AMMP. A new screen term was introduced to reproduce more correctly the electron distribution of atoms. The atomic partial charge was represented as a delocalized charge distribution instead of a point charge. The calculated protease-saquinavir interaction energies showed the highly significant correlation of 0.79 with free energy differences derived from the measured inhibition constants for all 10 models. Three different protonation states of indinavir were evaluated. The best indinavir model included a sulfate and gave a correlation coefficient of 0.68 between the calculated interaction energies and free energies from inhibition constants for nine models. The exception was R8Q with indinavir, probably due to differences in the solvation energy. No significant correlation was found using the standard molecular mechanics terms. The incorporation of the new screen correction resulted in better prediction of the effects of inhibitors on resistant protease variants and has potential for selecting more effective inhibitors for resistant virus.

On approximating electron repulsion integrals with linear combination of atomic-electron distributions

On approximating electron repulsion integrals with linear combination of atomic-electron distributions

Three-center expansion of electron repulsion integrals with linear combination of atomic electron distributions

A new systematic way of constructing auxiliary basis functions for approximating the evaluation of electron repulsion integrals is proposed and applied to SCF and MCSCF wavefunction calculations. In the approximation, the one-electron density is expanded in terms of a linear combination of atomic electron distributions (LCAD), and the four-center two-electron repulsion integrals are reduced to the three- and two-center quantities. This results in a high-accuracy approximation as well as a large reduction in disk storage and input/output requirement, proportional to N 3 rather than N 4, N being the number of basis functions. Numerical results indicate that the error from the present approximation decreases as the size of molecular basis functions increases and that the LCAD version of MCSCF calculations requires only a fractional amount of the CPU time required in the conventional procedure without loss of accuracy.

Three-dimensional structure of the ordered phases of Hg on Cu(001).

The structures of ordered phases following adsorption of mercury on Cu(001) have been identified using helium-beam scattering and low-energy electron diffraction. We found that three of the four observed ordered submonolayer phases are high-order commensurate phases. The three-dimensional structure of these phases brought about by a periodic variation of the height of the Hg atoms above the Cu(001) plane has been measured. Furthermore, from a combined analysis of helium-beam scattering and angle-resolved photoemission data for a low-density Hg ordered overlayer, we deduce and quantify the departure from the atomic electron distribution of Hg due to adsorption. A model to analyze diffraction data from all these phases is also presented. We show that second-layer structural and electronic properties are influenced by those of the first layer. Adsorption at the lowest substrate temperature obtainable proceeds in a layer-by-layer mode up to three layers.

Experimental electron density distribution of dopamine hydrochloride

Careful high-resolution x-ray diffraction measurements at 90 K have been used to map the electron density distribution in a single crystal of dopamine hydrochloride, a neurotransmitter. A least-squares refinement procedure has been used in which multipole parameters are added to describe the distortions of the atomic electron distributions from spherical symmetry. The refinement also yields improved estimates of the x-ray phases, which have been used to plot maps of the electron distribution. The most electron-rich areas of the molecule are the hydroxyl groups that show large buildups of electron density at the position of the nonbonded lone pairs. The sum of the net atomic charges for the ammonium group is +0.2(2). The net atomic charge for the chloride ion is −0.1(1).

The influence of the (2 × 1) reconstruction of the Si(1 0 0) surface on the SiL 2,3 VV Auger lineshape

The extreme surface sensitiveness of the SiL 2,3 VV Auger process and its ability to probe the atomic electron distribution in the direct neighbourhood of the L 2,3-core-hold makes this electron spectroscopic technique a candidate for investigations of the local changes in the electron distribution due to surface reconstruction. In this paper we show, explicitly, the influence of the (2 × 1) reconstruction of the Si(1 0 0) surface on the SiL 2,3 VV Auger lineshape. Furthermore, the calculated Auger lineshape will be compared with an experimentally obtained line profile.

Analysis of Structure-Activity Relation for Primaquine Antimalarial Drugs by a Quantum Pharmacological Approach

linear models for the electronic structure-activity relations of primaquines based on molecular orbital calculations and pharmacological data observed in laboratory animals have been investigated. The optimized models seem to allow an evaluation of the antimalarial activity of primaquine drugs from calculated electron distributions of atoms while at the same time give strong indications about the active center of these and related types of antimalarial drugs.

Extended Model of Bond Charges and Its Application in Calculation of Optical Properties of Crystals with Different Types of Chemical Bonds

AbstractA method for calculating the optical characteristics of crystals with different types of chemical bonds within the framework of the dielectric theory of chemical bond put forward by Philips and Van Vechten is suggested. The calculating scheme which does not contain adjustable parameters is based on the bond charge model designed by Levine, which is generalized for the case of multiple bonds and modified involving the density functional method data on the spatial distribution of electrons in atoms. The structural elements of the method are: the screened Coulomb potentials and radii of the atomic core, bond lengths and charges, and the distances from the nuclei to the centres of gravity of the latter. The calculated characteristics of the crystals (dielectric permittivity, quadratic and cubic non‐linear susceptibilities, electrooptical constants) are in good accordance with experimental findings. An attempt is made to predict the non‐linear optical characteristics according to precision X‐ray diffraction data on the electron structure of its only representative, lithium formate deuterate LiHCO2 · D2O, whereby a fairly good fit with the experimental data is achieved.

赤外・ラマンスペクトルの鉱物学への応用

The applications of infrared, far-infrared and Raman spectra to mineralogy are described. Problems of peak assignment are discussed by comparing the assignments determined by lattice dynamical calculations with those deduced from isotropic shifts. These assignments make it possible to predict the intracrystalline cation site preferences in olivine. The mode softening mechanism and the abnormal behaviuor o felastic constants near the α-β quartz transition temperature are explained by the contribution of potential energy terms to the potential energy. The emphasis is upon the nature of chemical bond in crystals. The effective charges deduced from thermochemical, spectroscopic and molecular orbital theories and accurate structure factors are compared with those determined by lattice dynamical calculations. The theoretical advances of the lattice dynamical calculation including the effect of the width of the atomic electron distribution provide us with a fundamental understanding of the chemical bond in silicates, because a wide range of physical properties is estimated by lattice dynamics.

Lattice dynamics of ?-quartz including the effect of the width of the atomic electron distribution

On the basis of the polarizable-ion model (PIM) the effect of the width of the atomic electron distribution on the lattice dynamics of α-quartz was taken into account using the Birman method. The frequencies of optical mode, elastic constants and piezoelectric constants were reproduced using the parameters of this model (an effective charge z, a width parameter w, an electronic polarizability α, and force constants). The width parameter of oxygen atom was found to be about 0.59 A, and the effective charge of the silicon atom 1.42 electron charges.