A. I. Stash

WinXPRO: a program for calculating crystal and molecular properties using multipole parameters of the electron density

The computer program WinXPRO enables the calculation of crystal and molecular properties using the multipole parameters of the electron density. The list of properties includes the electron density and its topological and electric field characteristics, the local kinetic and potential energies, the electron localization function, and the effective crystal potential. WinXPRO works under the Windows operating system and can utilize any existing graphics program to display output.

Determination of the electron localization function from electron density

Approximate determination of electron localization function (ELF) from electron density and its first and second derivatives is described. It is demonstrated that the second-order gradient expansion of the kinetic energy density yields the modified ELF, which exhibits all the features characterizing electron pairing. Calculations based on the accurate electron densities derived from X-ray diffraction data carried out for crystalline magnesium oxide, chlorine and urea: they demonstrate that the ELF reveals important peculiarities of crystal architecture.

Importance of the consideration of anharmonic motion in charge‐density studies: a comparison of variable‐temperature studies on two explosives, RDX and HMX

Extremely accurate X-ray data were obtained for the explosive RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine) at three different temperatures (20, 120 and 298 K). Collected reflections were integrated using the latest version of the program VIIPP which uses separate Kα(1)/Kα(2) contributions to the profile fitting during integration. For each temperature both anharmonic and harmonic descriptions of the atomic thermal motion were utilized in the model refinements along with the multipole expansion of the electron density. H atoms were refined anisotropically and agree well with a previous neutron study. Topological analysis [Bader (1990). Atoms in Molecules: A Quantum Theory. The International Series of Monographs of Chemistry, edited by J. Halpern & M. L. H. Green. Oxford: Clarendon Press] of the attained electron density followed. For 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX), old data collected at 20 and 120 K were re-integrated with the new version of VIIPP and refined in the same manner as for RDX. In both cases theoretical structure factors were also calculated based on the 20 K structures, and employed in comparison multipole refinements for the atoms at rest. Limiting the refinement to a harmonic model of the atomic displacements may result in a biased and erroneous electron density, especially when atomic vibrations are significant (as in RDX) and at temperatures higher than obtained by using liquid helium. Given the similarity of the two compounds the effects of anharmonic motion are strikingly more severe in the case of RDX. Our study reinforces the conclusion of Meindl et al. [Acta Cryst. (2010), A66, 362-371] that in certain cases it is necessary to include anharmonic term(s) of the probability density function (or temperature factor) in order to obtain a meaningful electron density suitable for topological analysis, even for compact (high-density) light-atom structures. For RDX it was observed that the oxygen lone-pair concentrations of electrons are located close to perpendicular to the N-O bond vectors, which is typical for explosive materials. Conjugation of the electron density in the -N-NO(2) fragment has been established based on the topological bond orders. Nine moderately strong hydrogen bonds and nine N-N, O-N and O-O bonding interactions were found and described. The RDX molecular electronic energy per mole is 4.02-4.04 a.u., very close to the reported value for HMX.

On functions and quantities derived from the experimental electron density.

Calculation of properties of molecules and crystals as obtained from a multipole electron-density model restored from the accurate X-ray diffraction data is considered. Electronic and exchange energy-density distributions are presented along with those of local temperature and local entropy. Integration of the local functions over atomic basins defined by the zero-flux condition allows properties of molecules and crystals to be expressed in terms of atomic contributions derived directly from X-ray diffraction experiments. Distributions of local Fermi momentum and one-electron potential are considered as well. The approach has been applied to diamond, sodium fluoride, sodium chloride, solid chlorine, alpha-oxalic acid dihydrate and YBa(2)Cu(3)O(6.98).

Electron density study of urea using TDS-corrected X-ray diffraction data: quantitative comparison of experimental and theoretical results

The electron-density distribution in urea, CO(NH(2))(2), was studied by high-precision single-crystal X-ray diffraction analysis at 148 (1) K. An experimental correction for TDS was applied to the X-ray intensities. R(merge)(F(2)) = 0.015. The displacement parameters agree quite well with results from neutron diffraction. The deformation density was obtained by refinement of 145 unique low-order reflections with the Hansen & Coppens [Acta Cryst. (1978), A34, 909-921] multipole model, resulting in R = 0.008, wR = 0.011 and S = 1.09. Orbital calculations were carried out applying different potentials to account for correlation and exchange: Hartree-Fock (HF), density-functional theory/local density approximation (DFT/LDA) and density-functional theory/generalized gradient approximation (DFT/GGA). Extensive comparisons of the deformation densities and structure factors were made between the results of the various calculations and the outcome of the refinement. The agreement between the experimental and theoretical results is excellent, judged by the deformation density and the structure factors [wR(HF) = 0.023, wR(DFT) = 0.019] and fair with respect to the results of a topological analysis. Density-functional calculations seem to yield slightly better results than Hartree-Fock calculations.

Modern Possibilities for Calculating Some Properties of Molecules and Crystals from the Experimental Electron Density

Methods for calculating some properties of molecules and crystals from the electron density reconstructed from a precise X-ray diffraction experiment using the multipole model are considered. These properties include, on the one hand, the characteristics of the electron density and the inner-crystal electrostatic field and, on the other hand, the local electronic energies (kinetic, potential, total), the exchange energy density, the electron-pair localization function, the localized-orbital locator, the effective crystal potential, and others. It is shown that the integration of these characteristics over pseudoatomic volumes bounded by the surfaces of the zero flux of the electron density gradient makes it possible to characterize directly from an experiment the properties of molecules and crystals in terms of the atomic contributions. The computer program WinXPRO2004, realizing these possibilities, is briefly described.

Template synthesis, structure and unusual series of phase transitions in clathrochelate iron(II) α-dioximates and oximehydrazonates formed by capping with functionalized boron-containing agents

Abstract A series of clathrochelate α-dioximates and oximehydrazonates with apical long-chain paraffin and allyl substituents has been synthesized and characterized by X-ray analysis. For the hexadecylboronic FeNx3(BHd)2 complex (where Nx2− is the cyclohexanedion-1,2-dioxime dianion) in the temperature range 100–305 K, two structural phase transitions have been detected by X-ray diffractometry and 57Fe Mossbauer spectroscopy.

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. Baders zero-flux condition has been employed to discuss the atomic contributions of these quantities. Two new concepts, characteristic radius r(s) of steric field and atomic steric charge q(s), are introduced in this work, which are intrinsic properties of a system and thus can be used to characterize atomic properties in a molecule or crystal. We anticipate that these steric effect related quantities together with the new concepts introduced in this work can be applied to characterize variety categories of the chemical bonds or weak interactions and provide in-depth insights to a wide range of organic, inorganic, and biological systems.

Characterization of bonding in cesium uranyl chloride: topological analysis of the experimental charge density.

The topological analysis of the charge density distribution in Cs(2)UO(2)Cl(4) obtained from an accurate X-ray diffraction experiment at 20K is reported. Details of the techniques applied during data collection and data refinement are discussed. A split Hansen-Coppens multipole model for uranium and cesium atoms has been used to describe the charge density features associated with valence electrons and core deformations. The analysis of the deformation density distribution, QTAIM space partitioning, the Laplacian of the electron density, and electron localization function are discussed. Local QTAIM descriptors for bonds to uranium and cesium are reported, as well as integrated properties of each individual atom. U(5f), U(6s), U(6p), U(6d), and U(7s) shells were required to describe the aspherical charge density of the uranium pseudoatom. Observed deformation of the cesium atom core was described by applying the multipole model to Cs(5s) and Cs(5p) shells.

Molecular and crystal properties of ethyl 4,6‐dimethyl‐2‐thioxo‐1,2,3,4‐tetrahydropyrimidine‐5‐carboxylate from experimental and theoretical electron densities

The electron density and electronic energy densities in ethyl 4,6-dimethyl-2-thioxo-1,2,3,4-tetrahydropyrimidine-5-carboxylate have been studied from accurate X-ray diffraction measurements at 110 K and theoretical single-molecule and periodic crystal calculations. The Quantum Theory of Atoms in Molecules and Crystals (QTAMC) was applied to analyze the electron-density and electronic energy-density features to estimate their reproducibility in molecules and crystals. It was found that the local electron-density values at the bond critical points derived by different methods are in reasonable agreement, while the Laplacian of the electron density computed from wavefunctions, and electron densities derived from experimental or theoretical structure factors in terms of the Hansen-Coppens multipole model differ significantly. This disagreement results from insufficient flexibility of the multipole model to describe the longitudinal electron-density curvature in the case of shared atomic interactions. This deficiency runs through all the existing QTAMC bonding descriptors which contain the Laplacian term. The integrated atomic characteristics, however, suffer noticeably less from the aforementioned shortcoming. We conclude that the electron-density and electronic energy QTAMC characteristics derived from wavefunctions, especially the integrated quantities, are nowadays the most suitable candidates for analysis of the transferability of atoms and atomic groups in similar compounds.