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

2006 ◽  
Vol 62 (4) ◽  
pp. 676-688 ◽  
Author(s):  
V. G. Tsirelson ◽  
A. I. Stash ◽  
V. A. Potemkin ◽  
A. A. Rykounov ◽  
A. D. Shutalev ◽  
...  
Keyword(s):  
Electron Density ◽  
Single Molecule ◽  
Electronic Energy ◽  
X Ray Diffraction ◽  
Local Electron ◽  
Electron Densities ◽  
Structure Factors ◽  
Crystal Properties ◽  
Atomic Interactions ◽  
Density Values

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.

Revisiting the charge density analysis of 2,5-dichloro-1,4-benzoquinone at 20 K

2017 ◽  
Vol 73 (4) ◽  
pp. 654-659 ◽  
Author(s):  
Zhijie Chua ◽  
Bartosz Zarychta ◽  
Christopher G. Gianopoulos ◽  
Vladimir V. Zhurov ◽  
A. Alan Pinkerton
Keyword(s):  
Charge Density ◽  
Electron Density ◽  
Topological Analysis ◽  
Diffraction Measurement ◽  
X Ray Diffraction ◽  
Total Electron Density ◽  
Total Electron ◽  
Structure Factors ◽  
Density Analysis ◽  
Experimental Charge Density

A high-resolution X-ray diffraction measurement of 2,5-dichloro-1,4-benzoquinone (DCBQ) at 20 K was carried out. The experimental charge density was modeled using the Hansen–Coppens multipolar expansion and the topology of the electron density was analyzed in terms of the quantum theory of atoms in molecules (QTAIM). Two different multipole models, predominantly differentiated by the treatment of the chlorine atom, were obtained. The experimental results have been compared to theoretical results in the form of a multipolar refinement against theoretical structure factors and through direct topological analysis of the electron density obtained from the optimized periodic wavefunction. The similarity of the properties of the total electron density in all cases demonstrates the robustness of the Hansen–Coppens formalism. All intra- and intermolecular interactions have been characterized.

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

2005 ◽  
Vol 61 (4) ◽  
pp. 418-428 ◽  
Author(s):  
Adam I. Stash ◽  
Kiyoaki Tanaka ◽  
Kazunari Shiozawa ◽  
Hitoshi Makino ◽  
Vladimir G. Tsirelson
Keyword(s):  
Electron Density ◽  
Topological Analysis ◽  
Electronic Energy ◽  
Ligand Interaction ◽  
Atomic Interactions ◽  
Particle Potential ◽  
Density Analysis ◽  
The One ◽  
Electron Density Analysis ◽  
Experimental Electron Density

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 (0.19 e to each) and two Cl atoms (0.93 e to each). All the atomic interactions were quantitatively characterized in terms of the electron density and the electronic energy-density features at the bond critical points. The Zr—C2 bond paths significantly curved towards the C1—C2 bond were found; no other bond paths connecting the Zr atom and indenyl ligand were located. At the same time, the π-electrons of the C1—C2 bond are significantly involved in the metal–ligand interaction. The electron density features indicate that the indenyl coordination can be approximately described as η1 with slippage towards η2. The `ligand-opposed' charge concentrations around the Zr atom were revealed using the Laplacian of the electron density and the one-particle potential; they were linked to the orbital representations. Bonds in the indenyl ligand were characterized using the Cioslowski–Mixon bond-order indices calculated directly from the experimental electron density.

Impact of electron density values from space-geodetic observation techniques on thermospheric density models

2020 ◽  
Author(s):  
Armin Corbin ◽  
Kristin Vielberg ◽  
Michael Schmidt ◽  
Jürgen Kusche
Keyword(s):  
Electron Density ◽  
Orbit Determination ◽  
General Circulation ◽  
Precise Orbit Determination ◽  
Circulation Model ◽  
Physical Models ◽  
Neutral Density ◽  
Atmospheric Drag ◽  
Electron Densities ◽  
Density Values

<p><span>The neutral density in the thermosphere is directly related to the atmospheric drag acceleration acting on satellites. In fact, the atmospheric drag acceleration, is the largest non-gravitational perturbation for satellites below 1000 km that has to be considered for precise orbit determination. There are several global empirical and physical models providing the neutral density in the thermosphere. However, there are significant differences between the modeled neutral densities and densities observed via accelerometers. More precise thermospheric density models are required for improving drag modeling as well as orbit determination. We study the coupling between ionosphere and thermosphere based on observations and model outputs of the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIE-GCM). At first, we analyse the model’s representation of the coupling using electron and neutral densities. In comparison, we study the coupling based on observations, i.e., accelerometer-derived neutral densities and electron densities from a 4D electron density model based on GNSS and satellite altimetry data as well as radio occultation measurements. We expect that increased electron densities can be related to increased neutral densities. This is indicated for example by a correlation of approximately 55% between the neutral densities and the electron densities computed by the TIE-GCM. Finally, we investigate whether neutral density simulations fit better to in-situ densities from accelerometry when electron densities are assimilated.</span></p>

Multipole electron densities and atomic displacement parameters in urea from accurate powder X-ray diffraction

2019 ◽  
Vol 75 (4) ◽  
pp. 600-609 ◽  
Author(s):  
Bjarke Svane ◽  
Kasper Tolborg ◽  
Lasse Rabøl Jørgensen ◽  
Martin Roelsgaard ◽  
Mads Ry Vogel Jørgensen ◽  
...  
Keyword(s):  
Electron Density ◽  
Molecular System ◽  
Atomic Displacement ◽  
High Symmetry ◽  
X Ray Diffraction ◽  
High Quality ◽  
Acta Cryst ◽  
X Ray ◽  
Density Determination ◽  
Structure Factors

Electron density determination based on structure factors obtained through powder X-ray diffraction has so far been limited to high-symmetry inorganic solids. This limit is challenged by determining high-quality structure factors for crystalline urea using a bespoke vacuum diffractometer with imaging plates. This allows the collection of data of sufficient quality to model the electron density of a molecular system using the multipole method. The structure factors, refined parameters as well as chemical bonding features are compared with results from the high-quality synchrotron single-crystal study by Birkedalet al.[Acta Cryst.(2004), A60, 371–381] demonstrating that powder X-ray diffraction potentially provides a viable alternative for electron density determination in simple molecular crystals where high-quality single crystals are not available.

Accurate charge densities from powder X-ray diffraction – a new version of the Aarhus vacuum imaging-plate diffractometer

2017 ◽  
Vol 73 (4) ◽  
pp. 521-530 ◽  
Author(s):  
Kasper Tolborg ◽  
Mads R. V. Jørgensen ◽  
Sebastian Christensen ◽  
Hidetaka Kasai ◽  
Jacob Becker ◽  
...  
Keyword(s):  
Electron Density ◽  
High Energy ◽  
Imaging Plate ◽  
High Symmetry ◽  
X Rays ◽  
X Ray Diffraction ◽  
Core Electron ◽  
X Ray ◽  
Peak Broadening ◽  
Structure Factors

In recent years powder X-ray diffraction has proven to be a valuable alternative to single-crystal X-ray diffraction for determining electron-density distributions in high-symmetry inorganic materials, including subtle deformation in the core electron density. This was made possible by performing diffraction measurements in vacuum using high-energy X-rays at a synchrotron-radiation facility. Here we present a new version of our custom-built in-vacuum powder diffractometer with the sample-to-detector distance increased by a factor of four. In practice this is found to give a reduction in instrumental peak broadening by approximately a factor of three and a large improvement in signal-to-background ratio compared to the previous instrument. Structure factors of silicon at room temperature are extracted using a combined multipole–Rietveld procedure and compared withab initiocalculations and the results from the previous diffractometer. Despite some remaining issues regarding peak asymmetry, the new diffractometer yields structure factors of comparable accuracy to the previous diffractometer at low angles and improved accuracy at high angles. The high quality of the structure factors is further assessed by modelling of core electron deformation with results in good agreement with previous investigations.

scholarly journals D-region electron density and effective recombination coefficients during twilight – experimental data and modelling during solar proton events

2009 ◽  
Vol 27 (10) ◽  
pp. 3713-3724 ◽  
Author(s):  
A. Osepian ◽  
S. Kirkwood ◽  
P. Dalin ◽  
V. Tereschenko
Keyword(s):  
Electron Density ◽  
Zenith Angle ◽  
Solar Zenith Angle ◽  
Solar Proton ◽  
Radio Waves ◽  
Electron Densities ◽  
Partial Reflection ◽  
D Region ◽  
Density Values ◽  
Solar Proton Events

Abstract. Accurate measurements of electron density in the lower D-region (below 70 km altitude) are rarely made. This applies both with regard to measurements by ground-based facilities and by sounding rockets, and during both quiet conditions and conditions of energetic electron precipitation. Deep penetration into the atmosphere of high-energy solar proton fluxes (during solar proton events, SPE) produces extra ionisation in the whole D-region, including the lower altitudes, which gives favourable conditions for accurate measurements using ground-based facilities. In this study we show that electron densities measured with two ground-based facilities at almost the same latitude but slightly different longitudes, provide a valuable tool for validation of model computations. The two techniques used are incoherent scatter of radio waves (by the EISCAT 224 MHz radar in Tromsø, Norway, 69.6° N, 19.3° E), and partial reflection of radio-waves (by the 2.8 MHz radar near Murmansk, Russia, 69.0° N, 35.7° E). Both radars give accurate electron density values during SPE, from heights 57–60 km and upward with the EISCAT radar and between 55–70 km with the partial reflection technique. Near noon, there is little difference in the solar zenith angle between the two locations and both methods give approximately the same values of electron density at the overlapping heights. During twilight, when the difference in solar zenith angles increases, electron density values diverge. When both radars are in night conditions (solar zenith angle >99°) electron densities at the overlapping altitudes again become equal. We use the joint measurements to validate model computations of the ionospheric parameters f+, λ, αeff and their variations during solar proton events. These parameters are important characteristics of the lower ionosphere structure which cannot be determined by other methods.

scholarly journals Nightside ionosphere of Mars studied with local electron densities: A general overview and electron density depressions

2011 ◽  
Vol 116 (A10) ◽  
pp. n/a-n/a ◽  
Author(s):  
F. Duru ◽  
D. A. Gurnett ◽  
D. D. Morgan ◽  
J. D. Winningham ◽  
R. A. Frahm ◽  
...  
Keyword(s):  
Electron Density ◽  
Local Electron ◽  
Electron Densities ◽  
General Overview

The mapping of electronic energy distributions using experimental electron density

2002 ◽  
Vol 58 (4) ◽  
pp. 632-639 ◽  
Author(s):  
Vladimir G. Tsirelson
Keyword(s):  
Energy Density ◽  
Electron Density ◽  
Electronic Energy ◽  
Kinetic Energy Density ◽  
Energy Distributions ◽  
Structure Factors ◽  
Experimental Electron Density ◽  
Experimental Structure ◽  
Comprehensive Characterization

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.

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

1999 ◽  
Vol 55 (1) ◽  
pp. 45-54 ◽  
Author(s):  
Valery Zavodnik ◽  
Adam Stash ◽  
Vladimir Tsirelson ◽  
Roelof de Vries ◽  
Dirk Feil
Keyword(s):  
Density Functional Theory ◽  
Electron Density ◽  
Density Functional ◽  
X Ray Diffraction ◽  
Functional Theory ◽  
X Ray ◽  
Hartree Fock ◽  
Deformation Density ◽  
Structure Factors ◽  
Theoretical Results

The electron-density distribution in urea, CO(NH2)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.

X-ray molecular orbital analysis. II. Application to diformohydrazide, (NHCHO)2

2021 ◽  
Vol 77 (6) ◽  
Author(s):  
Kiyoaki Tanaka ◽  
Yuko Wasada-Tsutsui
Keyword(s):  
Hydrogen Bond ◽  
Electron Density ◽  
Molecular Orbital ◽  
Intermolecular Hydrogen Bond ◽  
Saddle Points ◽  
Electron Densities ◽  
Multiple Diffraction ◽  
Molecular Plane ◽  
X Ray ◽  
Structure Factors

The molecular orbitals (MOs) of diformohydrazide have been determined from the electron density measured by X-ray diffraction. The experimental and refinement procedures are explained in detail and the validity of the obtained MOs is assessed from the crystallographic point of view. The X-ray structure factors were measured at 100 K by a four-circle diffractometer avoiding multiple diffraction, the effect of which on the structure factors is comparable to two-centre structure factors. There remained no significant peaks on the residual density map and the R factors reduced significantly. Among the 788 MO coefficients, 731 converged, of which 694 were statistically significant. The C—H and N—H bond distances are 1.032 (2) and 1.033 (3) Å, respectively. The electron densities of theoretical and experimental MOs and the differences between them are illustrated. The overall features of the electron density obtained by X-ray molecular orbital (XMO) analysis are in good agreement with the canonical orbitals calculated by the restricted Hartree Fock (RHF) method. The bonding-electron distribution around the middle of each bond is well represented and the relative phase relationships of the π orbitals are reflected clearly in the electron densities on the plane perpendicular to the molecular plane. However, differences are noticeable around the O atom on the molecular plane. The orbital energies obtained by XMO analysis are about 0.3 a.u. higher than the corresponding canonical orbitals, except for MO10 to MO14 which are about 0.7 a.u. higher. These exceptions are attributed to the N—H...O′′ intermolecular hydrogen bond, which is neglected in the MO models of the present study. The hydrogen bond is supported by significant electron densities at the saddle points between the H(N) and O′′ atoms in MO7, 8, 14 and 17, and by that of O′′-p extended over H(N) in MO21 and 22, while no peaks were found in MO10, 11, 13 and 15. The electron density of each MO clearly exhibits its role in the molecule. Consequently, the MOs obtained by XMO analysis give a fundamental quantum mechanical insight into the real properties of molecules.

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