Angular terms in the electron density for the phosphine molecule

1956 ◽  
Vol 52 (4) ◽  
pp. 703-711 ◽  
Author(s):  
R. A. Ballinger ◽  
N. H. March
Keyword(s):  
Variational Method ◽  
Charge Density ◽  
Electron Density ◽  
Legendre Polynomials ◽  
Molecular Axis ◽  
Thomas Fermi ◽  
Line Charge ◽  
Density Map ◽  
Circular Line

ABSTRACTAn attempt is made to calculate the first few angular terms in an expansion of the electron density for the phosphine molecule in Legendre polynomials. Such an expansion is appropriate for a model in which the three hydrogen nuclei are smeared to form a circular line charge. The Thomas–Fermi approximation has been used in conjunction with the variational method. The variational density employed includes p and f angular terms. An approximate charge density map is constructed for a plane containing the molecular axis in order to demonstrate the effect of the angular terms.

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.

Evolution of line charge density of steadily-developing upward positive leaders in triggered lightning

2013 ◽  
Vol 118 (10) ◽  
pp. 4670-4678 ◽  
Author(s):  
Mingli Chen ◽  
Dong Zheng ◽  
Yaping Du ◽  
Yijun Zhang
Keyword(s):  
Charge Density ◽  
Line Charge ◽  
Triggered Lightning

A Comparison of Two Algorithms for Electron-Density Map Improvement by Introduction of Atomicity: Skeletonization, and Map Sorting Followed by Refinement

1998 ◽  
Vol 54 (1) ◽  
pp. 81-85 ◽  
Author(s):  
F. M. D. Vellieux
Keyword(s):  
Electron Density ◽  
Initial Density ◽  
Acta Cryst ◽  
Density Maps ◽  
Resolution Electron ◽  
Crystallographic Symmetry ◽  
Density Map ◽  
Ornithine Transcarbamoylase ◽  
Electron Density Map ◽  
Pseudo Atom

A comparison has been made of two methods for electron-density map improvement by the introduction of atomicity, namely the iterative skeletonization procedure of the CCP4 program DM [Cowtan & Main (1993). Acta Cryst. D49, 148–157] and the pseudo-atom introduction followed by the refinement protocol in the program suite DEMON/ANGEL [Vellieux, Hunt, Roy & Read (1995). J. Appl. Cryst. 28, 347–351]. Tests carried out using the 3.0 Å resolution electron density resulting from iterative 12-fold non-crystallographic symmetry averaging and solvent flattening for the Pseudomonas aeruginosa ornithine transcarbamoylase [Villeret, Tricot, Stalon & Dideberg (1995). Proc. Natl Acad. Sci. USA, 92, 10762–10766] indicate that pseudo-atom introduction followed by refinement performs much better than iterative skeletonization: with the former method, a phase improvement of 15.3° is obtained with respect to the initial density modification phases. With iterative skeletonization a phase degradation of 0.4° is obtained. Consequently, the electron-density maps obtained using pseudo-atom phases or pseudo-atom phases combined with density-modification phases are much easier to interpret. These tests also show that for ornithine transcarbamoylase, where 12-fold non-crystallographic symmetry is present in the P1 crystals, G-function coupling leads to the simultaneous decrease of the conventional R factor and of the free R factor, a phenomenon which is not observed when non-crystallographic symmetry is absent from the crystal. The method is far less effective in such a case, and the results obtained suggest that the map sorting followed by refinement stage should be by-passed to obtain interpretable electron-density distributions.

Nonnuclear Maxima in the Charge Density

1993 ◽  
Vol 48 (1-2) ◽  
pp. 127-133 ◽  
Author(s):  
Kenneth E. Edgecombe ◽  
Vedene H. Smith, Jr. ◽  
Florian Müller-Plathe
Keyword(s):  
Charge Density ◽  
Electron Density ◽  
Electron Correlation ◽  
Basis Set ◽  
Valence Shell ◽  
Correlation Effects ◽  
Electron Correlation Effects

Abstract Basis-set and electron-correlation effects on the appearance and disappearance of nonnuclear maxima in the electron density are examined in Li2 , Na2 , Na4 and Na5 . It is shown that nonnuclear attractors can be removed in all cases except Li2 . The appearance of a pseudoatom in a lithium molecule correlates remarkably well with the size of the region, in an atomic calculation, of V2r(r) for the valence shell of the atom. This and the fact that the pseudoatom is also present in the promolecule indicate that the pseudoatoms are remnants of, or in fact are portions of, atoms that are not perturbed enough in the molecule to remove an essentially atomic characteristic.

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