Extracting charge density distributions from diffraction data: a model study on urea

2000 ◽  
Vol 56 (1) ◽  
pp. 118-123 ◽  
Author(s):  
R. Y. de Vries ◽  
D. Feil ◽  
V. G. Tsirelson
Keyword(s):  
Density Distribution ◽  
Electron Density ◽  
Diffraction Data ◽  
Experimental Situation ◽  
Original Structure ◽  
Random Errors ◽  
Density Distributions ◽  
Structure Factors ◽  
Multipole Refinement ◽  
Interaction Density

The quality of the extraction of electron density distributions by means of a multipole refinement method is investigated. Structure factors of the urea crystal have been obtained from an electron density distribution (EDD) resulting from a density function calculation with the CRYSTAL95 package. To account for the thermal motion of the atoms, the stockholder-partioned densities of the atoms have been convoluted with thermal smearing functions, which were obtained from a neutron diffraction experiment. A POP multipole refinement yielded a good fit, R = 0.6%. This disagreement factor is based on magnitudes only. Comparison with the original structure factors gave a disagreement of 0.8% owing to differences in magnitude and phase. The fitted EDD still showed all the characteristics of the interaction density. After random errors corresponding to the experimental situation were added to the structure factors, the refinement was repeated. The fit was R = 1.1%. This time the resulting interaction density was heavily deformed. Repetition with another set of random errors from the same distribution yielded a widely different interaction density distribution. The conclusion is that interaction densities cannot be obtained from X-ray diffraction data on non-centrosymmetric crystals.

scholarly journals Die zeitliche Änderung der radialen Elektronendichteverteilung beim Theta-Pinch

1963 ◽  
Vol 18 (8-9) ◽  
pp. 895-900
Author(s):  
Franz Peter Küpper
Keyword(s):  
Density Distribution ◽  
Electron Density ◽  
Electron Density Distribution ◽  
Electron Distribution ◽  
Radial Symmetry ◽  
Zero Order ◽  
Time Interval ◽  
Interferometric Method ◽  
Density Distributions ◽  
Theta Pinch

In a θ-pinch the radial symmetry of the electron density distribution as a function of time has been measured by a MACH—ZEHNDER interferometer. In a time interval of 400 nsec during a discharge an image converter made three pictures (exposure times of 10 nsec each) . Up to 100 nsec after the first compression, the experimental results show different density distributions for the cases of trapped parallel and antiparallel magnetic fields. Complete radial symmetry of the electron density distribution was not found.Another interferometric method for measuring the radial symmetry of the electron distribution by observing “zero order” fringes is described.

The application of evolution strategies to disordered structures

1999 ◽  
Vol 32 (5) ◽  
pp. 902-910 ◽  
Author(s):  
Karsten Knorr ◽  
Fritz Mädler
Keyword(s):  
High Pressure ◽  
Maximum Entropy ◽  
Electron Density ◽  
Structural Model ◽  
Evolution Strategies ◽  
Qualitative Model ◽  
Density Distributions ◽  
Disordered Structures ◽  
Structure Factors ◽  
Complex Anions

Evolution strategies are applied to refine structural fragments, like molecules or complex anions, of orientationally disordered crystals. Optimal geometric embedding of the fragments into electron density distributions, resulting from maximum-entropy (ME) reconstructions, are performed. The evolution paradigm is found to be also applicable for the refinement against structure factors, for which the structural model is carefully selected from the ME densities. Suitably modified, the method is used successfully to compute reorientation pathways and to predict disordered high-pressure configurations in a non-classical qualitative model.

Electron Density Distribution Obtained from X-Ray Powder Data by the Maximum Entropy Method

1991 ◽  
Vol 35 (A) ◽  
pp. 77-83 ◽  
Author(s):  
Makoto Sakata ◽  
Masaki Takata ◽  
Yoshiki Kubota ◽  
Tatsuya Uno ◽  
Shintaro Kuhazawa ◽  
...  
Keyword(s):  
Density Distribution ◽  
Maximum Entropy ◽  
Electron Density ◽  
Diffraction Data ◽  
Electron Density Distribution ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Nuclear Density ◽  
X Ray ◽  
Distribution Maps

AbstractThe electron density distribution maps for CaF2 and TiO2 (rutile) were obtained from profile fitting of powder diffraction data by a Maximum Entropy Method (MEM) analysis. The resultant electron density maps show clearly the nature of the chemical bonding. In order to interpret the results, the nuclear density distribution was also obtained for rutile from powder neutron diffraction data. In the electron density map for rutile obtained by HEM analysis from the X-ray data, both apical and equatorial bonding can be seen. On the other hand, the nuclear density of rutile Is very simple and shows the thermal vibration of nuclei.

The study on charge-density distribution in TiAl by quantitative electron crystallography method

1995 ◽  
Vol 10 (8) ◽  
pp. 1913-1916 ◽  
Author(s):  
Yu Miao ◽  
Jing Zhu ◽  
X.W. Lin ◽  
W.J. Jiang
Keyword(s):  
Density Distribution ◽  
Charge Density ◽  
Interatomic Bond ◽  
Electronic Charge ◽  
Electron Crystallography ◽  
Charge Density Distribution ◽  
Electronic Charge Density ◽  
Density Distributions ◽  
Structure Factors ◽  
Equiaxed Grain

Structure factors of μ-TiAl equiaxed grain in TiAl duplex intermetallic compound before and after V-alloying were measured by the quantitative electron crystallography method. Then the structure factors were transferred into charge-density distributions of real space. Comparing the charge-density distributions in γ-TiAl with those in V-alloyed γ-TiAl, it was found that V-alloying with the optimum amount decreases the electronic charge density in the Ti-Ti interatomic bond, and increases the electronic charge density in the Al-Al interatomic bond and Ti-Al interatomic bond. Thus, the anisotropy of charge-density distribution in γ-TiAl equiaxed grain is reduced.

Sign in / Sign up

Export Citation Format

Share Document