Transient electron density maps from femtosecond x-ray powder diffraction

2014 ◽  
Vol 70 (a1) ◽  
pp. C100-C100
Author(s):  
Vincent Juvé ◽  
Flavio Zamponi ◽  
Marcel Holtz ◽  
Michael Woerner ◽  
Thomas Elsaesser
Keyword(s):  
Charge Transfer ◽  
Electron Density ◽  
Powder Diffraction ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
X Rays ◽  
X Ray ◽  
Density Maps ◽  
Structure Factors ◽  
Diffraction Angle

Ultrashort hard x-ray pulses are sensitive probes of structural dynamics on the picometer length and femtosecond time scales of electronic and atomic motions. Using short hard x-ray pulses as probe in a pump-probe scheme allow to do femtosecond x-ray diffraction experiments [1], which provide transient electron density maps at a femtosecond timescale with a sub-angstrom spatial resolution. In a typical femtosecond x-ray powder diffraction experiment many Debye-Scherrer rings, up to a maximum diffraction angle 2θmax, are recorded for each time delay between the optical pump and the hard x-ray probe. From the diffraction pattern, the change of the diffracted intensity of each rings are monitored. The interference of diffracted x-rays from the many unexcited cells, with known structure factors coming from steady-state measurement, and diffracted x-rays from the few excited cells allows for the detection of the transients structure factors. Problems could arise if the 3D-Fourier transform is directly used because of the abrupt end of the collected information in the reciprocal space (maximum diffraction angle 2θmax). In order to overcome this problem, the Maximum Entropy Method is apply to the data and the transient electron density maps are derived. We apply the femtosecond x-ray powder diffraction technique and the Maximum Entropy Method to study the induced transient polarization by high optical fields on ionic crystals. Such polarizations are connected to a spatial redistribution of electronic charge, which corresponds to a charge transfer between the two ionic compounds [2]. While the charge transfer originates from the anion to the cation in the LiBH and the NaBH4, the LiH exhibits a peculiar behavior: the charge transfer occurs from the cation to the anion. As result from comparison with calculations in the COHSEX framework, this behavior is due to the strong electronic correlations in the LiH [3].

Electron-density distribution from X-ray powder data by use of profile fits and the maximum-entropy method

1990 ◽  
Vol 23 (6) ◽  
pp. 526-534 ◽  
Author(s):  
M. Sakata ◽  
R. Mori ◽  
S. Kumazawza ◽  
M. Takata ◽  
H. Toraya
Keyword(s):  
Density Distribution ◽  
Maximum Entropy ◽  
Electron Density ◽  
Electron Density Distribution ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Distribution Map ◽  
X Ray ◽  
Profile Decomposition ◽  
Structure Factors

Following the profile decomposition of CeO2 X-ray powder data into individual structure factors, the maximum-entropy method (MEM) has been used to obtain an electron-density-distribution map. In the profile decomposition process, it is impossible to avoid the problems of overlapping peaks which have the same magnitude of reciprocal vectors, such as d*(511) and d*(333), for a cubic crystal, or very severely overlapping reflections. The formalism to treat such overlapping reflections in the MEM analysis is to introduce combined structure factors. The maximum value of the scattering vector, 4π(sinθ)/λ, which was used in the present analysis is small (about 7.8 Å−1) but the resulting electron-density-distribution map is of a high quality and much superior to the conventional map. As a consequence, the ionic charge of Ce and O ions can be obtained with reasonable accuracy from the MEM density map. Furthermore, the map reveals the existence of electrons around the supposedly vacant site surrounded by eight O atoms, which is probably related to the high ionic conductivity of this substance.

Maximum entropy method and charge flipping, a powerful combination to visualize the true nature of structural disorder from in situ X-ray powder diffraction data

2010 ◽  
Vol 66 (2) ◽  
pp. 184-195 ◽  
Author(s):  
Ali Samy ◽  
Robert E. Dinnebier ◽  
Sander van Smaalen ◽  
Martin Jansen
Keyword(s):  
Crystal Structures ◽  
Electron Density ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Structure Factor ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Powder Diffraction Data ◽  
True Nature ◽  
Structure Factors

In a systematic approach, the ability of the Maximum Entropy Method (MEM) to reconstruct the most probable electron density of highly disordered crystal structures from X-ray powder diffraction data was evaluated. As a case study, the ambient temperature crystal structures of disordered α-Rb2[C2O4] and α-Rb2[CO3] and ordered δ-K2[C2O4] were investigated in detail with the aim of revealing the `true' nature of the apparent disorder. Different combinations of F (based on phased structure factors) and G constraints (based on structure-factor amplitudes) from different sources were applied in MEM calculations. In particular, a new combination of the MEM with the recently developed charge-flipping algorithm with histogram matching for powder diffraction data (pCF) was successfully introduced to avoid the inevitable bias of the phases of the structure-factor amplitudes by the Rietveld model. Completely ab initio electron-density distributions have been obtained with the MEM applied to a combination of structure-factor amplitudes from Le Bail fits with phases derived from pCF. All features of the crystal structures, in particular the disorder of the oxalate and carbonate anions, and the displacements of the cations, are clearly obtained. This approach bears the potential of a fast method of electron-density determination, even for highly disordered materials. All the MEM maps obtained in this work were compared with the MEM map derived from the best Rietveld refined model. In general, the phased observed structure factors obtained from Rietveld refinement (applying F and G constraints) were found to give the closest description of the experimental data and thus lead to the most accurate image of the actual disorder.

scholarly journals On avoiding negative electron density in Gram-Charlier refinements of anharmonic motion: the example of glutathione

2018 ◽  
Vol 233 (9-10) ◽  
pp. 695-706 ◽  
Author(s):  
Christian B. Hübschle ◽  
Charlotte Ruhmlieb ◽  
Anja Burkhardt ◽  
Sander van Smaalen ◽  
Birger Dittrich
Keyword(s):  
Electron Density ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Free Lunch ◽  
X Ray Diffraction ◽  
Third Order ◽  
X Ray ◽  
Density Maps ◽  
Anisotropic Displacement Parameters

Abstract The structure of glutathione, γ-l-Glutamyl-l-cysteinyl-glycine (C10H17N3O6S), was studied by multi-temperature single-crystal X-ray diffraction. Residual density maps from conventional independent atom model refinement gave indication of anharmonic motion in the molecule. This was further investigated by invariom refinement with anisotropic displacement parameters for all atoms, which described asphericity due to chemical bonding and lone pairs; afterwards only the residual-density signal of anharmonic motion remained. Treating anharmonicity with third-order Gram-Charlier displacement parameters led to regions with unphysical negative electron density. In contrast, a maximum entropy method (MEM) determination of the electron density successfully takes the features into account. Respective difference electron density plots (MEM minus prior and [Invariom+GC] minus invariom) agree well with each other. Challenges in treating and understanding the phenomenon are discussed. A procedure is proposed how unphysical negative electron density can be avoided. It is closely related to the free lunch algorithm.

scholarly journals Evaluating structures derived from X-ray powder diffraction data using entropy

2014 ◽  
Vol 70 (a1) ◽  
pp. C104-C104
Author(s):  
Dubravka Sisak Jung ◽  
Lynne McCusker ◽  
Christian Baerlocher ◽  
Christopher Gilmore
Keyword(s):  
Powder Diffraction ◽  
Evaluation Criteria ◽  
Entropy Method ◽  
Basis Set ◽  
Solution Quality ◽  
Powder Charge ◽  
X Ray ◽  
Density Maps ◽  
Straightforward Method ◽  
All Solutions

So far, in the field of X-ray powder diffraction, the maximum entropy method (MEM) has been used to (i) solve the phase problem, (ii) estimate the intensities of overlapping reflections, (iii) predict the intensities of missing reflections, and (iv) improve electron density maps generated during Rietveld refinement. We found a new application for MEM in a recent study, in which the powder charge flipping algorithm [1] in Superflip was applied to all-light-atom structures [2]. It proved to be difficult to identify the few fully interpretable maps within in the 200 generated in a typical Superflip job using the standard evaluation criteria. In 1992, Sato reported that entropy could be used as a solution evaluation criterion if the basis set is large, the phases are close to the correct ones, and the structure contains a small molecule [3]. Reasoning that these requirements would be fulfilled by the better Superflip solutions, all solutions were input to the MEM program MICE to calculate the corresponding ME maps and their entropies. Tests performed on several datasets showed no direct correlation between entropy and the solution quality. However, it was noted that a certain number of solutions show entropy values significantly lower than the others. This group usually contained one fully interpretable map. Refinement of the approach led to a relatively straightforward method for recognizing the better solutions. Furthermore, phase recycling based on this approach proved to be useful. As a result, guidelines for solving structures of different levels of complexity using the pCF algorithm could be devised.

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.

Element-selective charge density visualization of endohedral metallofullerenes using synchrotron X-ray multi-wavelength anomalous powder diffraction data

2013 ◽  
Vol 46 (3) ◽  
pp. 649-655 ◽  
Author(s):  
Sachiko Maki ◽  
Eiji Nishibori ◽  
Daisuke Kawaguchi ◽  
Makoto Sakata ◽  
Masaki Takata ◽  
...  
Keyword(s):  
Charge Density ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Rietveld Analysis ◽  
Entropy Method ◽  
Powder Diffraction Data ◽  
X Ray ◽  
Density Maps ◽  
Medium Resolution ◽  
Multi Wavelength

An algorithm for determining the element-selective charge density has been developed using the maximum entropy method (MEM), Rietveld analysis and synchrotron X-ray multi-wavelength anomalous powder diffraction data. This article describes in detail both experimental and analytical aspects of the developed method. A structural study of yttrium mono-metallofullerene, Y@C82, 1:1 co-crystallized with toluene using the present technique is reported in order to demonstrate the applicability of the method even when only medium resolution data are available (d> 1.32 Å). Element-selective MEM charge density maps, computed from synchrotron X-ray powder diffraction data collected at three distinct wavelengths around the yttriumK-absorption edge (∼0.727 A), are employed for determining three crystallographic sites of the disordered yttrium.

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 A chemical interpretation of protein electron density maps in the worldwide protein data bank

2019 ◽  
Author(s):  
Sen Yao ◽  
Hunter N.B. Moseley
Keyword(s):  
Protein Data Bank ◽  
Electron Density ◽  
Structural Model ◽  
Data Bank ◽  
X Ray ◽  
New Methods ◽  
Link Type ◽  
Density Maps ◽  
Structure Factors ◽  
Python Package

AbstractHigh-quality three-dimensional structural data is of great value for the functional interpretation of biomacromolecules, especially proteins; however, structural quality varies greatly across the entries in the worldwide Protein Data Bank (wwPDB). Since 2008, the wwPDB has required the inclusion of structure factors with the deposition of x-ray crystallographic structures to support the independent evaluation of structures with respect to the underlying experimental data used to derive those structures. However, interpreting the discrepancies between the structural model and its underlying electron density data is difficult, since derived electron density maps use arbitrary electron density units which are inconsistent between maps from different wwPDB entries. Therefore, we have developed a method that converts electron density values into units of electrons. With this conversion, we have developed new methods that can evaluate specific regions of an x-ray crystallographic structure with respect to a physicochemical interpretation of its corresponding electron density map. We have systematically compared all deposited x-ray crystallographic protein models in the wwPDB with their underlying electron density maps, if available, and characterized the electron density in terms of expected numbers of electrons based on the structural model. The methods generated coherent evaluation metrics throughout all PDB entries with associated electron density data, which are consistent with visualization software that would normally be used for manual quality assessment. To our knowledge, this is the first attempt to derive units of electrons directly from electron density maps without the aid of the underlying structure factors. These new metrics are biochemically-informative and can be extremely useful for filtering out low-quality structural regions from inclusion into systematic analyses that span large numbers of PDB entries. Furthermore, these new metrics will improve the ability of non-crystallographers to evaluate regions of interest within PDB entries, since only the PDB structure and the associated electron density maps are needed. These new methods are available as a well-documented Python package on GitHub and the Python Package Index under a modified Clear BSD open source license.Author summaryElectron density maps are very useful for validating the x-ray structure models in the Protein Data Bank (PDB). However, it is often daunting for non-crystallographers to use electron density maps, as it requires a lot of prior knowledge. This study provides methods that can infer chemical information solely from the electron density maps available from the PDB to interpret the electron density and electron density discrepancy values in terms of units of electrons. It also provides methods to evaluate regions of interest in terms of the number of missing or excessing electrons, so that a broader audience, such as biologists or bioinformaticians, can also make better use of the electron density information available in the PDB, especially for quality control purposes.Software and full results available athttps://github.com/MoseleyBioinformaticsLab/pdb_eda (software on GitHub)https://pypi.org/project/pdb-eda/ (software on PyPI)https://pdb-eda.readthedocs.io/en/latest/ (documentation on ReadTheDocs)https://doi.org/10.6084/m9.figshare.7994294 (code and results on FigShare)

Charge density studies utilizing powder diffraction and MEM. Exploring of high Tc superconductors, C60 superconductors and manganites

2001 ◽  
Vol 216 (2) ◽  
Author(s):  
M. Takata ◽  
E. Nishibori ◽  
M. Sakata
Keyword(s):  
Charge Density ◽  
Maximum Entropy ◽  
Powder Diffraction ◽  
Recent Progress ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
High Tc Superconductors ◽  
High Tc ◽  
X Ray

AbstractThe recent progress of the accurate charge density studies by the Maximum Entropy Method(MEM) utilizing X-ray powder diffraction is reviewed with some examples. Results for PrBCO (PrBa

A new type of constraint in the maximum-entropy method using ambiguous phase information from anomalous-scattering powder data

1999 ◽  
Vol 55 (4) ◽  
pp. 719-728 ◽  
Author(s):  
K. Burger ◽  
W. Prandl
Keyword(s):  
Maximum Entropy ◽  
Powder Diffraction ◽  
Entropy Method ◽  
Anomalous Scattering ◽  
X Rays ◽  
Synchrotron Source ◽  
Structure Factors ◽  
New Type ◽  
Types Of Information

Anomalous scattering of X-rays at a synchrotron source can be used for the ab initio structure determination of unknown crystal structures using only powder diffraction data. For noncentrosymmetric crystals, the phases of structure factors can only be determined with a remaining ambiguity, when one chemical element is used as resonant scatterer. A corresponding additional constraint function has been built into an enhanced version of the program MEED, so that now all types of information gained from an anomalous-scattering powder diffraction experiment can be used in a maximum-entropy calculation of the electron-density distribution: phased reflections, unphased reflections, intensities of groups of overlapping reflections, and now also reflections with a remaining ambiguity in the phase. This is important for practical use, since a lot of information is already lost in the powder diagram compared with single-crystal datasets and it is essential to use all remaining information. The new constraint is demonstrated with the structure of Cu5Zn8.

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