Towards extracting the charge density from normal-resolution data

2009 ◽  
Vol 42 (6) ◽  
pp. 1110-1121 ◽  
Author(s):  
B. Dittrich ◽  
C. B. Hübschle ◽  
J. J. Holstein ◽  
F. P. A. Fabbiani
Keyword(s):  
Charge Density ◽  
Dipole Moments ◽  
Atomic Displacement ◽  
Limiting Factor ◽  
Data Sets ◽  
Data Set ◽  
Redundant Data ◽  
Multipole Refinement ◽  
Atomic Displacement Parameters ◽  
Resolution Data

The limiting factor for charge-density studies is crystal quality. Although area detection and low temperatures enable redundant data collection, only compounds that form well diffracting single crystals without disorder are amenable to these studies. If thermal motion and electron density ρ(r) were de-convoluted, multipole parameters could also be refined with lower-resolution data, such as those commonly collected for macromolecules. Using the invariom database for first refining conventional parameters (x,y,zand atomic displacement parameters), de-convolution can be achieved. In a subsequent least-squares refinement of multipole parameters only, information on the charge density becomes accessible also for data not fulfilling charge-density requirements. A critical aspect of this procedure is the missing information on the correlation between refined and non-refined parameters. This correlation is investigated in detail by comparing a full multipole refinement on high-resolution and a blocked refinement on `normal-resolution' data sets of ciprofloxacin hexahydrate. Topological properties and dipole moments are shown to be in excellent agreement for the two refinements. A `normal-resolution' data set of ciprofloxacin hydrochloride 1.4-hydrate is also evaluated in this manner.

Charge Density of L-Alanyl-glycyl-L-alanine Based on X-Ray Data Collection Periods from 4 to 130 Hours

2007 ◽  
Vol 62 (5) ◽  
pp. 696-704 ◽  
Author(s):  
Diana Förster ◽  
Armin Wagner ◽  
Christian B. Hübschle ◽  
Carsten Paulmann ◽  
Peter Luger
Keyword(s):  
Synchrotron Radiation ◽  
Low Temperature ◽  
Charge Density ◽  
Data Sets ◽  
Data Set ◽  
X Ray ◽  
Atomic Properties ◽  
Multipole Refinement ◽  
Refinement Strategy ◽  
Experimental Charge Density

Abstract The charge density of the tripeptide L-alanyl-glycyl-L-alanine was determined from three X-ray data sets measured at different experimental setups and under different conditions. Two of the data sets were measured with synchrotron radiation (beamline F1 of Hasylab/DESY, Germany and beamline X10SA of SLS, Paul-Scherer-Institute, Switzerland) at temperatures around 100 K while a third data set was measured under home laboratory conditions (MoKα radiation) at a low temperature of 20 K. The multipole refinement strategy to derive the experimental charge density was the same in all cases, so that the obtained charge density properties could directly be compared. While the general analysis of the three data sets suggested a small preference for one of the synchrotron data sets (Hasylab F1), a comparison of topological and atomic properties gave in no case an indication for a preference of any of the three data sets. It follows that even the 4 h data set measured at the SLS performed equally well compared to the data sets of substantially longer exposure time.

Measurement of high-quality diffraction data with a Nonius KappaCCD diffractometer: finding the optimal experimental parameters

2003 ◽  
Vol 36 (3) ◽  
pp. 931-939 ◽  
Author(s):  
Henning Osholm Sørensen ◽  
Sine Larsen
Keyword(s):  
Charge Density ◽  
Diffraction Data ◽  
Topological Analysis ◽  
Measure Data ◽  
Data Sets ◽  
Electron Densities ◽  
Data Set ◽  
Redundant Data ◽  
Experimental Parameters

The influence of the different experimental parameters on the quality of the diffraction data collected on tetrafluoroterephthalonitrile (TFT) with a Nonius KappaCCD instrument has been examined. Data sets measured with different scan widths (0.25°, 0.50°, 1.0°) and scan times (70 s/° and 140 s/°) were compared with a highly redundant data set collected with an Enraf–Nonius CAD4 point detector diffractometer. As part of this analysis it was investigated how the parameters employed during the data reduction performed with theEvalCCDandSORTAVprograms affect the quality of the data. The KappaCCD data sets did not show any significant contamination from λ/2 radiation and possess good internal consistency with lowRintvalues. Decreasing the scan width seems to increase the standard uncertainties, which conversely are improved by an increase in the scan time. The suitability of the KappaCCD instrument to measure data to be used in charge density studies was also examined by performing a charge density data collection with the KappaCCD instrument. The same multipole model was used in the refinement of these data and of the CAD4 data. The two refinements gave almost identical parameters and residual electron densities. The topological analysis of the resulting static electron densities shows that the bond critical points have the same characteristics.

Strategies for solving neighboring-element problems: a case study using resonant X-ray diffraction and pulsed neutron diffraction to examine Sr8Ga16Ge30

2003 ◽  
Vol 36 (5) ◽  
pp. 1182-1189 ◽  
Author(s):  
Yuegang Zhang ◽  
Angus P. Wilkinson ◽  
George S. Nolas ◽  
Peter L. Lee ◽  
Jason P. Hodges
Keyword(s):  
Neutron Diffraction ◽  
Resonant Scattering ◽  
Atomic Displacement ◽  
Scattering Data ◽  
Data Sets ◽  
Type I ◽  
Neighboring Element ◽  
Data Set ◽  
X Ray ◽  
Atomic Displacement Parameters

The distribution of gallium and germanium over the available framework sites in the type-I clathrate Sr8Ga16Ge30(Pm\bar{3}n) has been determined by powder diffraction using several different combinations of resonant scattering data sets, collected at energies close to both the Ga and GeK-edges, and time-of-flight (TOF) neutron diffraction data. Based on a combined refinement using three X-ray data sets and a composition restraint, the fractional occupancies of the 6c, 16iand 24ksites by gallium are estimated to be 0.705 (5), 0.181 (3) and 0.376 (2), respectively. The required resonant scattering factors were determined by Kramers–Kronig transformation from X-ray absorption spectra. The results from refinements using single data sets and various combinations of data sets are compared. The high degree of scattering contrast that resonant diffraction can provide leads to very precise site occupancies. However, systematic errors in the resonant diffraction intensity data can considerably degrade the accuracy of the results. The use of a carefully chosen multiple-data-set strategy can minimize bias in the refinement results by reducing the correlations between site occupancies, atomic displacement parameters and histogram scale factors. The effect of errors in the resonant scattering factors on the refinement results was also examined.

scholarly journals Structural analysis and multipole modelling of quercetin monohydrate – a quantitative and comparative study

2010 ◽  
Vol 67 (1) ◽  
pp. 63-78 ◽  
Author(s):  
Sławomir Domagała ◽  
Parthapratim Munshi ◽  
Maqsood Ahmed ◽  
Benoît Guillot ◽  
Christian Jelsch
Keyword(s):  
Comparative Study ◽  
Charge Density ◽  
Topological Analysis ◽  
Atomic Displacement ◽  
X Ray Diffraction ◽  
Experimental Database ◽  
Figures Of Merit ◽  
Atom Model ◽  
Atomic Displacement Parameters ◽  
Model Approach

The multipolar atom model, constructed by transferring the charge-density parameters from an experimental or theoretical database, is considered to be an easy replacement of the widely used independent atom model. The present study on a new crystal structure of quercetin monohydrate [2-(3,4-dihydroxyphenyl)-3,5,7-trihydroxy-4H-chromen-4-one monohydrate], a plant flavonoid, determined by X-ray diffraction, demonstrates that the transferred multipolar atom model approach greatly improves several factors: the accuracy of atomic positions and the magnitudes of atomic displacement parameters, the residual electron densities and the crystallographic figures of merit. The charge-density features, topological analysis and electrostatic interaction energies obtained from the multipole models based on experimental database transfer and periodic quantum mechanical calculations are found to compare well. This quantitative and comparative study shows that in the absence of high-resolution diffraction data, the database transfer approach can be applied to the multipolar electron density features very accurately.

A Bayesian approach to modeling 2D gravity data using polygons

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. G1-G21 ◽  
Author(s):  
William J. Titus ◽  
Sarah J. Titus ◽  
Joshua R. Davis
Keyword(s):  
Gravity Data ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Limiting Factor ◽  
Data Sets ◽  
Data Set ◽  
Local Optima ◽  
Occupancy Probability ◽  
Compute Model ◽  
Parameter Values

We apply a Bayesian Markov chain Monte Carlo formalism to the gravity inversion of a single localized 2D subsurface object. The object is modeled as a polygon described by five parameters: the number of vertices, a density contrast, a shape-limiting factor, and the width and depth of an encompassing container. We first constrain these parameters with an interactive forward model and explicit geologic information. Then, we generate an approximate probability distribution of polygons for a given set of parameter values. From these, we determine statistical distributions such as the variance between the observed and model fields, the area, the center of area, and the occupancy probability (the probability that a spatial point lies within the subsurface object). We introduce replica exchange to mitigate trapping in local optima and to compute model probabilities and their uncertainties. We apply our techniques to synthetic data sets and a natural data set collected across the Rio Grande Gorge Bridge in New Mexico. On the basis of our examples, we find that the occupancy probability is useful in visualizing the results, giving a “hazy” cross section of the object. We also find that the role of the container is important in making predictions about the subsurface object.

Decision tree classification algorithm for non-equilibrium data set based on random forests

2020 ◽  
Vol 39 (2) ◽  
pp. 1639-1648
Author(s):  
Peng Wang ◽  
Ningchao Zhang
Keyword(s):  
Random Forest ◽  
Decision Tree ◽  
Wavelet Packet ◽  
Classification Algorithm ◽  
Data Sets ◽  
Data Set ◽  
Redundant Data ◽  
Decision Tree Classification ◽  
Equilibrium Data ◽  
Non Equilibrium

In order to overcome the problems of poor accuracy and high complexity of current classification algorithm for non-equilibrium data set, this paper proposes a decision tree classification algorithm for non-equilibrium data set based on random forest. Wavelet packet decomposition is used to denoise non-equilibrium data, and SNM algorithm and RFID are combined to remove redundant data from data sets. Based on the results of data processing, the non-equilibrium data sets are classified by random forest method. According to Bootstrap resampling method with certain constraints, the majority and minority samples of each sample subset are sampled, CART is used to train the data set, and a decision tree is constructed. Obtain the final classification results by voting on the CART decision tree classification. Experimental results show that the proposed algorithm has the characteristics of high classification accuracy and low complexity, and it is a feasible classification algorithm for non-equilibrium data set.

scholarly journals Transferable aspherical atom model refinement of protein and DNA structures against ultrahigh-resolution X-ray data

2016 ◽  
Vol 72 (6) ◽  
pp. 770-779 ◽  
Author(s):  
Maura Malinska ◽  
Zbigniew Dauter
Keyword(s):  
Charge Density ◽  
Atomic Displacement ◽  
Coulombic Interaction ◽  
Ultrahigh Resolution ◽  
Additional Advantage ◽  
X Ray ◽  
Atom Model ◽  
Density Maps ◽  
Atomic Displacement Parameters ◽  
The University

In contrast to the independent-atom model (IAM), in which all atoms are assumed to be spherical and neutral, the transferable aspherical atom model (TAAM) takes into account the deformed valence charge density resulting from chemical bond formation and the presence of lone electron pairs. Both models can be used to refine small and large molecules,e.g.proteins and nucleic acids, against ultrahigh-resolution X-ray diffraction data. The University at Buffalo theoretical databank of aspherical pseudo-atoms has been used in the refinement of an oligopeptide, of Z-DNA hexamer and dodecamer duplexes, and of bovine trypsin. The application of the TAAM to these data improves the quality of the electron-density maps and the visibility of H atoms. It also lowers the conventionalRfactors and improves the atomic displacement parameters and the results of the Hirshfeld rigid-bond test. An additional advantage is that the transferred charge density allows the estimation of Coulombic interaction energy and electrostatic potential.

The correction of reflection intensities for incomplete absorption of high-energy X-rays in the CCD phosphor

2002 ◽  
Vol 35 (3) ◽  
pp. 356-359 ◽  
Author(s):  
G. Wu ◽  
B. L. Rodrigues ◽  
P. Coppens
Keyword(s):  
Incident Angle ◽  
Atomic Displacement ◽  
High Energy ◽  
X Rays ◽  
Structural Refinement ◽  
Data Set ◽  
X Ray ◽  
Area Detector ◽  
Angle Dependence ◽  
Atomic Displacement Parameters

It is shown that incomplete absorption of the X-ray beam in the phosphor of an area detector causes an incident-angle dependence of the recorded X-ray intensities. An energy scan of a SMART-6000 CCD (charge-coupled device) phosphor using synchrotron radiation shows the correction to be of importance above about 17 keV. Intensities of single reflections, each collected several times at different angles of incidence on the phosphor surface, show a pronounced angle-dependence at shorter wavelengths. Both conventional structural refinement and multipole charge density studies confirm that an oblique-incidence correction leads to improved quality of the results. Atomic displacement parameters will be systematically biased when the correction is not applied. For a λ = 0.394 Å data set, neglecting the correction gives rise to artifacts in the deformation density maps that are likely to lead to misinterpretation of the experimental results.

scholarly journals Quantum crystallographic charge density of urea

IUCrJ ◽  
2016 ◽  
Vol 3 (4) ◽  
pp. 237-246 ◽  
Author(s):  
Michael E. Wall
Keyword(s):  
High Resolution ◽  
Charge Density ◽  
Model Building ◽  
Atomic Displacement ◽  
Free Atom ◽  
Quantum Model ◽  
X Ray ◽  
Atomic Displacement Parameters ◽  
A Charge ◽  
High Level

Standard X-ray crystallography methods use free-atom models to calculate mean unit-cell charge densities. Real molecules, however, have shared charge that is not captured accurately using free-atom models. To address this limitation, a charge density model of crystalline urea was calculated using high-level quantum theory and was refined against publicly available ultra-high-resolution experimental Bragg data, including the effects of atomic displacement parameters. The resulting quantum crystallographic model was compared with models obtained using spherical atom or multipole methods. Despite using only the same number of free parameters as the spherical atom model, the agreement of the quantum model with the data is comparable to the multipole model. The static, theoretical crystalline charge density of the quantum model is distinct from the multipole model, indicating the quantum model provides substantially new information. Hydrogen thermal ellipsoids in the quantum model were very similar to those obtained using neutron crystallography, indicating that quantum crystallography can increase the accuracy of the X-ray crystallographic atomic displacement parameters. The results demonstrate the feasibility and benefits of integrating fully periodic quantum charge density calculations into ultra-high-resolution X-ray crystallographic model building and refinement.

scholarly journals Validation of experimental charge-density refinement strategies: when do we overfit?

IUCrJ ◽  
2017 ◽  
Vol 4 (4) ◽  
pp. 420-430 ◽  
Author(s):  
Lennard Krause ◽  
Benedikt Niepötter ◽  
Christian J. Schürmann ◽  
Dietmar Stalke ◽  
Regine Herbst-Irmer
Keyword(s):  
Standard Deviation ◽  
Charge Density ◽  
Cross Validation ◽  
Data Sets ◽  
Topological Parameters ◽  
Visualization Tools ◽  
Multipole Refinement ◽  
The Given ◽  
Experimental Charge Density ◽  
Parameter Distributions

A cross-validation method is supplied to judge between various strategies in multipole refinement procedures. Its application enables straightforward detection of whether the refinement of additional parameters leads to an improvement in the model or an overfitting of the given data. For all tested data sets it was possible to prove that the multipole parameters of atoms in comparable chemical environments should be constrained to be identical. In an automated approach, this method additionally delivers parameter distributions ofkdifferent refinements. These distributions can be used for further error diagnostics,e.g.to detect erroneously defined parameters or incorrectly determined reflections. Visualization tools show the variation in the parameters. These different refinements also provide rough estimates for the standard deviation of topological parameters.

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