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Maximum Entropy Method (maximum + entropy_method)

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Chemistry90%

Selected Abstracts

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

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2010
Ali Samy
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 ,-Rb2[C2O4] and ,-Rb2[CO3] and ordered ,-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. [source]

Topological properties of hydrogen bonds and covalent bonds from charge densities obtained by the maximum entropy method (MEM)

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2009
Jeanette Netzel
Charge densities have been determined by the Maximum Entropy Method (MEM) from the high-resolution, low-temperature (T, 20,K) X-ray diffraction data of six different crystals of amino acids and peptides. A comparison of dynamic deformation densities of the MEM with static and dynamic deformation densities of multipole models shows that the MEM may lead to a better description of the electron density in hydrogen bonds in cases where the multipole model has been restricted to isotropic displacement parameters and low-order multipoles (lmax = 1) for the H atoms. Topological properties at bond critical points (BCPs) are found to depend systematically on the bond length, but with different functions for covalent C,C, C,N and C,O bonds, and for hydrogen bonds together with covalent C,H and N,H bonds. Similar dependencies are known for AIM properties derived from static multipole densities. The ratio of potential and kinetic energy densities |V(BCP)|/G(BCP) is successfully used for a classification of hydrogen bonds according to their distance d(H...O) between the H atom and the acceptor atom. The classification based on MEM densities coincides with the usual classification of hydrogen bonds as strong, intermediate and weak [Jeffrey (1997). An Introduction to Hydrogen Bonding. Oxford University Press]. MEM and procrystal densities lead to similar values of the densities at the BCPs of hydrogen bonds, but differences are shown to prevail, such that it is found that only the true charge density, represented by MEM densities, the multipole model or some other method can lead to the correct characterization of chemical bonding. Our results do not confirm suggestions in the literature that the promolecule density might be sufficient for a characterization of hydrogen bonds. [source]

Quantitative CARS Molecular Fingerprinting of Single Living Cells with the Use of the Maximum Entropy Method,

ANGEWANDTE CHEMIE, Issue 38 2010
Masanari Okuno
Der Prozess des Zelltods wurde in Echtzeit auf subzellulärer Ebene mithilfe von kohärenter Anti-Stokes-Raman-Mikrospektroskopie verfolgt. Diese Weiterentwicklung der Anti-Stokes-Raman-Streuungs(CARS)-Mikroskopie zeigt Veränderungen des chemischen Kontrastes beim Zelltod in deutlicher Auflösung (siehe Bild). [source]

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

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2010
Ali Samy
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 ,-Rb2[C2O4] and ,-Rb2[CO3] and ordered ,-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. [source]

Modulation functions of incommensurately modulated Cr2P2O7 studied by the maximum entropy method (MEM)

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2010
Liang Li
The maximum entropy method (MEM) has been used to determine electron density in superspace of incommensurately modulated chromium pyrophosphate from X-ray diffraction data measured by Palatinus et al. [(2006), Acta Cryst. B62, 556,566]. Chromium pyrophosphate, Cr2P2O7, contains ordered regions (83% of the volume) and regions with disorder. Analysis of the MEM density has allowed the determination of the displacive modulation functions within ordered regions. The disordered regions can be described as the alternate occupation of two conformations of the pyrophosphate group and two positions of the chromium atom, with occupational probabilities that depend continuously on the phase of modulation t. A structure model based on the interpretation of the MEM density provides a fit to the diffraction data of the same quality as the model given by Palatinus et al. (2006). The failure to find a model that better fits the data is attributed to the intrinsic inaccuracy of ,,0.01,Å for positions derived from the MEM and to the difficulties in constructing an appropriate model for the anharmonic ADPs and their modulation functions from electron densities. [source]

Modulated structure and phase transitions of Sr10Ga6O19

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2009
Hannes Krüger
The crystal structure of Sr10Ga6O19 was investigated by in situ single-crystal X-ray diffraction in the temperature range 298,673,K. At ambient conditions the compound shows a (3,+,1)-dimensional modulated structure in the superspace group C2/c(0,0)s0 [a = 34.9145,(13), b = 7.9369,(2), c = 15.9150,(7),Å and , = 103.551,(3)°] with a modulation wavevector of q = 0.4288,(2)b*. Whereas the presented structural model uses first-order harmonic modulation functions only, some features of the modulations are discussed utilizing an electron density derived by the maximum entropy method. Furthermore, two phase transitions were identified: between 453 and 503,K the incommensurate superstructure is replaced by a doubling of the a and b lattice constants, and between 503 and 673,K a phase with the basic cell is formed, identical to ,-Sr10Ga6O19. Under some cooling conditions crystals showing a combined diffraction pattern of both superstructures can be obtained. The relation of these results to ,-Sr10Ga6O19 [Kahlenberg (2001). J. Solid State Chem.160, 421,429] is discussed. [source]

Topological properties of hydrogen bonds and covalent bonds from charge densities obtained by the maximum entropy method (MEM)

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2009
Jeanette Netzel
Charge densities have been determined by the Maximum Entropy Method (MEM) from the high-resolution, low-temperature (T, 20,K) X-ray diffraction data of six different crystals of amino acids and peptides. A comparison of dynamic deformation densities of the MEM with static and dynamic deformation densities of multipole models shows that the MEM may lead to a better description of the electron density in hydrogen bonds in cases where the multipole model has been restricted to isotropic displacement parameters and low-order multipoles (lmax = 1) for the H atoms. Topological properties at bond critical points (BCPs) are found to depend systematically on the bond length, but with different functions for covalent C,C, C,N and C,O bonds, and for hydrogen bonds together with covalent C,H and N,H bonds. Similar dependencies are known for AIM properties derived from static multipole densities. The ratio of potential and kinetic energy densities |V(BCP)|/G(BCP) is successfully used for a classification of hydrogen bonds according to their distance d(H...O) between the H atom and the acceptor atom. The classification based on MEM densities coincides with the usual classification of hydrogen bonds as strong, intermediate and weak [Jeffrey (1997). An Introduction to Hydrogen Bonding. Oxford University Press]. MEM and procrystal densities lead to similar values of the densities at the BCPs of hydrogen bonds, but differences are shown to prevail, such that it is found that only the true charge density, represented by MEM densities, the multipole model or some other method can lead to the correct characterization of chemical bonding. Our results do not confirm suggestions in the literature that the promolecule density might be sufficient for a characterization of hydrogen bonds. [source]

Accurate charge density of the tripeptide Ala-Pro-Ala with the maximum entropy method (MEM): influence of data resolution

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 4 2007
Andreas Hofmann
The accurate electron density of Ala-Pro-Ala is determined by the maximum entropy method (MEM), employing the same reflection data measured at 100,K which was used for a multipole refinement by Kalinowski et al. [(2007), Acta Cryst. Accepted for publication]. Properties of the electron density are compared with the corresponding properties of the static electron density from the multipole model and to the dynamic MEM electron density of trialanine at 20,K. It is thus shown that the increased thermal smearing at 100,K leads to lower electron densities in the bond critical points and atomic charges closer to zero for Ala-Pro-Ala than has been obtained for trialanine at 20,K. The influence of the resolution of the data is investigated by a series of MEM calculations. Atomic charges and atomic volumes are found not to depend on the resolution, but the charge density in the BCPs decreases with decreasing resolution of the dataset. The origin of this dependence is found to lie mostly in the more accurate estimate of the atomic displacement parameters (ADPs) for the higher-resolution datasets. If these effects are taken into account, meaningful information on chemical bonding can be obtained with data at a resolution better than dmin = 0.63,Å. Alternatively, low-resolution X-ray diffraction data can be used in accurate electron-density studies by the MEM, if another source of accurate values of the ADPs is available, e.g. from refinements with multipole parameters from a database of transferable multipole parameters. [source]

Predicting the incidence of human campylobacteriosis in Finland with time series analysis

APMIS, Issue 8 2009
AYAKO SUMI
Sumi A, Hemilä H, Mise K, Kobayashi N. Predicting the incidence of human campylobacteriosis in Finland with time series analysis. APMIS 2009; 117: 614,22. Human campylobacteriosis is a common bacterial cause of gastrointestinal infections. In this study, we tested whether spectral analysis based on the maximum entropy method (MEM) is useful in predicting the incidence of campylobacteriosis in five provinces in Finland, which has been accumulating good quality incidence data under the surveillance program for water- and food-borne infections. On the basis of the spectral analysis, we identified the periodic modes explaining the underlying variations of the incidence data in the years 2000,2005. The optimum least squares fitting (LSF) curve calculated by using the periodic modes reproduced the underlying variation of the incidence data. We extrapolated the LSF curve to the years 2006 and 2007 and predicted the incidence of campylobacteriosis. Our study suggests that MEM spectral analysis allows us to model temporal variations of the disease incidence with multiple periodic modes much more effectively than using the Fourier model, which has been previously used for modeling seasonally varying incidence data. [source]