The maximum-entropy method in charge-density studies. II. General aspects of reliability

Jauch, W.

doi:10.1107/s0108767394004472

Cited by 38 publications

(34 citation statements)

References 5 publications

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“…The Cambridge algorithm gives solutions close to the true maximum-entropy (MaxEnt) conditions, while the ZSPA algorithm affords solutions far from the MaxEnt conditions (van Smaalen et al, 2003). Therefore, overestimation of ΔF j 's for a few strong low-Q reflections with the Cambridge algorithm is an intrinsic tendency of MEM analysis from X-ray diffraction data (Jauch, 1994). The use of multiple F constraints or static weighting on the basis of d j 2 in combination with the Cambridge algorithm corrected such a tendency, giving higher entropy electron densities with R indices comparable to those obtained with the ZSPA algorithm (Table I).…”

Section: A Taurinementioning

confidence: 99%

“…If a reflection with a very large d j value has the largest ΔF j , weighting on the basis of d j x is worth a try. At the solution of MEM with the classical F constraint, the following condition must be satisfied (Jauch, 1994):…”

Section: Mpf Analysis Guidelinesmentioning

confidence: 99%

“…One of the errors is caused by a seriestermination effect arising from the availability of only a limited number of reflections (Jauch, 1994;de Vries et al, 1996;Palatinus and van Smaalen, 2002), although this effect is much less significant in MEM than in Fourier synthesis. On the analysis of X-ray diffraction data, MEM also tends to give large residual errors for some low-Q reflections that contribute most significantly to information entropy, S. Such a tendency of MEM often generates artifacts in calculated electron densities even if accurate standard uncertainties, σ(h j ), of F obs (h j )'s are obtainable (de Vries et al, 1994;Palatinus and van Smaalen, 2002).…”

Section: Introductionmentioning

confidence: 99%

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Dysnomia, a computer program for maximum-entropy method (MEM) analysis and its performance in the MEM-based pattern fitting

et al. 2013

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A computer program, Dysnomia, for the maximum-entropy method (MEM) has been tested for the evaluation and advancement of MEM-based pattern fitting (MPF). Dysnomia is a successor to PRIMA, which was the only program integrated with RIETAN-FP for MPF. Two types of MEM algorithms, i.e., 0th-order single-pixel approximation and a variant of the Cambridge algorithm, were implemented in Dysnomia in combination with a linear combination of the "generalized F constraints" and arbitrary weighting factors for them. Dysnomia excels PRIMA in computation speed, memory efficiency, and scalability owing to parallel processing and automatic switching of discrete Fourier transform and fast Fourier transform depending on sizes of grids and observed reflections. These features of Dysnomia were evaluated for MPF analyses from X-ray powder diffraction data of three different types of compounds: taurine, Cu 2 CO 3 (OH) 2 (malachite), and Sr 9 In(PO 4 ) 7 . Reliability indices in MPF analyses proved to have been improved by using multiple F constraints and weighting factors based on lattice-plane spacings, d, in comparison with those obtained with PRIMA.

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Section: A Taurinementioning

confidence: 99%

Section: Mpf Analysis Guidelinesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dysnomia, a computer program for maximum-entropy method (MEM) analysis and its performance in the MEM-based pattern fitting

et al. 2013

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“…They will always tend to deteriorate the MEM map. Recently, Jauch (1994) has pointed out that MEM maps are susceptible to exhibiting similar artifacts to those inherent in Fourier inversion depending on data completeness, error accumulation at special positions etc. Consequently, it is very important to reduce all kinds of systematic errors as much as possible in order to construct an 'accurate' electron density from observed data with the MEM.…”

Section: Introductionmentioning

confidence: 99%

The Influence of the Completeness of the Data Set on the Charge Density Obtained with the Maximum-Entropy Method. A Re-examination of the Electron-Density Distribution in Si

Takata¹,

Sakata²

1996

Acta Cryst Sect A

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The charge densities derived with the maximum-entropy method (MEM) may be influenced to some extent by the completeness of the data set. In order to examine the effects of the incompleteness, structure-factor data of Si measured by the PendellOsung method [Saka & Kato (1986). Acta Cryst. A42, 469-478] were re-analysed by the MEM. This data set is incomplete: it contains all space-group-allowed reflections with sin 0/2 = 0.86i -I, and in addition 844 and 880 with sin0/2 = 1.04,~, -1. Results of a MEM analysis of the complete subset of data are compared with those from the full but incomplete set published previously [Sakata & Sato (1990). Acta Cryst. A46, 263-270]. The smaller but complete set was found to give a smooth charge-density distribution that is consistent with previous theoretical work. It is found that the sharp peak maximum at the bond midpoint reported previously is exaggerated owing to the highest-order reflection 880. The completeness of the data set appears to be one of the key factors for obtaining reliable charge densities with MEM. The incompleteness of the data set may cause non-physical fine features of the MEM density distribution.

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“…2a), suggests that some minor artifacts do crop up. In light of this, as well as the general criticisms put forward by Jauch & Palmer (1993) and Jauch (1994) concerning MAXENT reconstructions, it is important to view this as a qualitative tool, designed to reveal the general spin-density features and as an aid to model development. It is for the latter that we imagine MAXENT to be most useful, helping to suggest an appropriate description and checking existing models for consistency.…”

Section: Discussionmentioning

confidence: 99%

A General Maximum-Entropy Method for Model-Free Reconstructions of Magnetization Densities from Polarized Neutron Diffraction Data

Schleger¹,

Puig-Molina²,

Ressouche³

et al. 1997

Acta Cryst Sect A

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A general method for the model-free reconstruction of magnetization densities is presented. The technique is based upon the maximum-entropy principle and is valid for systems with any space-group symmetry, any physically reasonable ordered moment and allows for the incorporation of relevant corrections such as extinction. Thus, it is possible, for the first time, to reconstruct the real-space magnetization densities in essentially any physical system exhibiting a ferromagnetic spin alignment (either natural or induced) from polarized neutron diffraction experiments. The technique is illustrated for the purely organic ferromagnet, fl-4,4,5,5-tetramethyl-2-p-(nitrophenyl)-3-oxido-4,5-dihydroimidazolium 1-oxyl.

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The maximum-entropy method in charge-density studies. II. General aspects of reliability

Cited by 38 publications

References 5 publications

Dysnomia, a computer program for maximum-entropy method (MEM) analysis and its performance in the MEM-based pattern fitting

Dysnomia, a computer program for maximum-entropy method (MEM) analysis and its performance in the MEM-based pattern fitting

The Influence of the Completeness of the Data Set on the Charge Density Obtained with the Maximum-Entropy Method. A Re-examination of the Electron-Density Distribution in Si

A General Maximum-Entropy Method for Model-Free Reconstructions of Magnetization Densities from Polarized Neutron Diffraction Data

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