Probabilistic characterization of soil properties based on the maximum entropy method from fractional moments: model development, case study, and application

2021 ◽  
pp. 108218
Author(s):  
Jian Deng
Keyword(s):  
Soil Properties ◽  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Model Development ◽  
Entropy Method ◽  
Probabilistic Characterization ◽  
Fractional Moments

Electron densities by the maximum entropy method (MEM) for various types of prior densities: a case study on three amino acids and a tripeptide

2013 ◽  
Vol 69 (2) ◽  
pp. 203-213 ◽  
Author(s):  
Siriyara Jagannatha Prathapa ◽  
Swastik Mondal ◽  
Sander van Smaalen
Keyword(s):  
Maximum Entropy ◽  
Dynamic Model ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Topological Descriptors ◽  
Acta Cryst ◽  
Density Maps ◽  
Large Spread ◽  
Better Than

Dynamic model densities according to Mondalet al.[(2012),Acta Cryst.A68, 568–581] are presented for independent atom models (IAM), IAMs after high-order refinements (IAM-HO), invariom (INV) models and multipole (MP) models of α-glycine, DL-serine, L-alanine and Ala–Tyr–Ala atT≃ 20 K. Each dynamic model density is used as prior in the calculation of electron density according to the maximum entropy method (MEM). We show that at the bond-critical points (BCPs) of covalent C—C and C—N bonds the IAM-HO and INV priors produce reliable MEM density maps, including reliable values for the density and its Laplacian. The agreement between these MEM density maps and dynamic MP density maps is less good for polar C—O bonds, which is explained by the large spread of values of topological descriptors of C—O bonds in static MP densities. The density and Laplacian at BCPs of hydrogen bonds have similar values in MEM density maps obtained with all four kinds of prior densities. This feature is related to the smaller spatial variation of the densities in these regions, as expressed by small magnitudes of the Laplacians and the densities. It is concluded that the use of the IAM-HO prior instead of the IAM prior leads to improved MEM density maps. This observation shows interesting parallels to MP refinements, where the use of the IAM-HO as an initial model is the accepted procedure for solving MP parameters. A deconvolution of thermal motion and static density that is better than the deconvolution of the IAM appears to be necessary in order to arrive at the best MP models as well as at the best MEM densities.

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

2009 ◽  
Vol 65 (5) ◽  
pp. 624-638 ◽  
Author(s):  
Jeanette Netzel ◽  
Sander van Smaalen
Keyword(s):  
Hydrogen Bonds ◽  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Dynamic Deformation ◽  
Entropy Method ◽  
Topological Properties ◽  
Covalent Bonds ◽  
Charge Densities

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 (l max = 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.

scholarly journals Characterization of Local Distortions in Thermoelectric Lead Chalcogenides

2014 ◽  
Vol 70 (a1) ◽  
pp. C106-C106
Author(s):  
Niels Bindzus ◽  
Sebastian Christensen ◽  
Mogens Christensen ◽  
Bo Iversen
Keyword(s):  
Neutron Diffraction ◽  
Maximum Entropy ◽  
Diffraction Data ◽  
Thermoelectric Materials ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Neutron Diffraction Data ◽  
Lead Chalcogenides ◽  
X Ray

Thermoelectric materials are functional materials with the unique ability to interconvert heat and electricity, holding much promise for green energy solutions such as efficient waste heat recovery. The extraordinary thermoelectric performance of binary lead chalcogenides has caused huge research activity, but the mechanisms governing their unexpected low thermal conductivity still remain a controversial topic. It has been proposed to result from giant anharmonic phonon scattering or from local fluctuating dipoles on the Pb site, emerging with temperature on the Pb site.[1,2] No macroscopic symmetry change are associated with these effects, rendering them invisible to conventional crystallographic techniques. For this reason lead chalcogenides were until recently believed to adopt the ideal, undistorted rock-salt structure. In the present study, we probe the peculiar structural features in PbX (X = S, Se, Te) using multi-temperature synchrotron powder X-ray diffraction data in combination with the maximum entropy method. Distorted atoms are detected and quantified by refinement of anharmonic probability density functions. The charge density analysis is complemented by nuclear density distributions (NDDs) reconstructed from neutron diffraction data and by a novel method: Nuclear Enhanced X-ray Maximum Entropy Method (NEXMEM). NEXMEM offers an alternative route to experimental NDDs, exploiting the superior quality of synchrotron X-ray data compared to neutron diffraction data. The increased atomic resolution introduced by NEXMEM proved essential for resolving atomic distortions, see figure below showing Pb in the (100) plane. Our findings outline the extent of disorder and anharmonicity in binary lead chalcogenides, promoting our fundamental understanding of this class of high-performance thermoelectric materials. The applied approach can be used in general, opening up for widespread characterization of subtle features in crystals with unusual properties.

Direct comparison of phase-sensitive vibrational sum frequency generation with maximum entropy method: Case study of water

2011 ◽  
Vol 135 (22) ◽  
pp. 224701 ◽  
Author(s):  
Alex G. F. de Beer ◽  
Jean-Sebastièn Samson ◽  
Wei Hua ◽  
Zishuai Huang ◽  
Xiangke Chen ◽  
...  
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Sum Frequency Generation ◽  
Sum Frequency ◽  
Phase Sensitive ◽  
Frequency Generation

MEM Calculations on Apatites Containing Peroxide Using BAYMEM and TOPAS

2010 ◽  
Vol 651 ◽  
pp. 105-116 ◽  
Author(s):  
Ali Samy ◽  
Robert E. Dinnebier ◽  
Pavel E. Kazin ◽  
Sander van Smaalen ◽  
Martin Jansen
Keyword(s):  
Global Optimization ◽  
Least Squares ◽  
Maximum Entropy ◽  
Crystal Structures ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Optimization Program ◽  
User Friendly ◽  
Hydroxyl Apatite

A set of macros for the powerful least squares and global optimization program TOPAS has been written in order to create a user friendly interface to the maximum entropy method (MEM) program BayMem. As a case study, the crystal structures of pure strontium hydroxyl apatite and strontium hydroxyl apatite with approximately 10% of the hydroxyl anions substituted by peroxide anions were analyzed by TOPAS and BayMem. Although the concentration of peroxide is relatively small, distinct differences in the two crystal structures could be made visible by the MEM.

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