Charge density study with the Maximum Entropy Method on model data of silicon. A search for non-nuclear attractors

1996 ◽  
Vol 74 (6) ◽  
pp. 1054-1058 ◽  
Author(s):  
R.Y. de Vries ◽  
W.J. Briels ◽  
D. Fell ◽  
G. te Velde ◽  
E.J. Baerends
Keyword(s):  
Charge Density ◽  
Maximum Entropy ◽  
Density Functional ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
X Ray Diffraction ◽  
Functional Theory ◽  
Structure Factors ◽  
The Density Functional Theory ◽  
Structure Calculations

In 1990 Sakata and Sato applied the maximum entropy method (MEM) to a set of structure factors measured earlier by Saka and Kato with the Pendellösung method. They found the presence of non-nuclear attractors, i.e., maxima in the density between two bonded atoms. We applied the MEM to a limited set of Fourier data calculated from a known electron density distribution (EDD) of silicon. The EDD of silicon was calculated with the program ADF-BAND. This program performs electronic structure calculations, including periodicity, based on the density functional theory of Hohenberg and Kohn. No non-nuclear attractor between two bonded silicon atoms was observed in this density. Structure factors were calculated from this density and the same set of structure factors that was measured by Saka and Kato was used in the MEM analysis. The EDD obtained with the MEM shows the same non-nuclear attractors that were later obtained by Sakata and Sato. This means that the non-nuclear attractors in silicon are really an artefact of the MEM. Key words: Maximum Entropy Method, non-nuclear attractors, charge density. X-ray diffraction.

Charge density of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione. A comprehensive multipole refinement, maximum entropy method and density functional theory study

2020 ◽  
Vol 76 (3) ◽  
pp. 450-468
Author(s):  
Barbora Vénosová ◽  
Julia Koziskova ◽  
Jozef Kožíšek ◽  
Peter Herich ◽  
Karol Lušpai ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Charge Density ◽  
Maximum Entropy ◽  
Density Functional ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Experimental Results ◽  
Basis Set ◽  
Functional Theory ◽  
Radial Functions

The structure of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione (MTTOTHP) was investigated using X-ray diffraction and computational chemistry methods for determining properties of the nitrogen—oxygen bond, which is the least stable entity upon photochemical excitation. Experimentally measured structure factors have been used to determine and characterize charge density via the multipole model (MM) and the maximum entropy method (MEM). Theoretical investigation of the electron density and the electronic structure has been performed in the finite basis set density functional theory (DFT) framework. Quantum Theory of Atoms In Molecules (QTAIM), deformation densities and Laplacians maps have been used to compare theoretical and experimental results. MM experimental results and predictions from theory differ with respect to the sign and/or magnitude of the Laplacian at the N—O bond critical point (BCP), depending on the treatment of n values of the MM radial functions. Such Laplacian differences in the N—O bond case are discussed with respect to a lack of flexibility in the MM radial functions also reported by Rykounov et al. [Acta Cryst. (2011), B67, 425–436]. BCP Hessian eigenvalues show qualitatively matching results between MM and DFT. In addition, the theoretical analysis used domain-averaged fermi holes (DAFH), natural bond orbital (NBO) analysis and localized (LOC) orbitals to characterize the N—O bond as a single σ bond with marginal π character. Hirshfeld atom refinement (HAR) has been employed to compare to the MM refinement results and/or neutron dataset C—H bond lengths and to crystal or single molecule geometry optimizations, including considerations of anisotropy of H atoms. Our findings help to understand properties of molecules like MTTOTHP as progenitors of free oxygen radicals.

scholarly journals Structural and Charge Density Properties of Manganese Sulfide

2019 ◽  
Vol 9 (2S2) ◽  
pp. 313-315
Keyword(s):  
Charge Density ◽  
Maximum Entropy Method ◽  
Manganese Sulfide ◽  
Entropy Method ◽  
Data Sets ◽  
X Ray Diffraction ◽  
Structure Factors ◽  
Density Analysis ◽  
Distribution Studies ◽  
Profile Refinement

Single phased Manganese Sulfide was analyzed by powder X-ray diffraction (PXRD) data sets with cubic structure. The simulated XRD data sets were used to analyze the structure of manganese sulfide. The powder profile refinements were done by Rietveld profile refinement technique. The refinement results were subjected to analyze the charge density analysis using structure factors. The chemical bonding nature between Mn and S were analyzed by charge density distribution studies through maximum entropy method. From MEM analsysis, it found that the bonding between Mn and S atoms is ionic in nature.

scholarly journals Применение метода максимальной энтропии к временным рядам, получаемым в реальном времени в рамках нестационарной теории функционала плотности

2021 ◽  
pp. 64-73
Author(s):  
Y. Zempo ◽  
S.S. Kano
Keyword(s):  
Density Functional Theory ◽  
Spectral Analysis ◽  
Dipole Moment ◽  
Maximum Entropy ◽  
Density Functional ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Data Set ◽  
Functional Theory ◽  
Raw Data

The maximum entropy method is one of the key techniques for spectral analysis. The main feature is to describe spectra in low frequency with short timeseries data. We adopted the maximum entropy method to analyze the spectrum from the dipole moment obtained by the timedependent density functional theory calculation in real time, which is intensively studied and applied to computing optical properties. In the maximum entropy method analysis, we proposed that we use the concatenated data set made from severaltimes repeated raw data together with the phase. We have applied this technique to spectral analysis of the dynamic dipole moment obtained from timedependent density functional theory dipole moment of several molecules such as oligofluorene with n = 8. As a result, the higher resolution can be obtained without any peak shift due to the phase jump. The peak position is in good agreement to that of FT with just raw data. This paper presents the efficiency and characteristic features of this technique. Метод максимальной энтропии — один из основных в спектральном анализе. Его главная особенность — описание низкочастотных спектров короткими временными рядами данных. Авторы применили метод максимальной энтропии для анализа спектров дипольного момента, полученных расчетами в реальном времени по нестационарной теории функционала плотности. Данный вопрос интенсивно изучается и находит практическое применение при расчетах оптических свойств. При анализе методом максимальной энтропии предложено использовать объединенные наборы данных, включающие несколько повторяющихся последовательностей исходных данных с учетом фазы. Данный метод был применен при проведении спектрального анализа динамического дипольного момента, рассчитанного по нестационарной теории функционала плотности на основе дипольного момента нескольких молекул — в частности, молекул олигофлуорена при n = 8. В итоге удалось повысить разрешение без смещения максимумов из-за скачка фазы. Положение максимумов хорошо согласуется с результатами применения преобразования Фурье к необработанным исходным данным. В настоящей статье представлены особенности данного метода и показатели его эффективности.

scholarly journals Experimental and ab initio study of the structural and optical properties of ZnO coatings: Performance of the DFT+U approach

2020 ◽  
Vol 14 (4) ◽  
pp. 362-371
Author(s):  
Agustín Apaolaza ◽  
Diego Richard ◽  
Matías Tejerina
Keyword(s):  
Optical Properties ◽  
Density Functional ◽  
Spray Pyrolysis Technique ◽  
Optical Transmittance ◽  
Accurate Method ◽  
X Ray Diffraction ◽  
Functional Theory ◽  
The Density Functional Theory ◽  
Structure Calculations ◽  
Comprehensive Study

In this work, ZnO coatings were produced by the spray-pyrolysis technique and characterized by scanning electron microscopy, X-ray diffraction and optical transmittance spectroscopy. The experimental results were compared to predictions obtained from electronic-structure calculations based on the Density Functional Theory plus U (DFT+U) approach. To this purpose, the 2H, 4H and 6H polytypes of ZnO were theoretically analysed, and DFT+U was assessed for the calculation of structural, electronic and optical properties of the hexagonal ZnO structures. We found that DFT+U is an effective and accurate method that combined with experimental measurements, allows a deeper insight about the coatings of the wurtzite (2H) phase synthesized in the laboratory. This comprehensive study of the pure ZnO is the first step towards the study of more complex ZnO-based coatings.

scholarly journals Location of Cu2+in CHA zeolite investigated by X-ray diffraction using the Rietveld/maximum entropy method

IUCrJ ◽  
2014 ◽  
Vol 1 (6) ◽  
pp. 382-386 ◽  
Author(s):  
Casper Welzel Andersen ◽  
Martin Bremholm ◽  
Peter Nicolai Ravnborg Vennestrøm ◽  
Anders Bank Blichfeld ◽  
Lars Fahl Lundegaard ◽  
...  
Keyword(s):  
Maximum Entropy ◽  
Density Functional ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Membered Ring ◽  
Zeolite Catalysts ◽  
Structural Description ◽  
X Ray Diffraction ◽  
X Ray ◽  
Catalytically Active

Accurate structural models of reaction centres in zeolite catalysts are a prerequisite for mechanistic studies and further improvements to the catalytic performance. The Rietveld/maximum entropy method is applied to synchrotron powder X-ray diffraction data on fully dehydrated CHA-type zeolites with and without loading of catalytically active Cu2+for the selective catalytic reduction of NOxwith NH3. The method identifies the known Cu2+sites in the six-membered ring and a not previously observed site in the eight-membered ring. The sum of the refined Cu occupancies for these two sites matches the chemical analysis and thus all the Cu is accounted for. It is furthermore shown that approximately 80% of the Cu2+is located in the new 8-ring site for an industrially relevant CHA zeolite with Si/Al = 15.5 and Cu/Al = 0.45. Density functional theory calculations are used to corroborate the positions and identity of the two Cu sites, leading to the most complete structural description of dehydrated silicoaluminate CHA loaded with catalytically active Cu2+cations.

Maximum Entropy Method Charge Density Distributions of Novel Thermoelectric Clathrates

1999 ◽  
Vol 590 ◽  
Author(s):  
B. Iversen ◽  
A. Bentien ◽  
A. Palmqvist ◽  
D. Bryan ◽  
S. Latturner ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Charge Density ◽  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Mixed Valence ◽  
Entropy Method ◽  
X Ray Diffraction ◽  
X Ray ◽  
Density Distributions ◽  
Positively Charged

ABSTRACTRecently materials with promising thermoelectric properties were discovered among the clathrates. Transport data has indicated that these materials have some of the characteristics of a good thermoelectric, namely a low thermal conductivity and a high electrical conductivity. Based on synchrotron powder and conventional single crystal x-ray diffraction data we have determined the charge density distribution in Sr8Ga16Ge3O using the Maximum Entropy Method. The MEM density shows clear evidence of guest atom rattling, and this contributes to the reduction of the thermal conductivity. Analysis of the charge distribution reveals that Sr8Ga16Ge30 contains mixed valence alkaline earth guest atoms. The Sr atoms in the small cavities are, as expected, doubly positively charged, whereas the Sr atoms in the large cavities appear negatively charged. The MEM density furthermore suggests that the Ga and Ge atoms may not be randomly disordered on the framework sites as found in the conventional leastsquares refinements.

Nuclear and charge density distributions in ferroelectric PbTiO3: maximum entropy method analysis of neutron and X-ray diffraction data

2013 ◽  
Vol 28 (4) ◽  
pp. 276-280 ◽  
Author(s):  
Jinlong Zhu ◽  
Wei Han ◽  
Jianzhong Zhang ◽  
Hongwu Xu ◽  
Sven C. Vogel ◽  
...  
Keyword(s):  
Charge Density ◽  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Rietveld Analysis ◽  
Entropy Method ◽  
X Ray Diffraction ◽  
X Ray ◽  
Density Distributions ◽  
Increasing Temperature ◽  
Ionic States

We conducted in-situ high-temperature neutron and X-ray diffraction studies on tetragonal PbTiO3. Using a combination of Rietveld analysis and Maximum Entropy Method, the nuclear and charge density distributions were determined as a function of temperature up to 460 °C. The ionic states obtained from charge density distributions reveal that the covalency of Pb–O2 bonds gradually weakens with increasing temperature. The spontaneous polarizations calculated from the contributions of ionic state, ionic displacement, and nuclear polarization, are in good agreement with the experimental measurements. This method provides an effective approach to determine spontaneous polarizations in multiferroics with high-current leakage and low resistance.

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