Study of the BaTiO3electronic structure using the maximum entropy method and density functional theory calculations

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.

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

Успехи кибернетики / Russian Journal of Cybernetics ◽

10.51790/2712-9942-2021-2-2-5 ◽

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.

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

Canadian Journal of Chemistry ◽

10.1139/v96-118 ◽

1996 ◽

Vol 74 (6) ◽

pp. 1054-1058 ◽

Cited By ~ 12

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.

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Maximum Entropy Method Applied to Time-series Data in Real-time Time-Dependent Density Functional Theory

10.3390/entropy2021-09775 ◽

2021 ◽

Author(s):

Yasunari Zempo ◽

Satoru Kano

Keyword(s):

Density Functional Theory ◽

Time Series ◽

Density Functional ◽

Maximum Entropy Method ◽

Time Series Data ◽

Entropy Method ◽

Time Dependent ◽

Series Data ◽

Functional Theory ◽

Dependent Density

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A Joint Study on Juglone Metal Complexes by InfraredÂ Spectroscopy and Density Functional Theory Calculations

10.3390/ecsoc-17-e005 ◽

2013 ◽

Author(s):

Ines Mancini ◽

Andrea Defant ◽

Costantino Tomasi

Keyword(s):

Density Functional Theory ◽

Metal Complexes ◽

Density Functional ◽

Density Functional Theory Calculations ◽

Functional Theory ◽

Joint Study

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Is a Non-Transition Element Nitride Ferromagnet Ever Achievable? Indication of the N-N Pairing Instability

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc20061525 ◽

2006 ◽

Vol 71 (11-12) ◽

pp. 1525-1531 ◽

Cited By ~ 3

Author(s):

Wojciech Grochala

Keyword(s):

Density Functional Theory ◽

Density Functional ◽

Transition Element ◽

Density Functional Theory Calculations ◽

Functional Theory

The enthalpy of four polymorphs of CaN has been scrutinized at 0 and 100 GPa using density functional theory calculations. It is shown that structures of diamagnetic calcium diazenide (Ca2N2) are preferred over the cubic ferromagnetic polymorph (CaN) postulated before, both at 0 and 100 GPa.

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Tensor-structured algorithm for reduced-order scaling large-scale Kohn–Sham density functional theory calculations

npj Computational Materials ◽

10.1038/s41524-021-00517-5 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Chih-Chuen Lin ◽

Phani Motamarri ◽

Vikram Gavini

Keyword(s):

Density Functional Theory ◽

Density Functional ◽

Large Scale ◽

Density Functional Theory Calculations ◽

System Size ◽

Real Space ◽

Functional Theory ◽

Reduced Order ◽

Separable Approximation ◽

Tensor Basis

AbstractWe present a tensor-structured algorithm for efficient large-scale density functional theory (DFT) calculations by constructing a Tucker tensor basis that is adapted to the Kohn–Sham Hamiltonian and localized in real-space. The proposed approach uses an additive separable approximation to the Kohn–Sham Hamiltonian and an L1 localization technique to generate the 1-D localized functions that constitute the Tucker tensor basis. Numerical results show that the resulting Tucker tensor basis exhibits exponential convergence in the ground-state energy with increasing Tucker rank. Further, the proposed tensor-structured algorithm demonstrated sub-quadratic scaling with system-size for both systems with and without a gap, and involving many thousands of atoms. This reduced-order scaling has also resulted in the proposed approach outperforming plane-wave DFT implementation for systems beyond 2000 electrons.

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