scholarly journals Resolution of the Kohn-Sham equation using real space discretization with finite elements

Anales AFA ◽  
2013 ◽  
Vol 23 (1) ◽  
pp. 182-184
Author(s):  
A. Soba ◽  
E. A. Bea ◽  
G. Houzeaux
Keyword(s):  
Finite Elements ◽  
Real Space ◽  
Sham Equation ◽  
Space Discretization

A Kohn–Sham equation solver based on hexahedral finite elements

2012 ◽  
Vol 231 (8) ◽  
pp. 3166-3180 ◽  
Author(s):  
Jun Fang ◽  
Xingyu Gao ◽  
Aihui Zhou
Keyword(s):  
Finite Elements ◽  
Sham Equation

scholarly journals Three real-space discretization techniques in electronic structure calculations

2006 ◽  
Vol 243 (5) ◽  
pp. 1016-1053 ◽  
Author(s):  
T. Torsti ◽  
T. Eirola ◽  
J. Enkovaara ◽  
T. Hakala ◽  
P. Havu ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Electronic Structure Calculations ◽  
Real Space ◽  
Space Discretization ◽  
Structure Calculations

Towards Translational Invariance of Total Energy with Finite Element Methods for Kohn-Sham Equation

2016 ◽  
Vol 19 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Gang Bao ◽  
Guanghui Hu ◽  
Di Liu
Keyword(s):  
Finite Element ◽  
Total Energy ◽  
Finite Element Methods ◽  
Electronic System ◽  
Hamiltonian Operator ◽  
Real Space ◽  
Error Estimator ◽  
Adaptive Finite Element ◽  
Translational Invariance ◽  
Sham Equation

AbstractNumerical oscillation of the total energy can be observed when the Kohn- Sham equation is solved by real-space methods to simulate the translational move of an electronic system. Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure, but also for the study of molecular dynamics. In this paper, we study such unphysical oscillation based on the numerical framework in [G. Bao, G. H. Hu, and D. Liu, An h-adaptive finite element solver for the calculations of the electronic structures, Journal of Computational Physics, Volume 231, Issue 14, Pages 4967–4979, 2012], and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations, including a stabilized cubature strategy for Hamiltonian operator, and an a posteriori error estimator of the finite element methods for Kohn-Sham equation. The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.

High-resolution structure determination by ALCHEMI

1983 ◽  
Vol 41 ◽  
pp. 178-181 ◽  
Author(s):  
Peter G. Self ◽  
Peter R. Buseck
Keyword(s):  
Site Occupancy ◽  
Real Space ◽  
Unit Cell ◽  
Bragg Angle ◽  
Electron Current ◽  
High Resolution Structure ◽  
Beam Incident ◽  
Crystallographic Planes ◽  
Electron Beam Incident ◽  
Resolution Structure

ALCHEMI (Atom Location by CHanneling Enhanced Microanalysis) enables the site occupancy of atoms in single crystals to be determined. In this article the fundamentals of the method for both EDS and EELS will be discussed. Unlike HRTEM, ALCHEMI does not place stringent resolution requirements on the microscope and, because EDS clearly distinguishes between elements of similar atomic number, it can offer some advantages over HRTEM. It does however, place certain constraints on the crystal. These constraints are: a) the sites of interest must lie on alternate crystallographic planes, b) the projected charge density on the alternate planes must be significantly different, and c) there must be at least one atomic species that lies solely on one of the planes.An electron beam incident on a crystal undergoes elastic scattering; in reciprocal space this is seen as a diffraction pattern and in real space this is a modulation of the electron current across the unit cell. When diffraction is strong (i.e., when the crystal is oriented near to the Bragg angle of a low-order reflection) the electron current at one point in the unit cell will differ significantly from that at another point.

An Image Reconstruction System Applied to High Voltage Microscopy

1975 ◽  
Vol 33 ◽  
pp. 292-293
Author(s):  
D. E. Johnson
Keyword(s):  
High Voltage ◽  
Prior Information ◽  
Block Diagram ◽  
Three Dimensional ◽  
Real Space ◽  
Two Dimensional ◽  
Efficient Manner ◽  
Fourier Methods ◽  
Tilt Series ◽  
Methods Of Reconstruction

Increased specimen penetration; the principle advantage of high voltage microscopy, is accompanied by an increased need to utilize information on three dimensional specimen structure available in the form of two dimensional projections (i.e. micrographs). We are engaged in a program to develop methods which allow the maximum use of information contained in a through tilt series of micrographs to determine three dimensional speciman structure.In general, we are dealing with structures lacking in symmetry and with projections available from only a limited span of angles (±60°). For these reasons, we must make maximum use of any prior information available about the specimen. To do this in the most efficient manner, we have concentrated on iterative, real space methods rather than Fourier methods of reconstruction. The particular iterative algorithm we have developed is given in detail in ref. 3. A block diagram of the complete reconstruction system is shown in fig. 1.

Correlation averaging of two-dimensional crystals: basic strategy and refinements

1986 ◽  
Vol 44 ◽  
pp. 136-139
Author(s):  
W. Baumeister ◽  
R. Rachel ◽  
R. Guckenberger ◽  
R. Hegerl
Keyword(s):  
Low Dose ◽  
Signal To Noise Ratio ◽  
Real Space ◽  
Fourier Domain ◽  
Two Dimensional ◽  
Signal To Noise ◽  
Unit Cells ◽  
Lateral Displacements ◽  
Established Technique ◽  
Crystalline Array

IntroductionCorrelation averaging (CAV) is meanwhile an established technique in image processing of two-dimensional crystals /1,2/. The basic idea is to detect the real positions of unit cells in a crystalline array by means of correlation functions and to average them by real space superposition of the aligned motifs. The signal-to-noise ratio improves in proportion to the number of motifs included in the average. Unlike filtering in the Fourier domain, CAV corrects for lateral displacements of the unit cells; thus it avoids the loss of resolution entailed by these distortions in the conventional approach. Here we report on some variants of the method, aimed at retrieving a maximum of information from images with very low signal-to-noise ratios (low dose microscopy of unstained or lightly stained specimens) while keeping the procedure economical.

Probing vacancies and structural distortions at individual defects in ceramics using EELS

1996 ◽  
Vol 54 ◽  
pp. 678-679
Author(s):  
D. J. Wallis ◽  
N. D. Browning
Keyword(s):  
Structural Information ◽  
Core Loss ◽  
Nearest Neighbors ◽  
Ceramic Materials ◽  
Scanning Transmission Electron Microscope ◽  
Real Space ◽  
Atomic Scale ◽  
Structure Property ◽  
Scanning Transmission ◽  
Key Issues

In electron energy loss spectroscopy (EELS), the near-edge region of a core-loss edge contains information on high-order atomic correlations. These correlations give details of the 3-D atomic structure which can be elucidated using multiple-scattering (MS) theory. MS calculations use real space clusters making them ideal for use in low-symmetry systems such as defects and interfaces. When coupled with the atomic spatial resolution capabilities of the scanning transmission electron microscope (STEM), there therefore exists the ability to obtain 3-D structural information from individual atomic scale structures. For ceramic materials where the structure-property relationships are dominated by defects and interfaces, this methodology can provide unique information on key issues such as like-ion repulsion and the presence of vacancies, impurities and structural distortion.An example of the use of MS-theory is shown in fig 1, where an experimental oxygen K-edge from SrTiO3 is compared to full MS-calculations for successive shells (a shell consists of neighboring atoms, so that 1 shell includes only nearest neighbors, 2 shells includes first and second-nearest neighbors, and so on).

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