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Title: All-electron Kohn–Sham density functional theory on hierarchic finite element spaces

In this work, a real space formulation of the Kohn–Sham equations is developed, making use of the hierarchy of finite element spaces from different polynomial order. The focus is laid on all-electron calculations, having the highest requirement onto the basis set, which must be able to represent the orthogonal eigenfunctions as well as the electrostatic potential. A careful numerical analysis is performed, which points out the numerical intricacies originating from the singularity of the nuclei and the necessity for approximations in the numerical setting, with the ambition to enable solutions within a predefined accuracy. In this context the influence of counter-charges in the Poisson equation, the requirement of a finite domain size, numerical quadratures and the mesh refinement are examined as well as the representation of the electrostatic potential in a high order finite element space. The performance and accuracy of the method is demonstrated in computations on noble gases. In addition the finite element basis proves its flexibility in the calculation of the bond-length as well as the dipole moment of the carbon monoxide molecule.
Authors:
 [1] ;  [2]
  1. Institute of Applied Mechanics (CE) Chair I, University of Stuttgart, 70550 Stuttgart, Pfaffenwaldring 7 (Germany)
  2. Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305 (United States)
Publication Date:
OSTI Identifier:
22230801
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 250; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; BOND LENGTHS; CARBON MONOXIDE; DENSITY FUNCTIONAL METHOD; DIPOLE MOMENTS; EIGENFUNCTIONS; EIGENVALUES; ELECTRON DENSITY; FINITE ELEMENT METHOD; MOLECULES; NUCLEI; NUMERICAL ANALYSIS; POISSON EQUATION; POLYNOMIALS; POTENTIALS; QUADRATURES; RARE GASES; SINGULARITY; SPACE