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

Journal Article · Tue Oct 01 00:00:00 EDT 2013 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2013.04.020· OSTI ID:22230801

Schauer, Volker ^[1]; Linder, Christian ^[2]

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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)

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.

• OSTI ID: 22230801
• Journal Information: Journal of Computational Physics, Vol. 250; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

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