Premium
All‐electron calculations with finite elements
Author(s) -
Schauer Volker,
Linder Christian
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210165
Subject(s) - wave function , eigenvalues and eigenvectors , electron , coulomb , consistency (knowledge bases) , xenon , electronic structure , gravitational singularity , field (mathematics) , nonlinear system , noble gas , physics , quantum mechanics , atomic physics , mathematics , pure mathematics , geometry
The Kohn‐Sham equations resemble a nonlinear eigenvalue problem for the determination of the electronic structure of an atomic system, where the electrons are exposed to an effective potential, accounting for the Coulomb and quantum mechanical interactions between the particles. The effectiveness of the potential requires an iterative solution procedure, until self‐consistency is reached. This work illustrates the implementation of the self consistent field algorithm based on nested finite elements spaces and analyzes its properties in the case of all‐electron calculations on atoms as large as the noble gas Xenon. All‐electron calculations have maximal requirements onto the numerical basis, as it must be able to represent all the orthogonal electronic wavefunctions simultaneously together with the electrostatic potential, showing singularities at the positions of the atoms. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)