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Finite element solution of the Kohn‐Sham equations
Author(s) -
Schauer Volker,
Linder Christian
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110237
Subject(s) - kohn–sham equations , density functional theory , coulomb , electron , context (archaeology) , physics , magnetism , electronic density , finite element method , electronic structure , quantum , orbital free density functional theory , nonlinear system , quantum mechanics , time dependent density functional theory , thermodynamics , paleontology , biology
Many properties of condensed matter as for example electric conductivity, magnetism as well as the mechanical response upon external excitations are determined by the electronic structure of the material. Its evaluation represents a coupled, quantum mechanical many body problem, consisting of the positively charged atomic cores and the negatively charged, fermionic electrons. By the Hohenberg‐Kohn theorem a method was established to calculate the ground state electron density through a density functional. Then the Kohn‐Sham equations resemble a nonlinear, single electron problem with an effective potential, accounting for the Coulomb interactions between the particles as well as for quantum mechanical effects. They can be solved within a self consistent field procedure. In this work a real space formulation for the calculation of the electronic structure in the context of density functional theory is shown. In a first step a finite element based solution algorithm for the Kohn‐Sham equations is developed, based upon which the electron density is obtained in a non‐periodic setting. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)