All-electron calculations with finite elements



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)