title: Locally Refined Multigrid Solution of the All-Electron Kohn-Sham Equation.
abstract: We present a fully numerical multigrid approach for solving the all-electron Kohn-Sham equation in molecules. The equation is represented on a hierarchy of Cartesian grids, from coarse ones that span the entire molecule to very fine ones that describe only a small volume around each atom. This approach is adaptable to any type of geometry. We demonstrate it for a variety of small molecules and obtain high accuracy agreement with results obtained previously for diatomic molecules using a prolate-spheroidal grid. We provide a detailed presentation of the numerical methodology and discuss possible extensions of this approach.
authors.affiliation: Department of Materials and Interfaces, ‡Department of Physics of Complex Systems, and §Department of Applied Mathematics and Computer Science, Weizmann Institute of Science , Rehovoth 76100, Israel.
authors.forename: Or
authors.initials: O
authors.lastname: Cohen
authors.affiliation: Department of Materials and Interfaces, ‡Department of Physics of Complex Systems, and §Department of Applied Mathematics and Computer Science, Weizmann Institute of Science , Rehovoth 76100, Israel.
authors.forename: Leeor
authors.initials: L
authors.lastname: Kronik
authors.affiliation: Department of Materials and Interfaces, ‡Department of Physics of Complex Systems, and §Department of Applied Mathematics and Computer Science, Weizmann Institute of Science , Rehovoth 76100, Israel.
authors.forename: Achi
authors.initials: A
authors.lastname: Brandt