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Locally Refined Multigrid Solution of the All-Electron Kohn-Sham Equation
Or Cohen1, Leeor Kronik1, Achi Brandt1
1Department 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.
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.
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