Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:231

Article

Lin, Lin¹  Lu, Jianfeng²  Ying, Lexing^3,4  E, Weinan^5,6 

[1] Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA

[2] NYU, Courant Inst Math Sci, Dept Math, New York, NY 10012 USA

[3] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

[4] Univ Texas Austin, ICES, Austin, TX 78712 USA

[5] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[6] Princeton Univ, PACM, Princeton, NJ 08544 USA

关键词: Electronic structure;    Kohn-Sham density functional theory;    Discontinuous Galerkin;    Adaptive local basis set;    Enrichment functions;    Eigenvalue problem;   

DOI  :  10.1016/j.jcp.2011.11.032

来源: Elsevier

【 摘 要 】

Kohn-Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn-Sham Hamiltonian generally results in a large number of basis functions per atom in order to resolve the rapid oscillations of the Kohn-Sham orbitals around the nuclei. Previous attempts to reduce the number of basis functions per atom include the usage of atomic orbitals and similar objects, but the atomic orbitals generally require fine tuning in order to reach high accuracy. We present a novel discretization scheme that adaptively and systematically builds the rapid oscillations of the Kohn-Sham orbitals around the nuclei as well as environmental effects into the basis functions. The resulting basis functions are localized in the real space, and are discontinuous in the global domain. The continuous Kohn-Sham orbitals and the electron density are evaluated from the discontinuous basis functions using the discontinuous Galerkin (DG) framework. Our method is implemented in parallel and the current implementation is able to handle systems with at least thousands of atoms. Numerical examples indicate that our method can reach very high accuracy (less than 1 meV) with a very small number (4-40) of basis functions per atom. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free