TY - JOUR

T1 - Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I

T2 - Total energy calculation

AU - Lin, Lin

AU - Lu, Jianfeng

AU - Ying, Lexing

AU - E, Weinan

N1 - Funding Information:
This work is partially supported by DOE under Contract No. DE-FG02-03ER25587 and by ONR under Contract No. N00014–01-1–0674 (W. E and L. L.), and by a Sloan Research Fellowship and by NSF CAREER Grant DMS-0846501 (L. Y.). We thank the National Energy Research Scientific Computing Center (NERSC) , and the Texas Advanced Computing Center (TACC) for the support to perform the calculations. L. L. and J. L. thank the University of Texas at Austin for the hospitality where the idea of this paper starts.

PY - 2012/2/20

Y1 - 2012/2/20

N2 - 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.

AB - 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.

KW - Adaptive local basis set

KW - Discontinuous Galerkin

KW - Eigenvalue problem

KW - Electronic structure

KW - Enrichment functions

KW - Kohn-Sham density functional theory

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U2 - 10.1016/j.jcp.2011.11.032

DO - 10.1016/j.jcp.2011.11.032

M3 - Article

AN - SCOPUS:84855163569

VL - 231

SP - 2140

EP - 2154

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 4

ER -