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Title: Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory

Abstract

We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt$$_{2}$$, Au$$_{2}$$, TlF, and Bi$$_{2}$$Se$$_{3}$$ indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.

Authors:
; ;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1172731
Report Number(s):
LBNL-5960E
DOE Contract Number:  
DE-AC02-05CH11231
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Name: Journal of Computational Physics
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS AND COMPUTING

Citation Formats

Lin, Lin, Shao, Sihong, and E, Weinan. Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory. United States: N. p., 2012. Web.
Lin, Lin, Shao, Sihong, & E, Weinan. Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory. United States.
Lin, Lin, Shao, Sihong, and E, Weinan. Tue . "Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory". United States. https://www.osti.gov/servlets/purl/1172731.
@article{osti_1172731,
title = {Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory},
author = {Lin, Lin and Shao, Sihong and E, Weinan},
abstractNote = {We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt$_{2}$, Au$_{2}$, TlF, and Bi$_{2}$Se$_{3}$ indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.},
doi = {},
journal = {Journal of Computational Physics},
number = ,
volume = ,
place = {United States},
year = {2012},
month = {11}
}