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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:245

Article

Lin, Lin¹  Shao, Sihong^2,3  Weinan, E.^4,5,6 

[1] Lawrence Berkeley Natl Lab, Computat Res Div, Berkeley, CA 94720 USA

[2] Peking Univ, LMAM, Beijing 100871, Peoples R China

[3] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

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

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

[6] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China

关键词: Relativistic density functional theory;    Dirac-Kohn-Sham equations;    Spin-orbit coupling;    Iterative methods;    LOBPCG-F;    Variational collapse;    Spectral pollution;   

DOI  :  10.1016/j.jcp.2013.03.030

来源: Elsevier

【 摘 要 】

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 Bi2Se3 indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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