SCDM-k: Localized orbitals for solids via selected columns of the density matrix

JOURNAL OF COMPUTATIONAL PHYSICS

卷:334

Article

Damle, Anil¹  Lin, Lin^1,2  Ying, Lexing^3,4 

[1] Univ Calif, Dept Math, Berkeley, CA 94720 USA

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

[3] Stanford Univ, Inst Computat & Math Engn, Stanford, CA 94305 USA

[4] Stanford Univ, Dept Math, Stanford, CA 94305 USA

关键词: Kohn-Sham density functional theory;    Localized orbitals;    Brillouin zone sampling;    Density matrix;    Interpolative decomposition;   

DOI  :  10.1016/j.jcp.2016.12.053

来源: Elsevier

【 摘 要 】

The recently developed selected columns of the density matrix (SCDM) method (Damle et al. 2015, [16]) is a simple, robust, efficient and highly parallelizable method for constructing localized orbitals from a set of delocalized Kohn-Sham orbitals for insulators and semiconductors with r point sampling of the Brillouin zone. In this work we generalize the SCDM method to Kohn-Sham density functional theory calculations with k-point sampling of the Brillouin zone, which is needed for more general electronic structure calculations for solids. We demonstrate that our new method, called SCDM-k, is by construction gauge independent and a natural way to describe localized orbitals. SCDM-k computes localized orbitals without the use of an optimization procedure, and thus does not suffer from the possibility of being trapped in a local minimum. Furthermore, the computational complexity of using SCDM-k to construct orthogonal and localized orbitals scales as 0(N log N) where N is the total number of k-points in the Brillouin zone. SCDM-k is therefore efficient even when a large number of k-points are used for Brillouin zone sampling. We demonstrate the numerical performance of SCDM-k using systems with model potentials in two and three dimensions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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