Title: Spectral Quadrature method for accurate O ( N ) electronic structure calculations of metals and insulators

Abstract

We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw–Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order to exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N³) planewave results. In conclusion, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.

Authors:

Pratapa, Phanisri P. ^[1]; Suryanarayana, Phanish ^[1]; Pask, John E. ^[2]

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+ Show Author Affiliations

1. Georgia Inst. of Technology, Atlanta, GA (United States)
2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:

Wed Dec 02 00:00:00 EST 2015

Research Org.:

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:

USDOE

OSTI Identifier:

1331472

Alternate Identifier(s):

OSTI ID: 1246663

Report Number(s):

LLNL-JRNL-696700
Journal ID: ISSN 0010-4655

Grant/Contract Number:  

AC52-07NA27344; AC52-07-NA27344

Resource Type:

Accepted Manuscript

Journal Name:

Computer Physics Communications

Additional Journal Information:

Journal Volume: 200; Journal Issue: C; Journal ID: ISSN 0010-4655

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Density Functional Theory; spectral Quadrature; Clenshaw–Curtis; linear-scaling; metallic systems; atomic forces