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

Journal Article · Wed Dec 02 00:00:00 EST 2015 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2015.11.005· OSTI ID:1331472

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

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

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.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-07NA27344; AC52-07-NA27344
• OSTI ID: 1331472
• Alternate ID(s): OSTI ID: 1246663
• Report Number(s): LLNL-JRNL-696700
• Journal Information: Computer Physics Communications, Vol. 200, Issue C; ISSN 0010-4655
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

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