Spectral Quadrature method for accurate O ( N ) electronic structure calculations of metals and insulators
We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for realspace 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 infinitecell 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 largescale 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(N ^{3}) planewave results. In conclusion, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for largescale parallelmore »
 Authors:

^{[1]};
^{[1]};
^{[2]}
 Georgia Inst. of Technology, Atlanta, GA (United States)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Report Number(s):
 LLNLJRNL696700
Journal ID: ISSN 00104655
 Grant/Contract Number:
 AC5207NA27344; AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 Computer Physics Communications
 Additional Journal Information:
 Journal Volume: 200; Journal Issue: C; Journal ID: ISSN 00104655
 Publisher:
 Elsevier
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Density Functional Theory; spectral Quadrature; Clenshaw–Curtis; linearscaling; metallic systems; atomic forces
 OSTI Identifier:
 1331472
 Alternate Identifier(s):
 OSTI ID: 1246663
Pratapa, Phanisri P., Suryanarayana, Phanish, and Pask, John E.. Spectral Quadrature method for accurate O(N) electronic structure calculations of metals and insulators. United States: N. p.,
Web. doi:10.1016/j.cpc.2015.11.005.
Pratapa, Phanisri P., Suryanarayana, Phanish, & Pask, John E.. Spectral Quadrature method for accurate O(N) electronic structure calculations of metals and insulators. United States. doi:10.1016/j.cpc.2015.11.005.
Pratapa, Phanisri P., Suryanarayana, Phanish, and Pask, John E.. 2015.
"Spectral Quadrature method for accurate O(N) electronic structure calculations of metals and insulators". United States.
doi:10.1016/j.cpc.2015.11.005. https://www.osti.gov/servlets/purl/1331472.
@article{osti_1331472,
title = {Spectral Quadrature method for accurate O(N) electronic structure calculations of metals and insulators},
author = {Pratapa, Phanisri P. and Suryanarayana, Phanish and Pask, John E.},
abstractNote = {We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for realspace 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 infinitecell 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 largescale 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 largescale parallel computation.},
doi = {10.1016/j.cpc.2015.11.005},
journal = {Computer Physics Communications},
number = C,
volume = 200,
place = {United States},
year = {2015},
month = {12}
}