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Title: Real-space formulation of the stress tensor for O(N) density functional theory: Application to high temperature calculations

Abstract

We present an accurate and efficient real-space formulation of the Hellmann–Feynman stress tensor for O(N) Kohn–Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi–Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O(N) methods. We then describe its evaluation within the O(N) infinite-cell Clenshaw–Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. Here, we employ the new formulation to compute the viscosity of hydrogen at 106 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

Authors:
 [1]; ORCiD logo [2];  [3];  [2]; ORCiD logo [1]
+ Show Author Affiliations
  1. Georgia Inst. of Technology, Atlanta, GA (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); École Normale Supérieure de Lyon (France)
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); U.S. National Science Foundation (NSF)
OSTI Identifier:
1784614
Alternate Identifier(s):
OSTI ID: 1639126
Report Number(s):
LLNL-JRNL-813246
Journal ID: ISSN 0021-9606; 1020601; TRN: US2210342
Grant/Contract Number:  
AC52-07NA27344; 1663244
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 153; Journal Issue: 3; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Viscosity; Quantum chemical dynamics; Density functional theory; Density-matrix; High performance computing

Citation Formats

Sharma, Abhiraj, Hamel, Sebastien, Bethkenhagen, Mandy, Pask, John E., and Suryanarayana, Phanish. Real-space formulation of the stress tensor for O(N) density functional theory: Application to high temperature calculations. United States: N. p., 2020. Web. doi:10.1063/5.0016783.
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Sharma, Abhiraj, Hamel, Sebastien, Bethkenhagen, Mandy, Pask, John E., & Suryanarayana, Phanish. Real-space formulation of the stress tensor for O(N) density functional theory: Application to high temperature calculations. United States. https://doi.org/10.1063/5.0016783
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Sharma, Abhiraj, Hamel, Sebastien, Bethkenhagen, Mandy, Pask, John E., and Suryanarayana, Phanish. Mon . "Real-space formulation of the stress tensor for O(N) density functional theory: Application to high temperature calculations". United States. https://doi.org/10.1063/5.0016783. https://www.osti.gov/servlets/purl/1784614.
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@article{osti_1784614,
title = {Real-space formulation of the stress tensor for O(N) density functional theory: Application to high temperature calculations},
author = {Sharma, Abhiraj and Hamel, Sebastien and Bethkenhagen, Mandy and Pask, John E. and Suryanarayana, Phanish},
abstractNote = {We present an accurate and efficient real-space formulation of the Hellmann–Feynman stress tensor for O(N) Kohn–Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi–Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O(N) methods. We then describe its evaluation within the O(N) infinite-cell Clenshaw–Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. Here, we employ the new formulation to compute the viscosity of hydrogen at 106 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.},
doi = {10.1063/5.0016783},
journal = {Journal of Chemical Physics},
number = 3,
volume = 153,
place = {United States},
year = {Mon Jul 20 00:00:00 EDT 2020},
month = {Mon Jul 20 00:00:00 EDT 2020}
}
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https://doi.org/10.1063/5.0016783
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