Title: Real-space density kernel method for Kohn–Sham density functional theory calculations at high temperature

Abstract

Kohn–Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. In this work, we present a density matrix based method for Kohn–Sham calculations at high temperatures that eliminates the need for diagonalization entirely, thus reducing the cost of such calculations significantly. Specifically, we develop real-space expressions for the electron density, electronic free energy, Hellmann–Feynman forces, and Hellmann–Feynman stress tensor in terms of an orthonormal auxiliary orbital basis and its density kernel transform, the density kernel being the matrix representation of the density operator in the auxiliary basis. Using Chebyshev filtering to generate the auxiliary basis, we next develop an approach akin to Clenshaw–Curtis spectral quadrature to calculate the individual columns of the density kernel based on the Fermi operator expansion in Chebyshev polynomials and employ a similar approach to evaluate band structure and entropic energy components. We implement the proposed formulation in the SPARC electronic structure code, using which we show systematic convergence of the aforementioned quantities to exact diagonalization results, and obtain significant speedups relative to conventional diagonalization based methods. Finally, we employ the new method to compute the self-diffusion coefficientmore » and viscosity of aluminum at 116 045 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.« less

Authors:

Xu, Qimen ^[1]; Jing, Xin  ^[1];

• Search DOE PAGES for author "Jing, Xin"
• Search DOE PAGES for ORCID "0000-0002-0088-9116"

Zhang, Boqin ^[1]; Pask, John E. ^[2]; Suryanarayana, Phanish  ^[1]

• Search DOE PAGES for author "Suryanarayana, Phanish"
• Search DOE PAGES for ORCID "0000-0001-5172-0049"

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+ Show Author Affiliations

1. College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
2. Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA

Publication Date:

Wed Mar 02 00:00:00 EST 2022

Research Org.:

Georgia Institute of Technology, Atlanta, GA (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC); USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:

1867400

Alternate Identifier(s):

OSTI ID: 1847017; OSTI ID: 1866178

Report Number(s):

LLNL-JRNL-830272
Journal ID: ISSN 0021-9606; TRN: US2306170

Grant/Contract Number:  

SC0019410; AC52-07NA27344

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Chemical Physics

Additional Journal Information:

Journal Volume: 156; Journal Issue: 9; Journal ID: ISSN 0021-9606

Publisher:

American Institute of Physics (AIP)

Country of Publication:

United States

Language:

English

Subject:

70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY