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Title: Minimax rational approximation of the Fermi-Dirac distribution

Abstract

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ –1)) poles to achieve an error tolerance ϵ at temperature β –1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δ occ, the occupied energy interval. Furthermore, this is particularly beneficial when Δ >> Δ occ, such as in electronic structure calculations that use a large basis set.

Authors:
 [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1335130
Report Number(s):
SAND-2016-3915J
Journal ID: ISSN 0021-9606; JCPSA6; 638848
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 145; Journal Issue: 16; 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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Moussa, Jonathan E. Minimax rational approximation of the Fermi-Dirac distribution. United States: N. p., 2016. Web. doi:10.1063/1.4965886.
Moussa, Jonathan E. Minimax rational approximation of the Fermi-Dirac distribution. United States. doi:10.1063/1.4965886.
Moussa, Jonathan E. Thu . "Minimax rational approximation of the Fermi-Dirac distribution". United States. doi:10.1063/1.4965886. https://www.osti.gov/servlets/purl/1335130.
@article{osti_1335130,
title = {Minimax rational approximation of the Fermi-Dirac distribution},
author = {Moussa, Jonathan E.},
abstractNote = {Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ–1)) poles to achieve an error tolerance ϵ at temperature β–1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. Furthermore, this is particularly beneficial when Δ >> Δocc, such as in electronic structure calculations that use a large basis set.},
doi = {10.1063/1.4965886},
journal = {Journal of Chemical Physics},
number = 16,
volume = 145,
place = {United States},
year = {2016},
month = {10}
}

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