Minimax rational approximation of the Fermi-Dirac distribution
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.
- Publication Date:
- Report Number(s):
- SAND-2016-3915J
Journal ID: ISSN 0021-9606; JCPSA6; 638848
- Grant/Contract Number:
- AC04-94AL85000
- 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)
- Research Org:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org:
- USDOE National Nuclear Security Administration (NNSA)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
- OSTI Identifier:
- 1335130
Moussa, Jonathan E. Minimax rational approximation of the Fermi-Dirac distribution. United States: N. p.,
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. 2016.
"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}
}