Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Minimax rational approximation of the Fermi-Dirac distribution

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.4965886· OSTI ID:1335130
 [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
+ Show Author Affiliations

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.

Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1335130
Report Number(s):
SAND--2016-3915J; 638848
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 16 Vol. 145; ISSN JCPSA6; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (20)

Pole-Based approximation of the Fermi-Dirac function journal August 2009
Elimination of energy denominators in Møller—Plesset perturbation theory by a Laplace transform approach journal June 1991
Introduction to hierarchical matrices with applications journal May 2003
Low Scaling Algorithms for the Random Phase Approximation: Imaginary Time and Laplace Transformations journal May 2014
A Mnemonic Device for Molecular Orbital Energies journal March 1953
Communication: Padé spectrum decomposition of Fermi function and Bose function journal September 2010
Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange journal January 2014
Progress in the study of warm dense matter journal November 2005
Accelerating atomic orbital-based electronic structure calculation via pole expansion and selected inversion journal June 2013
The explicit inverses of two commonly occurring matrices journal January 1969
Integral representation of the Fermi distribution and its applications in electronic-structure calculations journal December 1993
Continued fraction representation of the Fermi-Dirac function for large-scale electronic structure calculations journal January 2007
Multipole representation of the Fermi operator with application to the electronic structure analysis of metallic systems journal March 2009
Partial fraction decomposition of the Fermi function journal August 2009
Fully self-consistent GW calculations for molecules journal February 2010
Finite-temperature linear conductance from the Matsubara Green’s function without analytic continuation to the real axis journal September 2010
Note on the Zolotarev optimal rational approximation for the overlap Dirac operator journal December 2002
Linear scaling electronic structure methods journal July 1999
Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals journal January 2008
A Divide-and-Conquer Algorithm for the Symmetric Tridiagonal Eigenproblem journal January 1995

Similar Records

Companion software to: Minimax Rational Approximation of the Fermi-Dirac Distribution v. 1.0
Software · 2016 · OSTI ID:code-54952
Fragility of Fermi arcs in Dirac semimetals
Journal Article · 2019 · Physical Review B · OSTI ID:1514886

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS