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Deriving approximate functionals with asymptotics

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Abstract

Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB expansion in one dimension, and modern approaches to asymptotic expansions. A mathematical framework for analyzing asymptotic behavior for the sums of energies unites both corrections to the gradient expansion of DFT and hyperasymptotics of sums. Simple examples are given for the model problem of orbital-free DFT in one dimension. In some cases, errors can be made as small as 10−32 Hartree suggesting that, if these new ingredients can be applied, they might produce approximate functionals that are much more accurate than those in current use. A variation of the Euler–Maclaurin formula generalizes previous results.

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Article information


Submitted
12 May 2020
Accepted
07 Jul 2020
First published
07 Jul 2020

Faraday Discuss., 2020, Advance Article
Article type
Paper

Deriving approximate functionals with asymptotics

K. Burke, Faraday Discuss., 2020, Advance Article , DOI: 10.1039/D0FD00057D

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