Convergent sum of gradient expansion of the kinetic-energy density functional up to the sixth order term using Padé approximant

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Abstract

The gradient expansion of the kinetic energy density functional, when applied to atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the integral by replacing the asymptotic series including the sixth order term in the integrand by a rational function. Padé approximants show moderate improvements in accuracy in comparison with partial sums of the series. The results are discussed for atoms and Hooke's law model for two-electron atoms.

Original languageEnglish
Article number012011
JournalJournal of Physics: Conference Series
Volume707
Issue number1
DOIs
Publication statusPublished - 4 May 2016

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flux density
kinetic energy
gradients
expansion
asymptotic series
atoms
rational functions
divergence
electrons
energy

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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title = "Convergent sum of gradient expansion of the kinetic-energy density functional up to the sixth order term using Pad{\'e} approximant",
abstract = "The gradient expansion of the kinetic energy density functional, when applied to atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the integral by replacing the asymptotic series including the sixth order term in the integrand by a rational function. Pad{\'e} approximants show moderate improvements in accuracy in comparison with partial sums of the series. The results are discussed for atoms and Hooke's law model for two-electron atoms.",
author = "A. Sergeev and Fahhad Alharbi and Raka Jovanovic and S. Kais",
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AU - Alharbi, Fahhad

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AU - Kais, S.

PY - 2016/5/4

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N2 - The gradient expansion of the kinetic energy density functional, when applied to atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the integral by replacing the asymptotic series including the sixth order term in the integrand by a rational function. Padé approximants show moderate improvements in accuracy in comparison with partial sums of the series. The results are discussed for atoms and Hooke's law model for two-electron atoms.

AB - The gradient expansion of the kinetic energy density functional, when applied to atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the integral by replacing the asymptotic series including the sixth order term in the integrand by a rational function. Padé approximants show moderate improvements in accuracy in comparison with partial sums of the series. The results are discussed for atoms and Hooke's law model for two-electron atoms.

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