Kinetic energy density for orbital-free density functional calculations by axiomatic approach

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2 Citations (Scopus)

Abstract

An axiomatic approach is herein used to determine the physically acceptable forms for general D-dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one-point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than 10-4 for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large-scale orbital free density functional theory calculations.

Original languageEnglish
JournalInternational Journal of Quantum Chemistry
DOIs
Publication statusAccepted/In press - 2017

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Kinetic energy
Density functional theory
flux density
functionals
kinetic energy
orbitals
education
routes
density functional theory
expansion
coefficients

Keywords

  • Kinetic energy density
  • Kinetic energy density functionals
  • Large-scale calculations
  • Orbital-free density functional theory

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

Cite this

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abstract = "An axiomatic approach is herein used to determine the physically acceptable forms for general D-dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one-point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than 10-4 for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large-scale orbital free density functional theory calculations.",
keywords = "Kinetic energy density, Kinetic energy density functionals, Large-scale calculations, Orbital-free density functional theory",
author = "Fahhad Alharbi and Sabre Kais",
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T1 - Kinetic energy density for orbital-free density functional calculations by axiomatic approach

AU - Alharbi, Fahhad

AU - Kais, Sabre

PY - 2017

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N2 - An axiomatic approach is herein used to determine the physically acceptable forms for general D-dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one-point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than 10-4 for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large-scale orbital free density functional theory calculations.

AB - An axiomatic approach is herein used to determine the physically acceptable forms for general D-dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one-point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than 10-4 for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large-scale orbital free density functional theory calculations.

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KW - Large-scale calculations

KW - Orbital-free density functional theory

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