Density functionals and dimensional renormalization for an exactly solvable model

S. Kais, D. R. Herschbach, N. C. Handy, C. W. Murray, G. J. Laming

Research output: Contribution to journalArticle

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Abstract

We treat an analytically solvable version of the "Hooke's Law" model for a two-electron atom, in which the electron-electron repulsion is Coulombic but the electron-nucleus attraction is replaced by a harmonic oscillator potential. Exact expressions are obtained for the ground-state wave function and electron density, the Hartree-Fock solution, the correlation energy, the Kohn-Sham orbital, and, by inversion, the exchange and correlation functionals. These functional pertain to the "intermediate" density regime (rs≥1.4) for an electron gas. As a test of customary approximations employed in density functional theory, we compare our exact density, exchange, and correlation potentials and energies with results from two approximations. These use Becke's exchange functional and either the Lee-Yang-Parr or the Perdew correlation functional. Both approximations yield rather good results for the density and the exchange and correlation energies, but both deviate markedly from the exact exchange and correlation potentials. We also compare properties of the Hooke's Law model with those of two-electron atoms, including the large dimension limit. A renormalization procedure applied to this very simple limit yields correlation energies as good as those obtained from the approximate functionals, for both the model and actual atoms.

Original languageEnglish
Pages (from-to)417-425
Number of pages9
JournalThe Journal of Chemical Physics
Volume99
Issue number1
Publication statusPublished - 1 Dec 1993
Externally publishedYes

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functionals
Electrons
Atoms
electrons
Electron gas
approximation
Wave functions
atoms
Ground state
Density functional theory
Carrier concentration
energy
harmonic oscillators
attraction
electron gas
wave functions
inversions
density functional theory
orbitals
nuclei

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Kais, S., Herschbach, D. R., Handy, N. C., Murray, C. W., & Laming, G. J. (1993). Density functionals and dimensional renormalization for an exactly solvable model. The Journal of Chemical Physics, 99(1), 417-425.

Density functionals and dimensional renormalization for an exactly solvable model. / Kais, S.; Herschbach, D. R.; Handy, N. C.; Murray, C. W.; Laming, G. J.

In: The Journal of Chemical Physics, Vol. 99, No. 1, 01.12.1993, p. 417-425.

Research output: Contribution to journalArticle

Kais, S, Herschbach, DR, Handy, NC, Murray, CW & Laming, GJ 1993, 'Density functionals and dimensional renormalization for an exactly solvable model', The Journal of Chemical Physics, vol. 99, no. 1, pp. 417-425.
Kais, S. ; Herschbach, D. R. ; Handy, N. C. ; Murray, C. W. ; Laming, G. J. / Density functionals and dimensional renormalization for an exactly solvable model. In: The Journal of Chemical Physics. 1993 ; Vol. 99, No. 1. pp. 417-425.
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