Relation between single-particle kinetic energy and exchange energy in DFT for the inhomogeneous electron liquid in the Be atom

Ferenc Boǵar, Ferenc Bartha, N. H. March

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In a recent study, the authors have used the semi empirical fine-tuned Hartree-Fock ground-state electron density n(r) of Cordero et al. [Phys. Rev. A 75, 052502 (2007)] for the Be atom to calculate the phase θ(r) from a non-linear pendulum-like equation. Since the density amplitude n(r)1/2 plus θ(r) determine, in turn, the idempotent Dirac density matrix γ(r, r'), we use n(r) and θ(r) first of all to calculate the exchange energy density eX(r) of the density functional theory (DFT). This enables us to obtain the Slater (Sl) approximation Vxsl(r) to the exchange-only potential. A comparison can then be made, by integrating the earlier predicted exchange-correlation force -∂VXC(r)/∂r, of VXC (r) with Vxsl(r). Relationship to the Becke semiempirical density gradient approximation for exchange is also established. Some brief discussion of the Perdew-Burke-Ernzerhof density functional is added.

Original languageEnglish
Pages (from-to)272-278
Number of pages7
JournalPhysics and Chemistry of Liquids
Issue number2
Publication statusPublished - Apr 1 2010



  • Beryllium atom
  • Exact Kohn-Sham potential
  • Exchange-correlation potential
  • Kinetic energy density
  • Slater's potential

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry
  • Materials Chemistry

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