### Abstract

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 e_{X}(r) of the density functional theory (DFT). This enables us to obtain the Slater (Sl) approximation V_{x}^{sl}(r) to the exchange-only potential. A comparison can then be made, by integrating the earlier predicted exchange-correlation force -∂V_{XC}(r)/∂r, of V_{XC} (r) with V_{x}^{sl}(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 language | English |
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Pages (from-to) | 272-278 |

Number of pages | 7 |

Journal | Physics and Chemistry of Liquids |

Volume | 48 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 1 2010 |

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### Keywords

- 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

### Cite this

*Physics and Chemistry of Liquids*,

*48*(2), 272-278. https://doi.org/10.1080/00319100903295743