### 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 |
---|---|

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 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
- Materials Chemistry
- Condensed Matter Physics
- Physical and Theoretical Chemistry

### Cite this

*Physics and Chemistry of Liquids*,

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

**Relation between single-particle kinetic energy and exchange energy in DFT for the inhomogeneous electron liquid in the Be atom.** / Bogár, F.; Bartha, Ferenc; March, N. H.

Research output: Contribution to journal › Article

*Physics and Chemistry of Liquids*, vol. 48, no. 2, pp. 272-278. https://doi.org/10.1080/00319100903295743

}

TY - JOUR

T1 - Relation between single-particle kinetic energy and exchange energy in DFT for the inhomogeneous electron liquid in the Be atom

AU - Bogár, F.

AU - Bartha, Ferenc

AU - March, N. H.

PY - 2010/4

Y1 - 2010/4

N2 - 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.

AB - 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.

KW - Beryllium atom

KW - Exact Kohn-Sham potential

KW - Exchange-correlation potential

KW - Kinetic energy density

KW - Slater's potential

UR - http://www.scopus.com/inward/record.url?scp=77951123088&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951123088&partnerID=8YFLogxK

U2 - 10.1080/00319100903295743

DO - 10.1080/00319100903295743

M3 - Article

VL - 48

SP - 272

EP - 278

JO - Physics and Chemistry of Liquids

JF - Physics and Chemistry of Liquids

SN - 0031-9104

IS - 2

ER -