### Abstract

In a recent publication [R.G. Parr and S. Liu, Chem. Phys. Lett. 267, 164(1997)], it has been argued that the total electron-electron repulsion energy density functional Veetp] can be expressed as a sum of functionals homogeneous of degrees one and two, with respect to density scaling. In this paper, starting from the Levy-Perdew virial relation, we demonstrate that one of the components of V_{ee}[ρ], the exchange energy density functional E_{x}[ρ], can be expressed reasonably well in this way in a simple form. Namely, E_{x}[ρ] can be expressed as a linear combination of the classical electron-electron repulsion J[ρ] and the various electrostatic potentials at nuclei due to the electrons. Numerical tests are made for atoms, ions, and a few molecules. Good agreement between the accurate and the estimated exchange energies is observed.

Original language | English |
---|---|

Pages (from-to) | 77-91 |

Number of pages | 15 |

Journal | Advances in Quantum Chemistry |

Volume | 36 |

Issue number | C |

DOIs | |

Publication status | Published - 1999 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Advances in Quantum Chemistry*,

*36*(C), 77-91. https://doi.org/10.1016/S0065-3276(08)60479-7

**Exchange-Energy Density Functionals as Linear Combinations of Homogeneous Functionals of Density.** / Liu, Shubin; Proft, Frank De; Nagy, A.; Parr, Robert G.

Research output: Contribution to journal › Article

*Advances in Quantum Chemistry*, vol. 36, no. C, pp. 77-91. https://doi.org/10.1016/S0065-3276(08)60479-7

}

TY - JOUR

T1 - Exchange-Energy Density Functionals as Linear Combinations of Homogeneous Functionals of Density

AU - Liu, Shubin

AU - Proft, Frank De

AU - Nagy, A.

AU - Parr, Robert G.

PY - 1999

Y1 - 1999

N2 - In a recent publication [R.G. Parr and S. Liu, Chem. Phys. Lett. 267, 164(1997)], it has been argued that the total electron-electron repulsion energy density functional Veetp] can be expressed as a sum of functionals homogeneous of degrees one and two, with respect to density scaling. In this paper, starting from the Levy-Perdew virial relation, we demonstrate that one of the components of Vee[ρ], the exchange energy density functional Ex[ρ], can be expressed reasonably well in this way in a simple form. Namely, Ex[ρ] can be expressed as a linear combination of the classical electron-electron repulsion J[ρ] and the various electrostatic potentials at nuclei due to the electrons. Numerical tests are made for atoms, ions, and a few molecules. Good agreement between the accurate and the estimated exchange energies is observed.

AB - In a recent publication [R.G. Parr and S. Liu, Chem. Phys. Lett. 267, 164(1997)], it has been argued that the total electron-electron repulsion energy density functional Veetp] can be expressed as a sum of functionals homogeneous of degrees one and two, with respect to density scaling. In this paper, starting from the Levy-Perdew virial relation, we demonstrate that one of the components of Vee[ρ], the exchange energy density functional Ex[ρ], can be expressed reasonably well in this way in a simple form. Namely, Ex[ρ] can be expressed as a linear combination of the classical electron-electron repulsion J[ρ] and the various electrostatic potentials at nuclei due to the electrons. Numerical tests are made for atoms, ions, and a few molecules. Good agreement between the accurate and the estimated exchange energies is observed.

UR - http://www.scopus.com/inward/record.url?scp=7544225036&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=7544225036&partnerID=8YFLogxK

U2 - 10.1016/S0065-3276(08)60479-7

DO - 10.1016/S0065-3276(08)60479-7

M3 - Article

AN - SCOPUS:7544225036

VL - 36

SP - 77

EP - 91

JO - Advances in Quantum Chemistry

JF - Advances in Quantum Chemistry

SN - 0065-3276

IS - C

ER -