### Abstract

A hierarchy of equations has been derived for the energy functionals of the density-functional theory using the virial theorem and the Levy-Perdew relation. In the local-density approximation, the solution of the equations of hierarchy for the kinetic and exchange energies provides the well-known Thomas-Fermi expression for the kinetic energy and the Slater-Gáspár-Kohn-Sham expression for the exchange. The truncation of the hierarchies of the kinetic and exchange energies results in rigorous lower bounds to the kinetic energy and upper bounds to the exchange energy in the plane-wave approximation.

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

Pages (from-to) | 2715-2719 |

Number of pages | 5 |

Journal | Physical Review A |

Volume | 47 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1993 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics

### Cite this

**Hierarchy of equations for the energy functional of the density-functional theory.** / Nagy, A.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 47, no. 4, pp. 2715-2719. https://doi.org/10.1103/PhysRevA.47.2715

}

TY - JOUR

T1 - Hierarchy of equations for the energy functional of the density-functional theory

AU - Nagy, A.

PY - 1993

Y1 - 1993

N2 - A hierarchy of equations has been derived for the energy functionals of the density-functional theory using the virial theorem and the Levy-Perdew relation. In the local-density approximation, the solution of the equations of hierarchy for the kinetic and exchange energies provides the well-known Thomas-Fermi expression for the kinetic energy and the Slater-Gáspár-Kohn-Sham expression for the exchange. The truncation of the hierarchies of the kinetic and exchange energies results in rigorous lower bounds to the kinetic energy and upper bounds to the exchange energy in the plane-wave approximation.

AB - A hierarchy of equations has been derived for the energy functionals of the density-functional theory using the virial theorem and the Levy-Perdew relation. In the local-density approximation, the solution of the equations of hierarchy for the kinetic and exchange energies provides the well-known Thomas-Fermi expression for the kinetic energy and the Slater-Gáspár-Kohn-Sham expression for the exchange. The truncation of the hierarchies of the kinetic and exchange energies results in rigorous lower bounds to the kinetic energy and upper bounds to the exchange energy in the plane-wave approximation.

UR - http://www.scopus.com/inward/record.url?scp=0000529309&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000529309&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.47.2715

DO - 10.1103/PhysRevA.47.2715

M3 - Article

AN - SCOPUS:0000529309

VL - 47

SP - 2715

EP - 2719

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 4

ER -