## Abstract

An orbital-dependent correlation energy functional E_{c} to be accompanied by the exact exchange energy functional E_{x} is proposed for applications of density-functional theory (DFT). The present E_{c} comprises spin-antiparallel and spin-parallel contributions, E_{c} ^{σ-σ} and E_{c}^{σσ}. E _{c}^{σ-σ} is a modification of the spin-antiparallel component of the Hartree energy functional with a factor of ḡ_{c}^{σ-σ}(r, r′) - 1 and E _{c}^{σσ} a modification of the spin-parallel component of the same energy functional with ḡ_{c} ^{σσ}(r, r′) where ḡ_{c} ^{σσ}(r, r′) (or ḡ_{c} ^{σ-σ}(r, r′)) is the spin-antiparallel(or the correlational part of the spin-parallel) coupling-constant-averaged pair correlation function. The present orbital-dependent ḡ ^{σ-σ}(r, r′) and ḡ_{c} ^{σσ}(r, r′) fulfill the symmetric property, the Pauli principle and the sum rules. In the limit of uniform density the two correlation functions are reduced to the very accurate analogues of the electron liquid that involve long-, intermediate-, and short-range correlations as well as their exchange counterparts. It is stressed that the correlation energy functional E_{c} in DFT should by its very nature be defined as a functional only of occupied Kohn-Sham orbitals and occupied Kohn-Sham energies for the purpose of employing the optimized potential method (OPM) to evaluate the correlation potential v_{c}(r). The present scheme for E _{c}, if applied to finite systems after making a suitable change in the treatment of long-range correlation, can give the correct asymptotic form of v_{c}(r) of order r^{-4} for large r as well as the van der Waals potential.

Original language | English |
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Pages (from-to) | 1402-1410 |

Number of pages | 9 |

Journal | Materials Transactions |

Volume | 45 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2004 May |

## Keywords

- Correlation energy functional
- Density-functional theory
- Electron liquid
- Optimized potential method