### Abstract

We prove the following results, relevant for the density functional theory: the Thomas-Fermi-Dirac theory, generalized to include the contribution due to the high electron density result of Gell-Mann and Brueckner for the correlation energy, is shown to lead to a differential equation for the self-consistent ground-state density n(r) in atoms and molecules in the form F(n,{∇n/n}^{2},∇^{2}n/n) = 1, where the function F is given explicitly. A straightforward extension yields a similar result for the equation determining the Pauli plus exchange-correlation potential and for the divergence of the many-electron force.

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

Pages (from-to) | 145-149 |

Number of pages | 5 |

Journal | International Journal of Quantum Chemistry |

Volume | 69 |

Issue number | 2 |

Publication status | Published - 1998 |

### Fingerprint

### Keywords

- Density functional theory
- Generalized Thomas-Fermi approximation
- Reduced density gradients
- Self-consistent density equation

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

**Self-consistent Thomas-Fermi-Dirac theory, extended by Gell-Mann and Brueckner correlation, in terms of density n and its two reduced gradients ∇ ^{2}n/n and ∇n/n.** / March, N. H.; Holas, A.; Nagy, A.

Research output: Contribution to journal › Article

^{2}n/n and ∇n/n',

*International Journal of Quantum Chemistry*, vol. 69, no. 2, pp. 145-149.

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TY - JOUR

T1 - Self-consistent Thomas-Fermi-Dirac theory, extended by Gell-Mann and Brueckner correlation, in terms of density n and its two reduced gradients ∇2n/n and ∇n/n

AU - March, N. H.

AU - Holas, A.

AU - Nagy, A.

PY - 1998

Y1 - 1998

N2 - We prove the following results, relevant for the density functional theory: the Thomas-Fermi-Dirac theory, generalized to include the contribution due to the high electron density result of Gell-Mann and Brueckner for the correlation energy, is shown to lead to a differential equation for the self-consistent ground-state density n(r) in atoms and molecules in the form F(n,{∇n/n}2,∇2n/n) = 1, where the function F is given explicitly. A straightforward extension yields a similar result for the equation determining the Pauli plus exchange-correlation potential and for the divergence of the many-electron force.

AB - We prove the following results, relevant for the density functional theory: the Thomas-Fermi-Dirac theory, generalized to include the contribution due to the high electron density result of Gell-Mann and Brueckner for the correlation energy, is shown to lead to a differential equation for the self-consistent ground-state density n(r) in atoms and molecules in the form F(n,{∇n/n}2,∇2n/n) = 1, where the function F is given explicitly. A straightforward extension yields a similar result for the equation determining the Pauli plus exchange-correlation potential and for the divergence of the many-electron force.

KW - Density functional theory

KW - Generalized Thomas-Fermi approximation

KW - Reduced density gradients

KW - Self-consistent density equation

UR - http://www.scopus.com/inward/record.url?scp=0242523845&partnerID=8YFLogxK

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M3 - Article

VL - 69

SP - 145

EP - 149

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 2

ER -