### Abstract

The properties of multi-electron densities are analyzed along with their behavior with respect to the two Hohenberg-Kohn theorems and the fundamental extension by Ziesche, Ayers and Levy in this manner. This analysis is continued with the form of density functionals and density differential and/or integral operators on different levels of dimensions between the variational principle (4N-dimension) and Hohenberg-Kohn theorems (3-dimension). The trend in ionization potentials is commented upon. The exact density functional operator of H-like atoms and one-electron systems is also discussed with the two-electron systems, not only as simple "forever prototypes", but as a certain projection of one-electron density formalism of N ≥ 1 electron systems to N = 1 and 2. The review part of this work is focusing primarily on functional analytical properties.

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

Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Journal of Molecular Structure: THEOCHEM |

Volume | 858 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Jun 15 2008 |

### Fingerprint

### Keywords

- Density functional theory
- Hohenberg-Kohn theorems
- Multi-electron density
- Trend in ionization potentials
- Variational principle

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Computational Theory and Mathematics
- Atomic and Molecular Physics, and Optics

### Cite this

**Properties of the multi-electron densities "between" the Hohenberg-Kohn theorems and variational principle.** / Kristyán, S.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Properties of the multi-electron densities "between" the Hohenberg-Kohn theorems and variational principle

AU - Kristyán, S.

PY - 2008/6/15

Y1 - 2008/6/15

N2 - The properties of multi-electron densities are analyzed along with their behavior with respect to the two Hohenberg-Kohn theorems and the fundamental extension by Ziesche, Ayers and Levy in this manner. This analysis is continued with the form of density functionals and density differential and/or integral operators on different levels of dimensions between the variational principle (4N-dimension) and Hohenberg-Kohn theorems (3-dimension). The trend in ionization potentials is commented upon. The exact density functional operator of H-like atoms and one-electron systems is also discussed with the two-electron systems, not only as simple "forever prototypes", but as a certain projection of one-electron density formalism of N ≥ 1 electron systems to N = 1 and 2. The review part of this work is focusing primarily on functional analytical properties.

AB - The properties of multi-electron densities are analyzed along with their behavior with respect to the two Hohenberg-Kohn theorems and the fundamental extension by Ziesche, Ayers and Levy in this manner. This analysis is continued with the form of density functionals and density differential and/or integral operators on different levels of dimensions between the variational principle (4N-dimension) and Hohenberg-Kohn theorems (3-dimension). The trend in ionization potentials is commented upon. The exact density functional operator of H-like atoms and one-electron systems is also discussed with the two-electron systems, not only as simple "forever prototypes", but as a certain projection of one-electron density formalism of N ≥ 1 electron systems to N = 1 and 2. The review part of this work is focusing primarily on functional analytical properties.

KW - Density functional theory

KW - Hohenberg-Kohn theorems

KW - Multi-electron density

KW - Trend in ionization potentials

KW - Variational principle

UR - http://www.scopus.com/inward/record.url?scp=43049154825&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43049154825&partnerID=8YFLogxK

U2 - 10.1016/j.theochem.2008.03.007

DO - 10.1016/j.theochem.2008.03.007

M3 - Article

VL - 858

SP - 1

EP - 11

JO - Computational and Theoretical Chemistry

JF - Computational and Theoretical Chemistry

SN - 2210-271X

IS - 1-3

ER -