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

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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 languageEnglish
Pages (from-to)1-11
Number of pages11
JournalJournal of Molecular Structure: THEOCHEM
Volume858
Issue number1-3
DOIs
Publication statusPublished - Jun 15 2008

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variational principles
Carrier concentration
theorems
Electrons
operators
electrons
Ionization potential
functionals
ionization potentials
projection
prototypes
formalism
trends
Atoms
atoms

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

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title = "Properties of the multi-electron densities {"}between{"} the Hohenberg-Kohn theorems and variational principle",
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.",
keywords = "Density functional theory, Hohenberg-Kohn theorems, Multi-electron density, Trend in ionization potentials, Variational principle",
author = "S. Kristy{\'a}n",
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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

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