There are no unfilled shells in unrestricted hartree-fock theory

Volker Bach; Élliott H. Lieb; Michael Loss; Jan Philip Solovej

doi:10.1007/3-540-27056-6_22

There are no unfilled shells in unrestricted hartree-fock theory

Volker Bach, Élliott H. Lieb, Michael Loss, Jan Philip Solovej

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We prove that in an exact, unrestricted Hartree-Fock calculation each energy level of the Hartree-Fock equation is either completely filled or completely empty. The only assumption needed is that the two-body interaction is-like the Coulomb interaction-repulsive; it could, however, be more complicated than a simple potential; e.g., it could have tensor forces and velocity dependence. In particular, the Hartree-Fock energy levels of atoms and molecules, often called shells, are never partially filled.

Original language	English (US)
Title of host publication	The Stability of Matter
Subtitle of host publication	From Atoms to Stars: Fourth Edition
Publisher	Springer Berlin Heidelberg
Pages	313-315
Number of pages	3
ISBN (Print)	3540420835, 9783540222125
DOIs	https://doi.org/10.1007/3-540-27056-6_22
State	Published - 2005

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1007/3-540-27056-6_22

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abstract = "We prove that in an exact, unrestricted Hartree-Fock calculation each energy level of the Hartree-Fock equation is either completely filled or completely empty. The only assumption needed is that the two-body interaction is-like the Coulomb interaction-repulsive; it could, however, be more complicated than a simple potential; e.g., it could have tensor forces and velocity dependence. In particular, the Hartree-Fock energy levels of atoms and molecules, often called shells, are never partially filled.",

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AU - Bach, Volker

AU - Lieb, Élliott H.

AU - Loss, Michael

AU - Solovej, Jan Philip

PY - 2005

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N2 - We prove that in an exact, unrestricted Hartree-Fock calculation each energy level of the Hartree-Fock equation is either completely filled or completely empty. The only assumption needed is that the two-body interaction is-like the Coulomb interaction-repulsive; it could, however, be more complicated than a simple potential; e.g., it could have tensor forces and velocity dependence. In particular, the Hartree-Fock energy levels of atoms and molecules, often called shells, are never partially filled.

AB - We prove that in an exact, unrestricted Hartree-Fock calculation each energy level of the Hartree-Fock equation is either completely filled or completely empty. The only assumption needed is that the two-body interaction is-like the Coulomb interaction-repulsive; it could, however, be more complicated than a simple potential; e.g., it could have tensor forces and velocity dependence. In particular, the Hartree-Fock energy levels of atoms and molecules, often called shells, are never partially filled.

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SP - 313

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BT - The Stability of Matter

PB - Springer Berlin Heidelberg

ER -

There are no unfilled shells in unrestricted hartree-fock theory

Abstract

All Science Journal Classification (ASJC) codes

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