Non-existence of a minimizer to the Hartree-Fock functional

Michael Melgaard; Mattias Enstedt

doi:10.21427/pbpd-j102

Non-existence of a minimizer to the Hartree-Fock functional

Michael Melgaard, Mattias Enstedt

Technological University Dublin

Research output: Contribution to journal › Article › peer-review

Abstract

In the presence of an external magnetic field, we prove absence of a ground state within the Hartree-Fock theory of atoms and molecules. The result is established for a wide class of magnetic fields when the number of electrons is greater than or equal to 2Z + K, where Z is the total charge of K nuclei. Positivity properties are instrumental in the proof of this bound for the maximal ionization

Original language	English
Pages (from-to)	653-666
Journal	Positivity
Volume	12
DOIs	https://doi.org/10.21427/pbpd-j102
Publication status	Published - 1 Jan 2008

Keywords

external magnetic field
Hartree-Fock theory
atoms
molecules
ground state
magnetic fields
electrons
total charge
nuclei
positivity properties
maximal ionization

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10.21427/pbpd-j102Licence: CC BY-NC-SA

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title = "Non-existence of a minimizer to the Hartree-Fock functional",

abstract = "In the presence of an external magnetic field, we prove absence of a ground state within the Hartree-Fock theory of atoms and molecules. The result is established for a wide class of magnetic fields when the number of electrons is greater than or equal to 2Z + K, where Z is the total charge of K nuclei. Positivity properties are instrumental in the proof of this bound for the maximal ionization",

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AU - Enstedt, Mattias

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N2 - In the presence of an external magnetic field, we prove absence of a ground state within the Hartree-Fock theory of atoms and molecules. The result is established for a wide class of magnetic fields when the number of electrons is greater than or equal to 2Z + K, where Z is the total charge of K nuclei. Positivity properties are instrumental in the proof of this bound for the maximal ionization

AB - In the presence of an external magnetic field, we prove absence of a ground state within the Hartree-Fock theory of atoms and molecules. The result is established for a wide class of magnetic fields when the number of electrons is greater than or equal to 2Z + K, where Z is the total charge of K nuclei. Positivity properties are instrumental in the proof of this bound for the maximal ionization

KW - external magnetic field

KW - Hartree-Fock theory

KW - atoms

KW - molecules

KW - ground state

KW - magnetic fields

KW - electrons

KW - total charge

KW - nuclei

KW - positivity properties

KW - maximal ionization

U2 - 10.21427/pbpd-j102

DO - 10.21427/pbpd-j102

M3 - Article

VL - 12

SP - 653

EP - 666

JO - Positivity

JF - Positivity

ER -

Non-existence of a minimizer to the Hartree-Fock functional

Abstract

Keywords

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