Existence of a Minimizer for the Quasi-Relativistic Kohn-Sham Model

Carlos Argáez García; Michael Melgaard

doi:10.21427/jpm9-sw52

Existence of a Minimizer for the Quasi-Relativistic Kohn-Sham Model

Carlos Argáez García, Michael Melgaard

Technological University Dublin

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

Abstract

We study the standard and extended Kohn-Sham models for quasirelativistic N-electron Coulomb systems; that is, systems where the kinetic energy of the electrons is given by the quasi-relativistic operator For spin-unpolarized systems in the local density approximation, we prove existence of a ground state (or minimizer) provided that the total charge Z _tot of K nuclei is greater than N -1 and that Z _tot is smaller than a critical charge Z _c = 2α ^-1π ^-1.

Original language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Electronic Journal of Differential Equations
Volume	2012
Issue number	18
DOIs	https://doi.org/10.21427/jpm9-sw52
Publication status	Published - 30 Jan 2012

Keywords

Concentration-compactness
Density operators
Ground state
Kohn-Sham equations
Variational methods

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abstract = "We study the standard and extended Kohn-Sham models for quasirelativistic N-electron Coulomb systems; that is, systems where the kinetic energy of the electrons is given by the quasi-relativistic operator For spin-unpolarized systems in the local density approximation, we prove existence of a ground state (or minimizer) provided that the total charge Z tot of K nuclei is greater than N -1 and that Z tot is smaller than a critical charge Z c = 2α -1π -1.",

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N2 - We study the standard and extended Kohn-Sham models for quasirelativistic N-electron Coulomb systems; that is, systems where the kinetic energy of the electrons is given by the quasi-relativistic operator For spin-unpolarized systems in the local density approximation, we prove existence of a ground state (or minimizer) provided that the total charge Z tot of K nuclei is greater than N -1 and that Z tot is smaller than a critical charge Z c = 2α -1π -1.

AB - We study the standard and extended Kohn-Sham models for quasirelativistic N-electron Coulomb systems; that is, systems where the kinetic energy of the electrons is given by the quasi-relativistic operator For spin-unpolarized systems in the local density approximation, we prove existence of a ground state (or minimizer) provided that the total charge Z tot of K nuclei is greater than N -1 and that Z tot is smaller than a critical charge Z c = 2α -1π -1.

KW - Concentration-compactness

KW - Density operators

KW - Ground state

KW - Kohn-Sham equations

KW - Variational methods

UR - https://www.scopus.com/pages/publications/84856790331

U2 - 10.21427/jpm9-sw52

DO - 10.21427/jpm9-sw52

M3 - Article

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SP - 1

EP - 20

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

IS - 18

ER -

Existence of a Minimizer for the Quasi-Relativistic Kohn-Sham Model

Abstract

Keywords

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