Existence of a minimizer for the quasi-relativistic Kohn-Sham model

Carlos Argaez; Michael Melgaard

Existence of a minimizer for the quasi-relativistic Kohn-Sham model

Carlos Argaez, Michael Melgaard^*

^*Corresponding author for this work

Science Institute

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

1 Citation (Scopus)

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
Publication status	Published - 30 Jan 2012

Other keywords

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

Cite this

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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.",

keywords = "Concentration-compactness, Density operators, Ground state, Kohn-Sham equations, Variational methods",

author = "Carlos Argaez and Michael Melgaard",

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AU - Melgaard, Michael

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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

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M3 - Article

AN - SCOPUS:84856790331

SN - 1072-6691

VL - 2012

SP - 1

EP - 20

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

Existence of a minimizer for the quasi-relativistic Kohn-Sham model

Abstract

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