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Title: Derivative of the Lieb definition for the energy functional of density-functional theory with respect to the particle number and the spin number

Abstract

The nature of the explicit dependence on the particle number N and on the spin number N{sub s} of the Lieb definition for the energy density functional is examined both in spin-independent and in spin-polarized density functional theory. It is pointed out that the nonuniqueness of the external magnetic field B(r{yields}) corresponding to a given pair of ground-state density n(r{yields}) and spin density s(r{yields}) in spin-polarized density functional theory implies the nonexistence of the total derivative of the SDFT Lieb functional F{sub N,N{sub s}{sup L}[n,s] with respect to N{sub s}}. By giving a suitable extension of F{sub N}{sup L}[n] and F{sub N,N{sub s}{sup L}[n,s] for N{ne}{integral}n(r{yields})dr{yields} and N{sub s{ne}{integral}}}s(r{yields})dr{yields}, it is then shown that their derivatives with respect to N and N{sub s} are equal to the derivatives, with respect to N and N{sub s}, of the total energies E[N,v] and E[N,N{sub s},v,B] minus the external-field energy components, respectively.

Authors:
;  [1]
  1. General Chemistry Department (ALGC), Member of the QCMM Alliance Ghent-Brussels, Free University of Brussels (VUB), B-1050 Brussels (Belgium)
Publication Date:
OSTI Identifier:
21408418
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 81; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.81.032512; (c) 2010 The American Physical Society; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 74 ATOMIC AND MOLECULAR PHYSICS; DENSITY; DENSITY FUNCTIONAL METHOD; ENERGY DENSITY; GROUND STATES; MAGNETIC FIELDS; SPIN; SPIN ORIENTATION; ANGULAR MOMENTUM; CALCULATION METHODS; ENERGY LEVELS; ORIENTATION; PARTICLE PROPERTIES; PHYSICAL PROPERTIES; VARIATIONAL METHODS

Citation Formats

Gal, T, and Geerlings, P. Derivative of the Lieb definition for the energy functional of density-functional theory with respect to the particle number and the spin number. United States: N. p., 2010. Web. doi:10.1103/PHYSREVA.81.032512.
Gal, T, & Geerlings, P. Derivative of the Lieb definition for the energy functional of density-functional theory with respect to the particle number and the spin number. United States. https://doi.org/10.1103/PHYSREVA.81.032512
Gal, T, and Geerlings, P. 2010. "Derivative of the Lieb definition for the energy functional of density-functional theory with respect to the particle number and the spin number". United States. https://doi.org/10.1103/PHYSREVA.81.032512.
@article{osti_21408418,
title = {Derivative of the Lieb definition for the energy functional of density-functional theory with respect to the particle number and the spin number},
author = {Gal, T and Geerlings, P},
abstractNote = {The nature of the explicit dependence on the particle number N and on the spin number N{sub s} of the Lieb definition for the energy density functional is examined both in spin-independent and in spin-polarized density functional theory. It is pointed out that the nonuniqueness of the external magnetic field B(r{yields}) corresponding to a given pair of ground-state density n(r{yields}) and spin density s(r{yields}) in spin-polarized density functional theory implies the nonexistence of the total derivative of the SDFT Lieb functional F{sub N,N{sub s}{sup L}[n,s] with respect to N{sub s}}. By giving a suitable extension of F{sub N}{sup L}[n] and F{sub N,N{sub s}{sup L}[n,s] for N{ne}{integral}n(r{yields})dr{yields} and N{sub s{ne}{integral}}}s(r{yields})dr{yields}, it is then shown that their derivatives with respect to N and N{sub s} are equal to the derivatives, with respect to N and N{sub s}, of the total energies E[N,v] and E[N,N{sub s},v,B] minus the external-field energy components, respectively.},
doi = {10.1103/PHYSREVA.81.032512},
url = {https://www.osti.gov/biblio/21408418}, journal = {Physical Review. A},
issn = {1050-2947},
number = 3,
volume = 81,
place = {United States},
year = {Mon Mar 15 00:00:00 EDT 2010},
month = {Mon Mar 15 00:00:00 EDT 2010}
}