Asymptotic nearnucleus structure of the electroninteraction potential in local effective potential theories
Abstract
In local effective potential theories of electronic structure, the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlationkinetic effects, are all incorporated in the local electroninteraction potential v{sub ee}(r). In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic nearnucleus expansion of this potential is v{sub ee}(r)=v{sub ee}(0)+{beta}r+O(r{sup 2}), with v{sub ee}(0) being finite. By assuming that the Schroedinger and local effective potential theory wave functions are analytic near the nucleus of atoms, we prove the following via quantal density functional theory (QDFT): (i) Correlations due to the Pauli principle and Coulomb correlations do not contribute to the linear structure; (ii) these Pauli and Coulomb correlations contribute quadratically; (iii) the linear structure is solely due to correlationkinetic effects, the contributions of these effects being determined analytically. We also derive by application of adiabatic coupling constant perturbation theory via QDFT (iv) the asymptotic nearnucleus expansion of the HohenbergKohnSham theory exchange v{sub x}(r) and correlation v{sub c}(r) potentials. These functions also approach the nucleus linearly with the linear term of v{sub x}(r) being solely due to the lowestorder correlation kinetic effects, and the linear term of v{sub c}(r) being due solely to themore »
 Authors:
 Department of Physics, Peking University, Beijing 100871 (China)
 (United States)
 Publication Date:
 OSTI Identifier:
 20982314
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032517; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; COULOMB FIELD; COUPLING CONSTANTS; DENSITY FUNCTIONAL METHOD; ELECTRONIC STRUCTURE; ELECTRONS; INTERACTIONS; NUCLEI; PAULI PRINCIPLE; PERTURBATION THEORY; POTENTIALS; SCHROEDINGER EQUATION; SPHERICAL CONFIGURATION; SYMMETRY; WAVE FUNCTIONS
Citation Formats
Qian, Zhixin, Sahni, Viraht, and Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210. Asymptotic nearnucleus structure of the electroninteraction potential in local effective potential theories. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.032517.
Qian, Zhixin, Sahni, Viraht, & Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210. Asymptotic nearnucleus structure of the electroninteraction potential in local effective potential theories. United States. doi:10.1103/PHYSREVA.75.032517.
Qian, Zhixin, Sahni, Viraht, and Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210. Thu .
"Asymptotic nearnucleus structure of the electroninteraction potential in local effective potential theories". United States.
doi:10.1103/PHYSREVA.75.032517.
@article{osti_20982314,
title = {Asymptotic nearnucleus structure of the electroninteraction potential in local effective potential theories},
author = {Qian, Zhixin and Sahni, Viraht and Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210},
abstractNote = {In local effective potential theories of electronic structure, the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlationkinetic effects, are all incorporated in the local electroninteraction potential v{sub ee}(r). In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic nearnucleus expansion of this potential is v{sub ee}(r)=v{sub ee}(0)+{beta}r+O(r{sup 2}), with v{sub ee}(0) being finite. By assuming that the Schroedinger and local effective potential theory wave functions are analytic near the nucleus of atoms, we prove the following via quantal density functional theory (QDFT): (i) Correlations due to the Pauli principle and Coulomb correlations do not contribute to the linear structure; (ii) these Pauli and Coulomb correlations contribute quadratically; (iii) the linear structure is solely due to correlationkinetic effects, the contributions of these effects being determined analytically. We also derive by application of adiabatic coupling constant perturbation theory via QDFT (iv) the asymptotic nearnucleus expansion of the HohenbergKohnSham theory exchange v{sub x}(r) and correlation v{sub c}(r) potentials. These functions also approach the nucleus linearly with the linear term of v{sub x}(r) being solely due to the lowestorder correlation kinetic effects, and the linear term of v{sub c}(r) being due solely to the higherorder correlation kinetic contributions. The above conclusions are equally valid for systems of arbitrary symmetry, provided spherical averages of the properties are employed.},
doi = {10.1103/PHYSREVA.75.032517},
journal = {Physical Review. A},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}

Local(multiplicative) effective potential energytheories of electronic structure comprise the transformation of the Schroedinger equation for interacting Fermi systems to model noninteracting Fermi or Bose systems whereby the equivalent density and energy are obtained. By employing the integrated form of the Kato electronnucleus cusp condition, we prove that the effective electroninteraction potential energy of these model fermions or bosons is finite at a nucleus. The proof is general and valid for arbitrary system whether it be atomic, molecular, or solid state, and for arbitrary state and symmetry. This then provides justification for all prior work in the literature based on themore »

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