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Phys. Rev. A 75, 032517 (2007) [8 pages]

Asymptotic near-nucleus structure of the electron-interaction potential in local effective potential theories

Zhixin Qian
Department of Physics, Peking University, Beijing 100871, China

Viraht Sahni
Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210, USA
Received 30 October 2006; published 26 March 2007

In local effective potential theories of electronic structure, the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects, are all incorporated in the local electron-interaction potential vee(r). In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic near-nucleus expansion of this potential is vee(r)=vee(0)+betar+O(r2), with vee(0) being finite. By assuming that the Schrödinger 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 correlation-kinetic 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 near-nucleus expansion of the Hohenberg-Kohn-Sham theory exchange vx(r) and correlation vc(r) potentials. These functions also approach the nucleus linearly with the linear term of vx(r) being solely due to the lowest-order correlation kinetic effects, and the linear term of vc(r) being due solely to the higher-order correlation kinetic contributions. The above conclusions are equally valid for systems of arbitrary symmetry, provided spherical averages of the properties are employed.

©2007 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevA.75.032517
DOI: 10.1103/PhysRevA.75.032517
PACS: 31.15.Ew; 71.15.Mb; 71.10.-w
  • 31.15.Ew
    Density-functional theory (atoms and molecules)
  • 71.15.Mb
    Density functional theory, local density approximation, gradient and other corrections (condensed matter electronic structure)
  • 71.10.-w
    Theories and models of many electron systems in condensed matter
  • YEAR: 2007
KEYWORDS: density functional theory, electron correlations, Schrodinger equation, wave functions, atomic structure

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