Symmetry of the atomic electron density in Hartree, Hartree-Fock, and density-functional theories

1999/09/30 by H. A. Fertig, W. Kohn · 2 citations
Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic and Molecular Physics #Cold Atom Physics and Bose-Einstein Condensates #cond-mat.mtrl-sci

paper · pdf · doi:10.1103/physreva.62.052511

published as Phys.Rev.A62:052511,2000 · 11 pages, 6 figures. Expanded discussion of spherical harmonic expansion of Hartree density. Some typos corrected, references added

arxiv created 2000/03/14 · openalex publication_date 2000/10/16 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The density of an atom in a state of well-defined total angular momentum has a specific finite spherical harmonic content, without and with interactions. Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and local density approximations, generally violate this feature. We analyze, by means of perturbation theory, the degree of this violation and argue that it is small. The correct symmetry of the density can be assured by a constrained-search formulation without significantly altering the calculated energies. We compare our procedure to the (different) common practice of spherically averaging the self-consistent potential. Kohn-Sham density functional theory with the exact exchange-correlation potential has the correct finite spherical harmonic content in its density; but the corresponding exact single-particle potential and wave functions contain an infinite number of spherical harmonics.

Citations

• The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and Methods
• Self-Consistent Equations Including Exchange and Correlation Effects

Cited by

• Degeneracy and size consistency in electronic density functional theory
• Multiconfiguration electron density function for the ATSP2K-package