Symmetry of the Atomic Electron Density in Hartree, Hartree-Fock, and Density Functional Theory

Details Symmetry of the Atomic Electron Density in Hartree, Hartree-Fock, and Density Functional Theory Symmetry of the Atomic Electron Density in Hartree, Hartree-Fock, and Density Functional Theory

1999-09-08

arxiv.org/abs/cond-mat/9909127v2

Phys.Rev.A62:052511,2000

Physics

Condensed Matter

Materials Science

11 pages, 6 figures. Expanded discussion of spherical harmonic expansion of Hartree density. Some typos corrected, references

Scientific paper

10.1103/PhysRevA.62.052511

The density of an atom in a state of well-defined 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 show 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 wavefunctions contain an infinite number of spherical harmonics.

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