Abstract
The fourth-order density-gradient expansion of the fermion kinetic energy contains terms which integrate over space to zero foranalytic densities, butnot for the densities of atoms or of those metal-surface models for which the expansion has been tested. Evaluation of these terms for spin-unpolarized atoms and in spin-density functional calculations for atoms, as well as for metal surfaces, show that the fourth-order expansion is not quite as accurate as it has been believed to be.
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