Relevance of the slowly-varying electron gas to atoms, molecules, and solids

Details Relevance of the slowly-varying electron gas to atoms, molecules, and solids Relevance of the slowly-varying electron gas to atoms, molecules, and solids

2006-05-06

arxiv.org/abs/quant-ph/0605062v2

Physics

Quantum Physics

5 pages, 4 figures, submitted at PRL

Scientific paper

10.1103/PhysRevLett.97.223002

Under a certain scaling, the electron densities of finite systems become both large and slowly-varying, so that the gradient expansions of the density functionals for the Kohn-Sham kinetic and exchange energies become asymptotically exact to order $\nabla^2$. Neutral atoms of large $Z$ scale similarly, but a cusp correction at the nucleus requires generalizing the gradient expansion for exchange, producing the wrong gradient coefficient in the slowly-varying limit. Meta-generalized gradient approximations (meta-GGA's) recover both the slowly-varying and large-$Z$ limits. GGA correlation energies of large-Z atoms are found to be accurate.

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