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

John P. Perdew·Lucian A. Constantin·Espen Sagvolden·Kieron Burke
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Abstract

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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John P. Perdew, Lucian A. Constantin, Espen Sagvolden, Kieron Burke. 2006-07-20. Relevance of the slowly-varying electron gas to atoms, molecules, and solids. https://doi.org/10.1103/physrevlett.97.223002

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