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We report the first three-dimensional wavevector analysis of the jelliumexchange-correlation (xc) surface energy in the random-phase approximation(RPA). The RPA accurately describes long-range xc effects which are challengingfor semi-local approximations, since it includes the universal small-wavevectorbehavior derived by Langreth and Perdew. We use these rigorous RPA calculationsfor jellium slabs to test RPA versions of nonempirical semi-localdensity-functional approximations for the xc energy. The local spin densityapproximation (LSDA) displays cancelling errors in the small and intermediatewavevector regions. The PBE GGA improves the analysis for intermediatewavevectors, but remains too low for small wavevectors (implying too-lowjellium xc surface energies). The nonempirical meta-generalized gradientapproximation of Tao, Perdew, Staroverov, and Scuseria (TPSS meta-GGA) gives arealistic wavevector analysis, even for small wavevectors or long-rangeeffects. We also study the effects of slab thickness and of short-rangecorrections to RPA.Comment: 7 pages, 7 figures, to appear in Phys. Rev.

physical review. b, condensed matter and materials physics

Wave-vector analysis of the jellium exchange-correlation surface energy in the random-phase approximation: Support for nonempirical density functionals