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Phys Rev Lett. 2003 Oct 3;91(14):146401. Epub 2003 Sep 30.

Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids.

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Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118, USA.


The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one- or two-electron densities and slowly varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approximations, above the local spin density and GGA rungs.

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