The ground-state energy, electron density, and related properties of
atoms, molecules, condensed matter, and surfaces can be computed
efficiently when the exchange-correlation energy as a functional of the
density is approximated semilocally. We propose the first
meta-generalized gradient approximation that is fully constrained
(obeying all 17 exact constraints that a meta-GGA can). It is also exact
for “appropriate norms” (not only the slowly-varying electron gas and
the H atom, but also rare-gas atoms). This nonempirical SCAN meta-GGA
can achieve remarkable accuracy when the exact exchange-correlation hole
is localized near its electron, and especially for geometries, weak
interactions, heats of formation, defect formation energies, etc.
(Supported in part by NSF-DMR 1305135).