The ground-state energy, electron density, and related properties of ordinary matter can be computed efficiently when the exchange-correlation energy as a functional of the density is approximated semilocally. We propose the first meta-GGA (meta-generalized gradient approximation) that is fully constrained, obeying all 17 known exact constraints that a meta-GGA can. It is also exact or nearly exact for a set of "appropriate norms", including rare-gas atoms and nonbonded interactions. This SCAN (strongly constrained and appropriately normed) meta-GGA achieves remarkable accuracy for systems where the exact exchange-correlation hole is localized near its electron, and especially for lattice constants and weak interactions.
3Over the past 50 years, Kohn-Sham density functional theory (KS-DFT) [1][2][3] has become an ab initio pillar of condensed matter physics and related sciences. In this theory, the ground-state electron density ( ) and total energy for non-relativistic interacting electrons in a multiplicative external potential can be found exactly by solving selfconsistent one-electron equations, given the uncomputable exact universal exchange-correlation energy [ ] as a functional of ∑ | , | , , with , a KS orbital. This xc energy term can be formally expressed as half the Coulomb interaction between every electron and its exchange-correlation hole in a double integral over space [4,5], but in practice its density functional must be approximated. Semilocal functionals approximate it with a single integral and thus are properly size-extensive and computationally efficient, especially for large unit cells, high-throughput materials searches, and ab initio molecular dynamics simulations.
Many features of the exact functionalknown. Nonempirical functionals, constructed to satisfy exact constraints on this density functional [6][7][8][9], are reliable over a wide range of systems (e.g., atoms, molecules, solids, and surfaces), including many that are unlike those for which these functionals have been tested and validated. In this letter, we present a nonempirical semilocal functional that satisfies all known possible exact constraints for the first time, and is appropriately normed 4 on systems for which semilocal functionals can be exact or extremely accurate.Semilocal approximations can be written as [ , ] ( , , , , , ).Here ( ) and ( ), the electron spin densities, are the only ingredients of the local spin density approximation (LSDA) [1,10,[11][12][13][14]. Spin-density gradients are added in a generalized gradient approximation (GGA) [6,[14][15][16][17][18][19], and the positive orbital kinetic energy densities ∑ | , | (implicit nonlocal functionals of ( ))) are further added in a meta-GGA [7][8][9]20,21]. The broad usefulness of nonempirical semilocal functionals is evidenced by the fact that the PBE GGA construction paper [6] is the 16th most-cited scholarly article of all time [22].The LSDA was based on what we call an "appropriate norm": It was by construction exact for the only set of electron...
