Strongly Constrained and Appropriately Normed Semilocal Density Functional

Abstract

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...

Synergy of van der Waals and self-interaction corrections in transition metal monoxides

“…This results in a more negative vdW correction to the total energy for the RS phase than for the ZB one. In meta-GGAs, the intermediate-range vdW interaction mainly arises from electron density with α ≫ 1 [33,52]. In Fig.…”

“…with τ the kinetic energy density of the valence electrons, and τ W and τ 0 the von Weizsäcker and uniform electron gas kinetic energy densities [33,52]. For more discussion, we refer to Ref.…”

“…We numerically test this proposal with four representative DFT flavors: the standard PBE-GGA [6], the strongly constrained and appropriately normed (SCAN) meta-GGA [33], the rev-vdW-DF2 (revDF2) vdW functional for solids [34], and the Heyd-Scuseria-Ernzerhof range-separated hybrid functional (HSE06) [15]. SIC is applied to PBE, SCAN and revDF2 via DFT+U [12], vdWC to PBE and HSE06 via the Tkatchenko-Scheffler (TS) method [35,36], and vdWC to SCAN via the rVV10 non-local correlation [37] (a revised form of VV10 [38]).…”

Kinetic and Exchange Energy Densities near the Nucleus

“…Meta-generalized gradient approximations (meta-GGAs) [31][32][33][34][35][36][37][38][39][40][41][42] are the most sophisticated semilocal functionals, incorporating important exact conditions and having an improved overall accuracy with respect to the GGA functionals. The meta-GGA functionals use as an additional ingredient to the GGA ones the Kohn-Sham positive KE density:…”

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

“…[143][144][145][146][147] Moreover, a KS can distinguish and quantify the orbital overlap, [148] the nonlocality of the KED at the nuclear cusp, [133] in the tail of the density, [133,149] and in the quasi-two-dimensional regime. [150] Due to these remarkable features, a KS is the main KED dependent ingredient for recent nonempirical (or semi-empirical) [66,67,148,[151][152][153] and highly empirical [28] meta-GGA XC functionals. …”