Background
Due to its accuracy and efficiency, density functional theory (DFT) is the choice to calculate electronic structures in chemistry, condensed matter physics, and materials science. In principle, DFT is exact for the ground state electron density and energy. Its exchange correlation energy as a functional of electron density however must be approximated. DFT with the local density approximation (LDA) became popular in condensed matter physics, and then in quantum chemistry after generalized gradient approximations (GGAs) and hybrid GGAs were introduced. Along with its successes however come challenges to DFT, among which is to describe simultaneously accurately various types of bonds forming between atoms and molecules with strengths ranging from several meV to several eV.
The local density approximation (LDA), the earliest approximation in DFT, constructs a local energy density at position from just the local electron density , where the are occupied KohnSham orbitals (spin is suppressed here). Derived from and exact for any uniform electron gas, LDA tends to minimize the inhomogeneity of electron densities of real materials and overestimates the strengths of all bonds near equilibrium. By building in the electron density gradient to reduce this tendency, generalized gradient approximations (GGAs) soften the bonds. Depending on how the electron density gradient is built in, a GGA can be rather accurate for structures or energies, but not both. This dilemma reflects a formal limitation: A GGA cannot satisfy all the known exact constraints appropriate to a semilocal functional (LDA, GGAs, and metaGGAs) where the exchangecorrelation energy is efficiently evaluated as a single integral over threedimensional space. By mixing GGAs with nonlocal exact exchange, hybrid GGAs can further improve the description of covalent, ionic, and hydrogen bonds. However, hybrid GGAs still fail to describe vdW interactions. The computational cost of a hybrid functional can be 10 to 100 times that of a semilocal functional in standard planewave codes, even more so for metallic systems. Another problem with hybrids is that a universal exactexchange mixing parameter is not determined by any exact condition.
The inclusion of the kinetic energy density on top of and its gradient enables metaGGAs to have the flexibility to satisfy more exact constraints and thus circumvent the “structure or energy” dilemma experienced by GGAs. By using a dimensionless variable properly constructed from , metaGGAs can recognize the slowlyvarying densities (alpha~1, characterizing metallic bonds), the singleorbital systems (alpha=0, characterizing covalent single bonds), and noncovalent bonds with between two closed shells. is directly related to the electron localization function (ELF) with , and therefore identifies different chemical bonds.
The local density approximation (LDA), the earliest approximation in DFT, constructs a local energy density at position from just the local electron density , where the are occupied KohnSham orbitals (spin is suppressed here). Derived from and exact for any uniform electron gas, LDA tends to minimize the inhomogeneity of electron densities of real materials and overestimates the strengths of all bonds near equilibrium. By building in the electron density gradient to reduce this tendency, generalized gradient approximations (GGAs) soften the bonds. Depending on how the electron density gradient is built in, a GGA can be rather accurate for structures or energies, but not both. This dilemma reflects a formal limitation: A GGA cannot satisfy all the known exact constraints appropriate to a semilocal functional (LDA, GGAs, and metaGGAs) where the exchangecorrelation energy is efficiently evaluated as a single integral over threedimensional space. By mixing GGAs with nonlocal exact exchange, hybrid GGAs can further improve the description of covalent, ionic, and hydrogen bonds. However, hybrid GGAs still fail to describe vdW interactions. The computational cost of a hybrid functional can be 10 to 100 times that of a semilocal functional in standard planewave codes, even more so for metallic systems. Another problem with hybrids is that a universal exactexchange mixing parameter is not determined by any exact condition.
The inclusion of the kinetic energy density on top of and its gradient enables metaGGAs to have the flexibility to satisfy more exact constraints and thus circumvent the “structure or energy” dilemma experienced by GGAs. By using a dimensionless variable properly constructed from , metaGGAs can recognize the slowlyvarying densities (alpha~1, characterizing metallic bonds), the singleorbital systems (alpha=0, characterizing covalent single bonds), and noncovalent bonds with between two closed shells. is directly related to the electron localization function (ELF) with , and therefore identifies different chemical bonds.
What is SCAN?
The nonempirical strongly constrained and appropriately normed (SCAN) metaGGA was recently developed. SCAN is the first metaGGA that is fully constrained, obeying all 17 known exact constraints that a semilocal functional can. It is also exact or nearly exact for a set of “appropriate norms”, including raregas atoms and nonbonded interactions. SCAN predicts accurate geometries and energies of diverselybonded molecules and materials (including covalent, metallic, ionic, hydrogen, and van der Waals bonds), significantly and systematically improving at comparable efficiency over its predecessors, the GGAs. Often SCAN matches or improves upon the accuracy of a computationally expensive hybrid functional, at almostGGA cost. SCAN is therefore expected to have a broad impact on chemistry, condensed matter physics, and materials science.
Right Figure SCAN remarkably captures the intermediate range, manybody vdW interactions necessary for a quantitative description of various ices and gasphase water hexamers. (a) The relative lattice energy ∆E0=E0 (ice phase)E0(Ih) and equilibrium volume change ∆V0 per water molecule of seven hydrogenordered ice phases with respect to the ground state ice Ih illustrate that SCAN is the only functional tested that predicts the relative stability of ice phases in quantitative agreement with experimental results. E0 is the lattice energy needed to break an ice into isolated water molecules. (b) The relative binding energy per water molecule of four lowenergy water hexamers similarly illustrates that SCAN is the only semilocal density functional approximation that predicts the known energetic ordering of these clusters, evidenced by the agreement between SCAN and CCSD(T). The zeropoint energy effects have been removed from the experimental results for ice. Lines are guides to the eye. Details can be found in Ref. 2[J. Sun et al., Nat. Chem. 8, 831 (2016)].

Unique Features

Potential Impact
