Molecular and solid-state tests of density functional approximations: LSD, GGAs, and meta-GGAs

Results from numerical tests of nine approximate exchange–correlation energy functionals are reported for various systems—atoms, molecules, surfaces, and bulk solids. The functional forms can be divided into three categories: (1) the local spin density (LSD) approximation, (2) generalized gradient approximations (GGAs), and (3) meta-GGAs. In addition to the spin densities and their first gradients, the input to a meta-GGA includes other semilocal information such as Laplacians of the spin densities or orbital kinetic energy densities. We present a way to visualize meta-GGA nonlocality which generalizes that for GGA nonlocality, and which stresses the different meta-GGA descriptions of iso-orbital and orbital overlap regions of space. While some of the tested approximations were constructed semiempirically with many parameters fitted to chemical data, others were constructed to incorporate key properties of the exact exchange–correlation energy. The latter functionals perform well for both small and extended systems, with the best performance achieved by a meta-GGA which recovers the correct gradient expansion. While the semiempirical functionals can achieve high accuracy for atoms and molecules, they are typically less accurate for surfaces and solids. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 889–909, 1999