Semilocal density functional obeying a strongly tightened bound for exchange

Significance Efficient calculation of the properties of atoms, molecules, and solids on the computer requires a semilocal approximation to the density functional for the exchange-correlation energy, which becomes thereby a single integral over three-dimensional space. A recent, strongly tightened lower bound on the exchange energy has been built into the approximation “meta-generalized gradient approximations made very simple,” or MGGA-MVS, with accurate results for heats of formation, energy barriers, and weak interactions of molecules, and for lattice constants of solids. This would not have been possible without the use of a third ingredient (the local kinetic energy density) in addition to the standard two (the local electron density and its gradient). This third ingredient permits accurate energies even with the drastically tightened bound. Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The Lieb–Oxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generalized gradient approximations (GGAs) and meta-GGAs. Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one- and two-electron densities, and conjectured for all densities. In this article, we present a realistic “meta-GGA made very simple” (MGGA-MVS) for exchange that respects this optimal bound, which no previous beyond-LSDA approximation satisfies. This constraint might have been expected to worsen predicted thermochemical properties, but in fact they are improved over those of the Perdew–Burke–Ernzerhof GGA, which has nearly the same correlation part. MVS exchange is however radically different from that of other GGAs and meta-GGAs. Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound. When this nonempirical MVS meta-GGA is hybridized with 25% of exact exchange, the resulting global hybrid gives excellent predictions for atomization energies, reaction barriers, and weak interactions of molecules.