Relevance of the Pauli kinetic energy density for semilocal functionals

A meta-generalized gradient approximation (meta-GGA) exchange functional, based only on the Pauli kinetic enhancement factor, is proposed for quantum chemistry and solid-state physics. The underlining construction of this exchange energy functional is based on a nonlinear equation found from a generalization of the Becke-Roussel approach, where we use the cuspless hydrogen exchange hole density model. We combine the meta-GGA exchange with a simple GGA correlation. The resulting exchange-correlation semilocal functional is remarkably accurate for several thermochemical test cases and quite efficient for the structural and energetic properties of bulk solids. It also provides, in the generalized Kohn-Sham scheme, better orbital energies of atoms and band gaps of semiconductors than other popular semilocal functionals. The present construction is showing the high relevance of the Pauli kinetic energy density for the functional development.