Effect of the orbital-overlap dependence on Meta Generalized Gradient Approximation

The dimensionless inhomogeneity parameter, $\alpha $, characterizing the extent of orbital overlap, is disentangled from the other dimensionless inhomogeneity parameter, s, the reduced density gradient, in terms of constructing a meta generalized gradient approximation (MGGA) for the exchange functional. We show that the formation of the intershell region inside an atom is associated with increase of$\alpha $, which suggests MGGA should expect a monotonically decreasing $\alpha $ dependence for a wide range of density. This leads to a simple nonempirical MGGA exchange functional, which interpolates between the sigle-orbital regime for confinement systems, where $\alpha $=0, and the slowly varying density regime, where $\alpha \approx \mbox{1}$, and then extrapolates to $\alpha \to \infty $. The new MGGA exchange functional, combined with the variant of the Perdew-Burke-Erzerhof (PBE) GGA correlation as used in the revised Tao-Perdew-Staroverov-Scuseria (revTPSS) MGGA [1], performs equally well for atoms, molecules, surfaces, and solids, with an implication of a tight Lieb-Oxford bound. \\[4pt] [1] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, L.A. Constantin, and J. Sun, Phys. Rev. Lett. 103, 026403 (2009).