A meta-GGA made free of the order of limits anomaly

We have improved the revised Tao-Perdew-Staroverov-Scuseria (revTPSS) meta-generalized gradient approximation (GGA) in order to remove the order of limits anomaly in its exchange energy. The revTPSS meta-GGA recovers the second-order gradient expansion for a wide range of densities and therefore provides excellent atomization energies and lattice constants. For other properties of materials, however, even the revTPSS does not give the desired accuracy. The revTPSS does not perform as well as expected for the energy differences between different geometries for the same molecular formula and for the related nonbarrier height chemical reaction energies. The same order of limits problem might lead to inaccurate energy differences between different crystal structures and to inaccurate cohesive energies of insulating solids. Here we show a possible way to remove the order of limits anomaly with a weighted difference of the revTPSS exchange between the slowly varying and iso-orbitals (one- or two-electron) limits. We show that the new regularized (regTPSS) gives atomization energies comparable to revTPSS and preserves the accurate lattice constants as well. For other properties, the regTPSS gives at least the same performance as the revTPSS or TPSS meta-GGAs.