Consistent deorbitalization and new deorbitalizers for meta-GGA exchange-correlation functionals

A key challenge for use of Kohn-Sham density functional theory is to improve the quality and accuracy of low-computational cost exchange-correlation (XC) density functional approximations (DFAs). De-orbitalization, the replacement of the KS kinetic energy density in a meta-GGA with an explicit function of n(r), its gradient, and its laplacian, is a recently successful approach with the SCAN and r²SCAN DFAs [Phys. Rev. A 96, 052512 (2017); Phys. Rev. B 102, 121109 (2020)]. Their procedure was not entirely consistent. Here we reparametrize the α switching function consistently with the atomic densities of the parent DFAs. The result is almost indistinguishable from the original: slight improvements on heats of formation (G3/99X), bond lengths (T96-R), and vibration frequencies (T82-F). We also have extended consistent deorbitalization to the original, regularized, and revised regularized Tao-Mo DFAs [Phys. Rev. Letter. 117, 073001 (2016); J. Chem. Phys. 153, 184112 (2020); J. Chem. Phys. 155, 024103 (2021)] with good results.