Reworking the Tao-Mo exchange-correlation functional. I. Reconsideration and simplification

The revised, regularized Tao-Mo (rregTM) exchange-correlation density functional approximation (DFA) [A. Patra, S. Jana, and P. Samal, J. Chem. Phys. 153, 184112 (2020) and Jana et al., J. Chem. Phys. 155, 024103 (2021)] resolves the order-of-limits problem in the original TM formulation while preserving its valuable essential behaviors. Those include performance on standard thermochemistry and solid data sets that is competitive with that of the most widely explored meta-generalized-gradient-approximation DFAs (SCAN and r2SCAN) while also providing superior performance on elemental solid magnetization. Puzzlingly however, rregTM proved to be intractable for de-orbitalization via the approach of Mejía-Rodríguez and Trickey [Phys. Rev. A 96, 052512 (2017)]. We report investigation that leads to diagnosis of how the regularization in rregTM of the z indicator functions (z = the ratio of the von-Weizsäcker and Kohn-Sham kinetic energy densities) leads to non-physical behavior. We propose a simpler regularization that eliminates those oddities and that can be calibrated to reproduce the good error patterns of rregTM. We denote this version as simplified, regularized Tao-Mo, sregTM. We also show that it is unnecessary to use rregTM correlation with sregTM exchange: Perdew-Burke-Ernzerhof correlation is sufficient. The subsequent paper shows how sregTM enables some progress on de-orbitalization.