Performance improvement of deorbitalized exchange-correlation functionals

Deorbitalization of a conventional meta-generalized-gradient exchange-correlation approximation replaces its dependence upon the Kohn-Sham (KS) kinetic energy density with a dependence on the density gradient and Laplacian. In principle, that simplification should provide improved computational performance relative to the original meta-generalized-gradient-approximation form because of the shift from an orbital-dependent generalized KS potential to a true KS local potential. Often that prospective gain is lost because of problematic roughness in the density caused by the density Laplacian and consequent roughness in the exchange-correlation potential from the resulting higher-order spatial derivatives of the density in it. We address the problem by constructing a deorbitalizer based on the ``${\mathrm{r}}²\mathrm{SCAN}$ piecewise polynomial'' (RPP) deorbitalizer from A. D. Kaplan and J. P. Perdew [Phys. Rev. Mater. 6, 083803 (2022)] with comparative smoothness of the potential along with retention of constraint satisfaction as design goals. Applied to the ${\mathrm{r}}²\mathrm{SCAN}$ exchange-correlation functional presented by J. W. Furness et al. [J. Phys. Chem. Lett. 11, 8208 (2020)], we find substantial timing improvements for solid-state calculations over both ${\mathrm{r}}²\mathrm{SCAN}$ and its earlier deorbitalization for high-precision calculations of structural properties, while improving upon the accuracy of RPP deorbitalization for both solids and molecules.