Enhancing the computational efficiency of de-orbitalized metaGGA exchange-correlation functionals

Conventional metaGGA exchange-correlation functionals in the Kohn-Sham (KS) scheme (Phys. Rev. 140, A1133 (1965)) are used widely because of their accuracy in describing chemical and physical properties. However, these functionals have the disadvantage of higher computational costs than for GGAs because of their explicit dependence on the KS orbitals via the kinetic energy density τ_s.

De-orbitalization of metaGGA functionals removes that dependence by use of an approximation to τ_s that depends solely on the density, its gradient, and its Laplacian (Phys. Rev. A 96, 052512 (2017)). De-orbitalized metaGGA functionals (metaGGA-L) can achieve precision levels close to those for their parent metaGGA functionals. Though the computational cost per self-consistent field cycle of a metaGGA-L is lower than for its parent functional, instabilities introduced by the density Laplacian can increase the number of cycles, so the overall calculation time for a metaGGA-L is not improved.

We report results for the r²SCAN-L functional (Phys. Rev. B 102, 121109 (2020)) of applying common function smoothing techniques to the density Laplacian (moving average, gaussian smoothing, median filtering, cubic splines, etc.) as measured by computational costs for various molecular test sets (heats of formation, bond distances, frequencies).