Designing computationally efficient Laplacian-based kinetic energy density functionals.

Deorbitalized meta-GGA functionals for the exchange-correlation energy [1], which replace the noninteracting kinetic energy (KE) density used in a meta-GGA with a pure functional of the density, show promise as a cost-effective alternative to conventional meta-GGAs. Most successful deorbitalizations are based on the Perdew-Constantin KE density functional (Phys. Rev. B 75, 155109 (2007)), and use the Laplacian of the density as an indicator of electron localization. However, use of the density Laplacian can create unphysical features in the exchange potential and lead to slow convergence and noisy results. We construct a measure of the noisiness of a deorbitalized potential, using it to help construct smoothed KE density functionals derived from PC and the recent RPP [2] which was designed to restore gradient-expansion constraints to the r2SCAN metaGGA. Applied to structural test sets for molecules and solids, these perform on par or better than the parent functional vis-a-vis accuracy, and, for VASP calculations for solids, in two-thirds the wall time on a single compute node of University of Florida's Hipergator. However, convergence to self-consistency takes longer for Laplacian-based potentials, particularly for molecular dynamics, indicating instabilities that remain to be resolved.

[1] D. Mejia-Rodriguez and S. B. Trickey Phys. Rev. A 96, 052512 (2017)

[2] A Kaplan and J Perdew Phys. Rev. Materials 6, 083803 (2022)