Optimization of kinetic energy functionals for orbital-free exchange-correlation meta-GGAs.

Orbital-free (OF) meta-GGA functionals for the exchange-correlation energy [1,2] have shown promise as a cost-effective alternative to conventional meta-GGAs. These replace the noninteracting kinetic energy (KE) density used in a meta-GGA with a pure functional of the density. One family of KE functionals, based on the Perdew-Constantin functional (Phys. Rev. B 75, 155109 (2007)), uses the Laplacian of the density to switch from the slowly varying electron gas to the von Weizsacker or localized electron-pair limits, resulting in an accurate OF model for the KE density. Unfortunately use of the density Laplacian creates unphysically spiky Pauli potentials that are numerically slow to converge and lead to noisy results. We discuss the construction of a measure of smoothness of functional potentials and the implementation of an optimization procedure for minimizing fluctuations in the potential based on the Poisson equation. This is used to generate modifications of the PC and related functionals. Tests on small atoms demonstrate the issue of noise in Laplacian-based potentials and the value of incorporating potential smoothness as a design goal for developing such functionals.

[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)