Optimizing kinetic energy functionals for cost-effective de-orbitalized exchange-correlation at the meta-GGA level

Deorbitalized meta-GGAs for the exchange-correlation energy replace the noninteracting kinetic energy density with a pure functional of the density, serving as a cost-effective alternative to conventional meta-GGAs. Most successful deorbitalizations use the Laplacian of the density to switch from the limit of a slowly varying electron gas to that of a localized electron-pair. However, this creates unphysical features in the exchange potential that lead to slow convergence and noisy results.

We present a measure of potential noisiness for Laplacian-based functionals and an optimization procedure to minimize fluctuations on a set of test densities, which we use to develop smoothed XC functionals.  We develop functionals for use with the LAK and r2SCAN metaGGAs, modifying the RPP kinetic energy functional [1].  Replacing the satisfaction of conventional norms in the RPP with that of smoothness of atomic potentials can lead to significantly less noisy potentials.  To date [2], overall run times for equation of state calculations show modest improvement over the parent functional.

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

[2] H Francisco, B Thapa, SB Trickey, AC Cancio, arXiv:2509.00953 (2025)