Constrained Machine Learning de-orbitalization of meta-GGA exchange-correlation functionals

The Strongly Constrained and Appropriately Normed (SCAN) density functional, which has shown impressive performance for diverse problems [1], takes the orbital kinetic energy density τ(r) as an ingredient in its construction. While theoretically convenient, the orbital dependence of τ(r) complicates the exchange-correlation potential and increases computational cost. Recently, Rodriguez and Trickey used the density Laplacian ▽²n(r) to produce a “de-orbitalized” SCAN, without significantly degrading accuracy [2]. This suggests an intriguing but unclear relationship between τ(r) and ▽²n(r). We use deep neural network to construct a machine learned functional model that exploits this relationship to de-orbitalize SCAN (SCAN_ML) and augment it with by enforcing simple exact constraints on the model’s output. The performance and transferability of the machine learned functional is established for molecular and periodic systems.

[1] Jianwei Sun et al. Phys. Rev. Lett. 115,036402 (2015)
[2] Mejia-Rodriguez et al. Phys. Rev. A 96, 052512 (2017)