Variational optimization of Pauli potentials for orbital-free density functional theory.*

In Kohn-Sham density functional theory, the kinetic energy (KE) functional is described by fictitious orbitals. These can create a computational bottleneck for large systems. Orbital-Free Density Functional Theory attempts to model the KE as a functional of ingredients derived from the density directly, avoiding the need for orbitals. In particular, the Perdew-Constantin metaGGA model [1] utilizes the Laplacian of the density to switch between slowly varying electron gas to the von Weizsacker or single electron-pair limits. It and later improvements [2] produce a highly accurate KE density, reproducing the shell structure of atoms for example. With the use of the Laplacian an issue arises of unphysical Pauli potentials that are difficult to find convergent solutions for. We construct a smoothness measure based on the variational description of Poisson's equation. Variational optimization of this measure for Laplacian-based model improve the Pauli potential's smoothness. For hydrogen, results are improved by a factor of 15 in best case scenarios. Results are mixed for atoms, with regions near the nucleus and far from the atom still unreliable.

[1] J. P. Perdew and L. A. Constantin, Phys. Rev. B 75, (2007).
[2] A. Cancio, D. Stewart and A. Kuna, JCP 144, (2016).