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

The goal of Orbital-Free Density Functional Theory is to model the Kohn-Sham noninteracting kinetic energy as a functional of ingredients derived from the density directly, so as to remove the bottleneck of computing orbitals in large systems.  The Perdew-Constantin KE meta-GGA [1] and later improvements [2] use the Laplacian of the density to switch from the slowly varying electron gas to the von Weizsacker or single electron-pair limits. While producing an accurate KE density, that use of the density Laplacian creates unphysically spiky Pauli potentials that are numerically difficult to solve and lead to noisy results. To ameliorate this problem, we construct and test a smoothness measure based on the variational description of Poisson's equation, applied to the Laplacian-generated terms in the potential. Optimization of PC-like models with respect to this measure under the constraint of preserving the total kinetic energy can substantially but not completely remove unphysical features in the Pauli potentials of small atoms.   We discuss prospects for using the result in deorbitalized meta-GGA functionals.

[1] J. P. Perdew and L. A. Constantin, Phys. Rev. B 75, 155109 (2007)

[2] A. Cancio, D. Stewart and A. Kuna, JCP 144, 084107 (2016)