Methods of corrections to to GEA approximations of the Pauli potential

In recent years many advances have been made in Orbital-Free Density Functional Theory (OFDFT), which attempts to remove orbitals from the Kohn-Sham DFT approach, either completely, or by approximating the kinetic energy density from meta-GGA exchange correlation functionals. The difficulty in OFKE models is in modeling the Pauli energy, the contribution to the KE of Pauli statistics. One aspect of this problem is correctly producing the OF Pauli potential, the functional derivative of the Pauli KE. Recent mathematical analysis of orbital free kinetic energy models based on Gradient Expansion Approximations (GEA)s, like the Airy gas model, have offered insight in modeling the Pauli potential for neutral atoms. However all of these models suffer from gross inaccuracies in the nuclear cusp region, as well as an unexpected deviation in the core. The exact Pauli potential approaches a constant near the nucleus related eigenvalue of the lowest occupied atomic orbital, but all GEAs become infinitely negative at the singularity. We propose a smooth non-analytic stitching function to correct the error in the near nuclear region for Pauli potential GEAs, and explore the outer core. This is similar to work done by Perdew and Constantin as well as previous work from this group done on KEDs.