Large Z scaling of Atomic Pauli potentials

Modeling the Pauli energy, the contribution to kinetic energy of Pauli statistics, without using orbitals is an open problem for electronic structure theory. One aspect of this problem is correctly producing the Pauli potential, which is its response to a change in density. A powerful tool to analyze any density functional quantity is Lieb-Simon scaling, taking its limit in non-relativistic neutral atomic systems as nuclear charge and particle number approach infinity. We calculate the exact orbital-dependent Pauli potential for closed-shell atoms out to element Z=976. Lieb and Simon proposed five distinct regions of behavior in the large Z limit, of which our results show four: a region of constant potential near the nucleus, a core where the potential oscillates about the TF potential, a transition region where the potential deviates unexpectedly from the TF potential, and an evanescent region where it decays exponentially. We compare the exact potential to several models that are variations on the gradient expansion to test their utility as orbital-free approximations. This research may provide insight into semi-classical description of Pauli statistics, and new limiting behaviors to aid the improvement of orbital-free DFT functionals.