Asymptotic Analysis of Atomic Pauli Potentials

In orbital free (OF) DFT, the functional derivative of the Pauli contribution to the Kohn-Sham kinetic energy, the Pauli potential, is key to solving for the density. It can be expressed as the Pauli kinetic energy per particle, plus a response potential which describes the response of this quantity to a change in density. We have constructed the exact response and Pauli potentials for closed shell atoms for which the former becomes an exact eigenvalue expression, extended to large Z atoms attainable only in theory. We have done this non-relativistically because of the known asymptotic behavior of a semi-classical Fermi-electron gas, which is the limit of the core electrons of an atom as nuclear charge approaches infinity. In this limit and as radius approaches zero, we can show that the Pauli potential approaches the magnitude of the lowest energy eigenvalue. We have also compared several gradient expansions to test their utility as orbital free approximations to the response potential. This research may help produce orbital free approximations to the Pauli potential with proper Z scaling, and by extension may generate OFDFT models that can solve for the density of both homogeneous and inhomogeneous systems.