Sanibel Symposium

In orbital-free density functional theory (OFDFT), the functional derivative of the Pauli contribution to the Kohn-Sham kinetic energy, the Pauli potential, is key to solving for the density. We construct the exact Pauli potential for closed shell atoms and extend to large Z atoms attainable only in theory. The asymptotic behavior of the KED of core electrons and the integrated KE in this limit tends to that of the semiclassical Fermi-electron gas, providing a disciplined way to develop a density functional approximation to it. We show that the Pauli potential tends to the magnitude of the lowest energy eigenvalue as radius approaches zero and Z approaches infinity. In marked contrast to the case of the Pauli energy density, we find that the potential only converges onto the Thomas-Fermi limit for the inner 50% of electrons and tends to a different limiting behavior for the outer core. Finally, the behavior of the potential in the evanescent region far from the nucleus shows a strong dependence on column of the periodic table, with the potential of noble gases, with a closed p valence shell diverging to infinity and that of atoms with closed s and d valence shells tending to zero. These results should aid the construction of orbital-free approximations to the Pauli potential with proper scaling to high density and particle number, and ultimately better OFDFT models.