By extrapolating the energies of nonrelativistic atoms and their ions with up to 3000 electrons within Kohn-Sham density functional theory, we find that the ionization potential remains finite and increases across a row of the periodic table, even as Z → ∞. The local density approximation for the exchange contribution becomes more accurate (or even exact) in this limit. Extended Thomas-Fermi theory matches the shell average of both the ionization potential and density change.
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