  We study the asymptotic expansion of the neutral-atom energy as the atomic
number Z goes to infinity, presenting a new method to extract the coefficients
from oscillating numerical data. We find that recovery of the correct expansion
is an exact condition on the Kohn-Sham kinetic energy that is important for the
accuracy of approximate kinetic energy functionals for atoms, molecules and
solids, when evaluated on a Kohn-Sham density. For example, this determines the
small gradient limit of any generalized gradient approximation, and conflicts
somewhat with the standard gradient expansion. Tests are performed on atoms,
molecules, and jellium clusters. We also give a modern, highly accurate
parametrization of the Thomas-Fermi density of neutral atoms.
