Condition on the Kohn-Sham kinetic energy and modern parametrization of the Thomas-Fermi density

We study the asymptotic expansion of the neutral-atom energy as the atomic number Z ->infinity, presenting a new method to extract the coefficients from oscillating numerical data. Recovery of the correct expansion yields a condition on the Kohn-Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules, and solids. 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 using densities constructed from Kohn-Sham orbitals. We also give a modern, highly accurate parametrization of the Thomas-Fermi density of neutral atoms.