Convergence of the Density Gradient Expansion for Atoms

The inhomogeneity correction to the correlation energy of an electron gas is added to the Thomas-Fermi energy-density functional for atoms. The density is significantly modified only inside a radius of the order $Z^{\frac{-1\mathrm{}}{3}}\times {10}^{-5\mathrm{}}$ Bohr radii. This does not reduce the density gradient sufficiently to make the expansion convergent.