  Under a certain scaling, the electron densities of finite systems become both
large and slowly-varying, so that the gradient expansions of the density
functionals for the Kohn-Sham kinetic and exchange energies become
asymptotically exact to order $\nabla^2$. Neutral atoms of large $Z$ scale
similarly, but a cusp correction at the nucleus requires generalizing the
gradient expansion for exchange, producing the wrong gradient coefficient in
the slowly-varying limit. Meta-generalized gradient approximations (meta-GGA's)
recover both the slowly-varying and large-$Z$ limits. GGA correlation energies
of large-Z atoms are found to be accurate.

Quantum Physics;Materials Science