Density-functional theory of the correlation energy in atoms and ions: A simple analytic model and a challenge

give good results for the correlation energies of neutral atoms, in contrast to LSD which overestimates these energies by a factor of 2. However, all three approximations show an incorrect lnZ leading behavior when the nuclear charge Z tends to infinity at fixed electron number N. It is hard to see how any a priori electron-gas approximation can reproduce the exact leading behavior, which is constant or linear in Z according to the value of N.