Atomic correlation energies and the generalized gradient approximation
  Careful extrapolation of atomic correlation energies suggests that $E_c$ tends to $-AZ\log{Z} + BZ$ as $Z$ tends to infinity, where $Z$ is the atomic number, $A$ is known, and $B$ is about 38 milliHartrees. The coefficients roughly agree with those of the high-density limit of the real-space construction of the generalized gradient approximation. An asymptotic coefficient, missed by previous derivations, is included in a revised approximation. The exchange is also corrected, reducing atomic errors considerably. 
Kieron Burke, Antonio Cancio, Tim Gould and Stefano Pittalis
cond-mat.mtrl-sci cond-mat.other physics.chem-ph quant-ph