Correlation energy per particle from the coupling-constant integration

The adiabatic connection can be used in density functional theory to define the unknown ~exchange and! correlation density functional. Using conventional wave-function techniques, accurate estimates of thus defined ~exchange and! correlation energy densities can be obtained for specified systems. In this paper, numerical results are presented for the He and the Be atom, as well as the isoelectron Ne ions. A generalized gradient approximation is tested against these results. The comparison shows that the generalized gradient approximation has the ability to detect local features ~the shell structure!. In one case (Ne), however, it turns out that the accurate correlation energy per particle is lower than that obtained within the local-density approximation, and thus not properly corrected by the generalized gradient approximation.