Density-functional approach to the calculation of correlation energies of two-electron atoms and ions

The correlation-energy density functional is studied here through an exact solution of a two-electron system bound by a harmonic-oscillator external potential. Since the correlation energy is a universal functional of density in density-functional theory, the same functional form is valid for two-electron atoms and ions as well. Using this fact we have proposed here density-functional schemes, within a local-density approximation as well as nonlocal considerations, for the study of correlation energies of two-electron atomic and ionic systems. The nonlocal scheme leads to significant improvement over the local ones, yielding results that show good agreement with the standard values.