Unambiguous Exchange-Correlation Energy Density For Hooke'S Atom

Recently, we used Helmholtz's theorem to construct an unambiguous exchange-correlation energy density for use in density functional theory. This energy density requires only knowledge of the density dependence of the exchange-correlation energy functional, E-XC, for its calculation. We calculate this energy density for Hooke's atom in three different regimes: the high-density (or weakly correlated) limit; a moderate density, comparable to that of the He atom; and a low density, in which the system is strongly correlated. We compare the exact unambiguous energy density with approximate energy densities found from approximate energy functionals. The exchange-correlation energy can be deduced directly from the density in the highly correlated limit and a new formula for the high-density limit of the correlation energy is given. (C) 1998 John Wiley & Sons, Inc.