Unambiguous exchange–correlation energy density for Hooke's atom

Abstract

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, EXC, 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. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 583–589, 1998