Exchange-correlation in inhomogeneous systems- a comment on the surface energy problem

The local-density approximation is more accurate for the sum of exchange and correlation energy than for either alone. For the exchange and the correlation energy separately, a power series in density gradients does not exist, and from this behavior we infer that the error in the local-density approximation to either is larger than it is for the sum of the two, for which the density-gradient power series does exist. This is confirmed here for the widely discussed test case of the surface energy in the infinite-barrier model of a bounded metal, by showing that the error in the local-density approximation to the exchange part of the surface energy is sharply reduced by using a short-ranged (Yukawa) interaction, for which the density-gradient power series exists. © 1975.