  We analyze a decomposition of the Coulomb electron-electron interaction into
a long-range and a short-range part in the framework of density functional
theory, deriving some scaling relations and the corresponding virial theorem.
We study the behavior of the local density approximation in the high-density
limit for the long-range and the short-range functionals by carrying out a
detailed analysis of the correlation energy of a uniform electron gas
interacting via a long-range only electron-electron repulsion. Possible
definitions of exchange and correlation energy densities are discussed and
clarified with some examples.
