  By splitting the Coulomb interaction into long-range and short-range
components, we decompose the energy of a quantum electronic system into
long-range and short-range contributions. We show that the long-range part of
the energy can be efficiently calculated by traditional wave function methods,
while the short-range part can be handled by a density functional. The analysis
of this functional with respect to the range of the associated interaction
reveals that, in the limit of a very short-range interaction, the short-range
exchange-correlation energy can be expressed as a simple local functional of
the on-top pair density and its first derivatives. This provides an explanation
for the accuracy of the local density approximation (LDA) for the short-range
functional. Moreover, this analysis leads also to new simple approximations for
the short-range exchange and correlation energies improving the LDA.
