  The combination of density functional theory with other approaches to the
many-electron problem through the separation of the electron-electron
interaction into a short-range and a long-range contribution is a promising
method, which is raising more and more interest in recent years. In this work
some properties of the corresponding correlation energy functionals are derived
by studying the electron-electron coalescence condition for a modified
(long-range-only) interaction. A general relation for the on-top (zero
electron-electron distance) pair density is derived, and its usefulness is
discussed with some examples. For the special case of the uniform electron gas,
a simple parameterization of the on-top pair density for a long-range only
interaction is presented and supported by calculations within the ``extended
Overhauser model''. The results of this work can be used to build
self-interaction corrected short-range correlation energy functionals.

Materials Science;Chemical Physics