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 parametrization 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.
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Gori‐Giorgi et al. (2006) studied this question.
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