Abstract
The maximum-entropy formalism is used to obtain approximations to the spherically averaged electron-pair density h(u) in terms of the first few interelectronic moments. This method leads to the least biased results by the information not used. In particular, tight analytical and numerical approximations to the electron-electron repulsion energy ${\mathit{E}}_{\mathit{e}\mathit{e}}$ and to the central electron-pair density h(0) are obtained. Chebyshev inequalities are also applied to obtain bounds on h(u), showing the complementarity of both methods. For illustration, the accuracy of the bounds and approximations obtained are studied by means of Hylleraas-type wave functions.
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