The spherically averaged intracule density I(r) is calculated with minimal and split-valence basis sets in the ground state of the hydrogen molecule. Restricted Hartree-Fock calculations indicate a high probability of interelectronic distances (r) of the order of 1 au as the internuclear separation (R) goes to infinity due to the incorrect dissociation of H₂. The inadequacy of the restricted Hartree-Fock I(r) at large R is further illustrated by calculating (1/r) as a function of R. Configuration interaction calculations are shown to yield the correct qualitative form for I(r) at large R and when combined with the Hartree-Fock results yield the approximate Coulomb hole in H₂ as a function of internuclear separation. Explicit formulae for the evaluation of I(r) and its moments with s-type Gaussian basis functions are included.