Computation of Coulomb and exchange radial intracule densities

The computation of the Coulomb and exchange components J(u) and K(u), respectively, of the Hartree–Fock radial intracule density within the PRISM approach is discussed. Formulae are presented for the even-origin derivatives of these quantities and for the even-order moments of J(u). For molecular systems, we demonstrate that J(u) has, as expected, long-range nature comparable with the molecular extent but, in contrast, that K(u) is relatively short-range, with delocalisation effects providing additional structure and enhancing the range of the intracule.