This paper presents high-accuracy correlation energies, intracule densities and Coulomb hole(s) for the lithium cation, helium, hydride ion and the system with the critical nuclear charge, Z C , for binding two electrons. The fully correlated (FC) wave function and the Hartree-Fock (HF) wave function are both determined using a Laguerre-based wave function. It is found that for the lithium cation and the helium atom a secondary Coulomb hole is present, in agreement with a previous literature finding, confirming a counterintuitive conclusion that electron correlation can act to bring distant electrons closer together. However, no evidence for a tertiary Coulomb hole is found. For the hydride anion and the system just prior to electron detachment only a single Coulomb hole is present and electron correlation decreases the probability of finding the electrons closer together at all radial distances. The emergence of a secondary Coulomb hole is investigated and found to occur between Z = 1.15 and Z = 1.20. The FC and HF energies and intracule densities (in atomic units) used to calculate the correlation energy and Coulomb hole, respectively, are accurate to at least the nano-scale for helium and the cation and at least the micro-scale for the anions.
Keywords: Coulomb hole; critical nuclear charge for binding; electron correlation; intracule density; two-electron systems.