Data from: Hartree–Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms

An implementation of the Hartree–Fock (HF) method using a Laguerre-based
wave function is described and used to accurately study the ground state
of two-electron atoms in the fixed nucleus approximation, and by
comparison with fully correlated (FC) energies, used to determine accurate
electron correlation energies. A variational parameter A is included in
the wave function and is shown to rapidly increase the convergence of the
energy. The one-electron integrals are solved by series solution and an
analytical form is found for the two-electron integrals. This methodology
is used to produce accurate wave functions, energies and expectation
values for the helium isoelectronic sequence, including at low nuclear
charge just prior to electron detachment. Additionally, the critical
nuclear charge for binding two electrons within the HF approach is
calculated and determined to be ZHFC=1.031 177 528.