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

Abstract

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 twoelectron 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 oneelectron 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 ZHF C =1.031 177 528. This article is part of the theme issue 'Modern theoretical chemistry'.