A Hartree–Fock study of the confined helium atom: Local and global basis set approaches

•Two different basis set methods for atomic Hartree–Fock theory.•Galerkin finite element method and modified Slater-type orbitals.•Confined atom model (helium) under small-to-extreme confinement radii.•Detailed analysis of the electron wave-function and the cusp condition.

Two different basis set methods are used to calculate atomic energy within Hartree–Fock theory. The first is a local basis set approach using high-order real-space finite elements and the second is a global basis set approach using modified Slater-type orbitals. These two approaches are applied to the confined helium atom and are compared by calculating one- and two-electron contributions to the total energy. As a measure of the quality of the electron density, the cusp condition is analyzed.