Approximate Wave Functions for the Ground State of Helium

Approximate ${}_{}{}^1{}_{}{}^{}S$ electronic wave functions for the ground state of the helium atom have been obtained by the method of superposition of configurations. Parameters determining the radial factors of orbitals, with spherical harmonic angular factors up to $l=3\mathrm{}$, were varied to minimize the calculated energy. For each choice of the ten parameters varied in this way, a complete calculation was carried out, involving the construction and diagonalization of the twenty-by-twenty configuration interaction matrix obtained from all independent ${}_{}{}^1{}_{}{}^{}S$ functions determined by the ten independent orbital radial factors. The best energy obtained was -2.90276 atomic units, differing from the experimental value by 0.001 atomic unit.