Finite element Hartree–Fock calculations in three dimensions for atoms and small molecules

The present contribution describes a three dimensional finite element approach to the solution of the closed shell Hartree–Fock equations for small molecules. The computational method used to perform such three dimensional finite element Hartree–Fock calculations is based on the use of a factorized Green’s function for both the solution of the three dimensional Schrödinger-type equations as well as of the Poisson equation. Results of such calculations are reported for the helium atom, the beryllium atom, and the three molecules methane, water and ammonia and are compared with highly accurate literature values for the atoms and the results of Gaussian basis set calculations performed with NWCHEM for the molecules.