A three-dimensional finite element approach towards molecular SCF computations

Fully three‐dimensional, SCF ground‐state computations for the Hartree equation are carried out by a finite element approach that completely avoids forming or storing the Fock matrix. A combination of strategies is used to reduce storage and computational requirements by orders of magnitude over the traditional finite element approach, which makes three‐dimensional molecular orbital computations feasible. Results using the three‐dimensional formulation and computer program are shown for one‐electron systems: He+ and H2+, and for two‐electron systems: He and H2. The best results are within about 30–100 micro‐Hartrees of the exact values of the total energies for the ground states of these systems, indicating that our three‐dimensional approach has been correctly implemented in the computer code.