We present the finite-element method in its application to solving quantum-mechanical problems for diatomic molecules. Results for Hartree-Fock calculations of ${\mathrm{H}}_2$ and Hartree-Fock-Slater calculations for molecules like ${\mathrm{N}}_2$ and CO are presented. The accuracy achieved with fewer than 5000 grid points for the total energies of these systems is ${10}^{\mathrm{-}8}$ a.u., which is about two orders of magnitude better than the accuracy of any other available method.

• Received 13 June 1988

DOI:https://doi.org/10.1103/PhysRevA.38.4994