Accurate finite-element multi-grid (FEM-MG) description for angular momentum and spin dependences of Kohn–Sham density functionals for axially restricted calculations on first-row atoms and dimers

A comparative study of various combinations of exchange and correlation density functionals was made possible by the finite element multi-grid method which has a controlled accuracy and became fast enough for large-scale applications on atoms and diatomic molecules under axial symmetry. The open-shell atoms B, C and O exhibit particularly interesting behaviour on occupation number variation, differing strongly in a spin polarized and unpolarized approach. In the molecule C2, the singlet ground state and the triplet excited state are characteristically differently well described, independent of the specific density functional. A symmetry dilemma of present density functionals carried on from atoms to the C2 dimer becomes obvious.