Local-density theory of multiplet structure

In order to obtain multiplet energies and therefore energies of excited states of atoms and molecules, the local-density theory of Hohenberg, Kohn, and Sham has recently been extended to give the lowest energy of a specified angular momentum and spin symmetry. It is explained why this method does not work if the exchange correlation functional is taken to be symmetry independent. Instead it is shown how the local-density theory can be used to estimate the energies of states of mixed symmetry and how the multiplet splittings are obtained from these estimates. The new method is tested on light atoms and the local-density theory with exchange only reproduces the Hartree-Fock results within 0.1 eV. With correlation included, the error in the local-density approach is typically a factor of 3 less than in the Hartree-Fock approach.