Excitation energies from time-dependent density-functional formalism for small systems

As a test of the time-dependent local-density approximation (TDLDA), we study the (1)Sigma(g)(+) --> (1)Sigma(u)(+) excitation of H-2 as a function of the nuclear distance d. We find rather accurate results for intermediate d but not for small and large d. At large d, TDLDA fails due to the strong non-locality and energy dependence of the exact functional. The spin-dependent formalism gives a qualitative improvement for large d. To analyze the results, we compare with the 2s --> 2p excitation for He, Li and Be for small and intermediate d and with the Hubbard model for large d. The fairly accurate results for Li and Be are related to the accuracy of the ground-state formalism for a few electrons.