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

Abstract

As a test of the time-dependent local-density approximation (TDLDA), we study the 1Σg+ → 1Σu+ excitation of H2 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.