Ab initio methods for the optical properties of CdSe clusters

We have performed time-dependent density functional theory and GW/Bethe-Salpeter calculations of the optical properties of a series of CdSe clusters ranging in size from 10 to 82 atoms and passivated by fictitious atoms of half-integer charge. The two methods predict a different character of the optical excitations of the CdSe clusters. In time-dependent density functional theory, the lowest-energy excitation is mainly due to a single-level to single-level transition. In GW/Bethe-Salpeter, there is a strong mixture of several different transitions, which is attributed to excitonic effects. Furthermore, GW/Bethe-Salpeter calculations predict the presence of dark transitions (optically forbidden) before the first bright transition for all but one of the clusters studied, whereas time-dependent density functional theory predicts the presence of dark transitions for only the two largest clusters. In this paper, we plot and analyze the effective valence and empty state charge densities of these clusters. We determine that the mixing in transitions observed in the GW/Bethe-Salpeter calculations is mostly due to the Bethe-Salpeter kernel and not from the fact that quasiparticle wave functions are a linear combination of wave functions obtained from density functional theory. We calculate the radiative decay lifetime of the excitations, and we explain the selection rules that lead to the presence of dark transitions in two of the clusters: Cd17Se28 and Cd32Se50. Finally, we compare time-dependent density functional theory and GW/Bethe-Salpeter absorption spectra to that of Mie theory, which has recently been shown to yield surprisingly accurate results for Si clusters.