A GW+Bethe-Salpeter calculation on photoabsorption spectra of (CdSe)3 and (CdSe)6 clusters.

Photoabsorption spectra are calculated for the magic number clusters, (CdSe)(3) and (CdSe)(6), using an all-electron mixed basis GW scheme with the excitonic effect incorporated by solving the Bethe-Salpeter equation (BSE). The GW+BSE calculation provided clear size dependence of the optical gap as expected, while magnitude of the gap is overestimated compared to available experimental one. The gap is found very similarly overestimated when using the local density approximation (LDA) within the density functional theory because accidental error cancellation occurs between the significantly underestimated LDA gap and the excitonic effect neglected therein. The excitonic states are described by superposition of many one-particle states that would not be properly described within a one-particle theory, as clearly visualized in the plot of the exciton wavefunctions.