Calculation of optical absorption spectra of hydrogenated Si clusters: Bethe-Salpeter equation versus time-dependent local-density approximation

We present calculations of the optical absorption spectra of clusters ${\mathrm{SiH}}_4,$ ${\mathrm{Si}}_{10}{\mathrm{H}}_{16},$ ${\mathrm{Si}}_{17}{\mathrm{H}}_{36},$ ${\mathrm{Si}}_{29}{\mathrm{H}}_{24},$ and ${\mathrm{Si}}_{35}{\mathrm{H}}_{36},$ as determined from two different methods: the Bethe-Salpeter equation (BSE) with a model dielectric function, and the time-dependent density-functional theory within the adiabatic local-density approximation (TDLDA). Single-particle states are obtained from local-density approximation (LDA) calculations and, for the BSE calculation, a quasiparticle gap correction is provided by quantum Monte Carlo calculations. We find that the exchange-correlation kernel of the TDLDA has almost no effect on the calculated spectra, while the corresponding attractive part of the electron-hole interaction of the BSE produces enhanced absorptive features at low energies. For the smallest cluster ${\mathrm{SiH}}_4,$ the two methods produce markedly different results, with the TDLDA spectra appearing closer to the experimental result. The gross features of the TDLDA and BSE spectra for larger clusters are however similar, due to the strong repulsive Coulomb kernel present in both treatments.