First Principles Absorption Spectra of Si$_n$ ($n=20-28$) Clusters: TDLDA versus Predictions from Mie Theory

First-principles absorption spectra calculated within the time- dependent local-density approximation for Si$_n$ ($n=20-28$) clusters reveal that prolate and compact clusters have distinct shape signatures, but no clear size dependence for a given shape.\footnote{Idrobo, Jackson, Yang, and Ogut, Phys. Rev. B {\bf 74}, 153410 (2006)} The shape dependence and size independence of the spectra and most of the peak positions and intensities can be explained remarkably well within the {\em classical} Mie theory, developed for light absorption by {\em metallic} particles using the {\em bulk} dielectric function of Si. Moreover, the experimental spectrum of Si$_{21}$ is in very good agreement with the theoretical spectrum of the prolate cluster, which is lower in energy than the compact one at this size.