We recently proposed a structural model for the Si!331"-!12!1" surface reconstruction containing silicon pentamers and adatoms as elementary structural building blocks. Using first-principles density functional theory we here investigate the stability of a variety of adatom configurations and determine the lowest-energy configuration. We also present a detailed comparison of the energetics between our model for Si!331"-!12 !1" and the adatom-tetramer-interstitial model for Si!110"-!16!2", which shares the same structural building blocks.