Local density calculations are presented on the Si(111)- ×3 x ×3 -Ag surface in the so-called HCT model. The following questions are addressed: (a) Why does the substrate assume a missing top layer (MTL) configuration, instead of the familiar double layer? (b) What is the driving force for the trimerization exhibited by the MTL surface? (c) Why does this trimerization not occur for Ag/Ge? Simple arguments would estimate the Si(111) MTL surface to have a surface energy 4.60 eV per surface atom higher than an intact double layer surface. Cluster calculations show that due to the formation of silicon trimers this figure is reduced to approximately 1.1 eV per surface atom. This implies that interaction with the silver atoms is required to make the observed HCT model the most stable surface structure. Both trimerization of the resulting surface and its reactivity towards silver are understood from the highest occupied cluster orbitals. Slab calculations confirm the cluster picture. Similar calculations on a germanium substrate show that the formation of trimers is energetically much less favorable for a Ge MTL surface. This confirms the existing models for silver adsorption on silicon (Si trimers) and germanium (no Ge trimers) substrates.