When a silver film is grown on the Si(001) surface at room temperature, it forms a monolayer density film with a (2 × 2) periodicity. Previous models of this (2 × 2) surface, simulated by density functional theory (DFT), are found to be inconsistent with experimental observations. The DFT simulations provide evidence that a new model, the square tetramer model, describes the structure of the observed (2 × 2)-Ag phase and is fully consistent with scanning tunneling microscopy data. Theoretical evidence of a covalent bond shared between the Ag and Si is found that matches previous experiments. Interestingly, the simulations also show that the stoichiometry between Si and Ag changes with metal coverage as adsorbate−adsorbate and adsorbate−substrate interactions balance out. At low coverages, when individual Ag adatoms interact solely with Si, a two-to-one Si−Ag−Si interaction scheme is energetically preferred. At 1 monolayer, when Ag−Ag interactions must be considered, a one-to-one Si− Ag interaction scheme is preferred, as it maximizes Ag−Ag interactions.