The binding of palladium metal atoms and dimeric clusters in the zeolite gmelinite has been studied using nonlocal density functional theory. For a single atom, the preferred location is found to be one where there is a significant interaction with silicon of the framework due to similar energies of the frontier orbitals of the species. This type of binding is found to be similar regardless of whether the material is purely siliceous or if aluminum is present, though the binding is stronger in the latter case. When a second palladium is coordinated to form a dimer this atom only interacts with oxygen of the framework, leading to a polarized charge distribution on the dimer. Adsorption of carbon monoxide on palladium is found to completely alter the situation, with the PdCO complex binding just to a framework oxygen, while the interaction with silicon is lost. The CObridged dimer preferentially forms a seven-ring species by straddling two framework oxygens that are three bonds apart. Binding energies for carbon monoxide are largely unperturbed for the metal particles in the siliceous region of the zeolite, while they are lowered below the gas-phase value for an aluminosilicate material.