The bonding of atomic oxygen on Pt(111) and Rh(111) was examined using density functional theory in order to understand their different chemical properties. The oxygen-surface interactions were modeled by bonding atomic oxygen to 10-atom clusters of Pt and Ph designed to model the (111) surface. Density functional theory was applied using the local density and generalized gradient approximations; results were obtained for both double-zeta and triple-zeta basis sets. Optimized geometries and binding energies were computed and favorably compared to available experimental values. Interestingly, the ionic bonding in the two cases is nearly the same, based on the similarities in the charge on oxygen. The Hirshfeld charges on oxygen were -0.225 and -0.207 for Rh-10-O and Pt-10-O, respectively, using the double-zeta basis set. A more detailed analysis of the covalent bonding using crystal orbital overlap populations indicated that the 2p orbitals of oxygen interact in a greater bonding fashion with both the sp and d orbitals of Ph than with those of Pt. Additional calculations with adsorbed hydroxyl on these metal clusters show differences in covalent bonding similar to that of oxygen. In this case, however, differences in ionic bonding play a role; oxygen in hydroxyl has a greater charge on Pt than Ph. This leads to smaller differences in the interaction energies of hydroxyl on Ph and Pt compared with oxygen, resulting in differences in chemical reactivity between the two metals, especially with respect to reactions involving hydrogen transfer.