Using density functional theory (DFT) with gradient-corrected exchange-correlation functionals (B3LYP), we systematically study the electronic structure and bonding of oxygen to various Pt-clusters. Our aim is to understand how the cluster size and shape affect the chemistry of dispersed catalysts and to find the smallest cluster suitable for modeling surface reactions on the Pt(111)-surface. We find that the dependence of binding on the sites of these clusters is well described in terms of the interstitial electron model (IEM). The results show that the 28-atom three-layer Pt-9.10.9-cluster gives a good representation of the Pt(111)-surface for various adsorption sites. These results indicate that an O atom binds most strongly to the 3-fold hollow site with a binding energy of 3.28 eV for fcc and 2.95 eV for hcp. The binding energies for the other sites are 2.73 eV (bridge) and 2.02 eV (on-top). A one-layer 12-atom cluster does well at describing the bonding for all sites except the hcp site. These cluster results agree well with experimental results and with the best calculations on this surface: all results agree that the eta(3)-fcc site is favored with a bond distance approximate to 2.01 Angstrom. In addition, our calculated bond energy of 3.28 eV is consistent with experiment at low coverage (3.43 to 3.71 eV) and with the best DFT calculations on a surface (3.43 eV). We interpret the bonding of O to the eta(3) sites (both fcc and hcp) in terms of the IEM localized covalent bonding model, in which the two singly occupied orbitals of 0 bond to singly occupied orbitals of Pt, and the lone pair of p orbitals on the O coordinates to the third Pt of an eta(3) site to form a donor-acceptor bond. This leads to two bonds of 2.01 Angstrom and one of 2.21 Angstrom.