In this paper, various energies and geometries of pure platinum nanoparticles and those of platinum nanoparticles with adsorbed OH were investigated. Ten different platinum clusters of up to 28 atoms were studied using spin-unrestricted density functional theory (DFT) with a double numerical plus polarization basis set. Three different shapes were presented, and the effect of cluster size on binding energy, total energy, and HOMO-LUMO energy gap was investigated. The same set of calculations was performed for selected clusters with OH adsorbate on the Pt(111) surface. The results show that the stability of both the pure clusters and the clusters with adsorbed OH molecule increases with an increase of cluster size. This fact indicates that direct influence of the size of Pt cluster on the reaction rate is possible, and the understanding of how cluster size would affect binding energy is important. The effect of cluster size on total energy of molecule was shown to be a linear function independent of cluster type, as expected. We also found that optimized (stable) Pt clusters were bigger in size than that of the initial clusters, or clusters with bulk geometry.