We investigated the interaction between the platinum and oxide support based on the HSAB (Hard-Soft-Acid-Base) concept to obtain guidelines for a superior exhaust-gas purification catalyst. The Density Functional Theory (DFT) calculation provided the chemical potential (μ) and chemical hardness (η) via the eigenvalue of the Valence Band Maximum and Conduction Band Minimum. Moreover, it was found that the interaction depends on the μ and η, e.g., the metallic Pt cluster (Pt1, Pt3) had a greater interaction with the oxide supports having a lower η, on the other hand, the oxidized Pt cluster (Pt1O1, Pt1O2, Pt1O3, Pt1O4, Pt3O6) tends to be stabilized on the oxide support with a higher μ. These results could be explained by the HSAB concept. It was also found that the oxidation energy of the supported Pt cluster well corresponds to the actual valency of the supported Pt, furthermore, the particle size of the Pt after the thermal treatment depends on the μ of the oxide supports. The activities of the Pt catalysts were successfully analyzed by a regression analysis. The activities of the supported Pt catalysts also depended on the μ and η values. Hence, the catalytic activities might be predicted by estimation of μ and η, i.e., the DFT calculation should be able to accelerate the development of the exhaust-gas purification catalyst with a higher efficiency and reasonable cost.