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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.