[en] Highlights: • Pt atom binding on Al-terminated α-Al₂O₃ (0001) surface is stronger than Ag, Au and Pd. • Free Pt_n clusters geometries are significantly altered on the alumina surface. • Interfacial bonding between cluster and support deteriorates spin orbit coupling effect. • Alumina support induces charge into platinum cluster leading to activation of cluster. - Abstract: The fundamental understanding of the electronic and geometric structures of small platinum clusters on metal oxide support is important to design the futuristic Pt-based novel materials for heterogeneous catalysis. Here we report a systematic theoretical study on the trend in the structural and electronic properties of alumina supported Pt_n (n = 1–7 and 10) clusters with a focus to highlight the effect on the substrate. All calculations were carried out using the plane wave based pseudo-potential approach. The model for the support has been designed by using Al-terminated α-Al₂O₃ (0001) surface which is the most stable surface termination under ultrahigh vacuum conditions. The results show that the binding of Pt atom with the Al₂O₃ surface releases 1.84 eV energy which is significantly higher than atomic adsorption energy of other noble metal atoms (Ag, Au, and Pd). As a consequence, the equilibrium geometries of free Pt_n clusters (n = 3–7) are significantly altered on the alumina surface. Whilst Pt₁₀ cluster favors tetracapped prism structure in the gas phase, on alumina support it prefers a layered structure. The geometrical changes of Pt clusters on the alumina surface have been attributed to the energy balance between the Pt-Pt and Pt-substrate interactions. The nature of interaction between the Pt_n clusters and surface has been verified using the electronic density of states analysis. Surface induced electronic charge on the deposited cluster results in red shift in its energy levels, indicating electron rich activation of platinum clusters. The inclusion of spin-orbit coupling(SOC) significantly changes the electronic structure of gas phase platinum cluster; however, the extent of SOC influence reduces due to interfacial bonding with alumina support.