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We present results of a density functional theory study of the structure and energetics of small Pt clusters. The method of calculation is based on the non-selfconsistent Harris functional version of LDA (as formulated by Sankey and Niklewski, and generalized to include d orbitals in the basis set), which produces excellent results for bulk Pt. We used a dynamical quenching algorithm to obtain minimum-energy structures of clusters for n= 2-6. The clusters with n= 4-6 are shown to be planar. For we found that there is a variety of low-symmetry geometries that are lower in energy than the icosahedral and cubo-octahedral structures. We also compute the vibrational states of n= 2-4, and show that the calculated vibrational frequency and bond energy of the Pt dimer are in good agreement with experiments.