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Nanoclusters usually display exotic physical and chemical properties due to their intriguing geometric structures in contrast to their bulk counterparts. By means of first-principles calculations within density functional theory, we find that heavy noble metal Pt_N nanoclusters around the size N = 55 begin to prefer an open configuration, rather than previously reported close-packed icosahedron or core-shell structures. Particularly, for Pt_N, the widely supposed icosahedronal magic cluster is changed to a three-atomic-layered structure with D_6h symmetry, which can be well addressed by our recently established generalized Wulff construction principle (GWCP). But, the magic number of Pt_N clusters around 55 ismore » shifted to a new odd number of 57. The high symmetric three-layered Pt-57 motif is mainly stabilized by the enhanced covalent bonding contributed by both spin-orbital coupling effect and the open d orbital (5d⁹6s¹) of Pt, which result in a delicate balance between the enhanced Pt-Pt covalent bonding of the interlayers and negligible d dangling bonds on the cluster edges. Our findings about Pt_N clusters are also applicable to Ir_N clusters, but qualitatively different from their earlier neighboring element Os and their later neighboring element Au. The magic numbers for Os and Au are even, being 56 and 58, respectively. Finally, the findings of the new odd magic number 57 are the important supplementary of the recently established GWCP.« less