Structures of 13-atom clusters of fcc transition metals by ab initio and semiempirical calculations

We report the results of ab initio calculations of the structures and magnetic moments of Ni-13, Pd-13, Pt-13, Cu-13, Ag-13, and Au-13 that were performed using a density-functional method that employs linear combinations of pseudoatomic orbitals as basis sets (SIESTA). Our structural results for Pt-13, Cu-13, Ag-13, and Au-13 show that a buckled biplanar structure (BBP) is more stable than the icosahedral configuration, in keeping with results obtained recently by Chang and Chou [Phys. Rev. Lett. 93, 133401 (2004)] using the Vienna ab initio simulation package with a plane-wave basis. However, for Ni-13 and Pd-13 we found that the icosahedral structure is more stable than BBP. For all these clusters, two semiempirical methods based on spherically symmetric potentials both found the icosahedral structure to be the more stable, while the modified embedded atom model method, which uses a direction-dependent potential, found BBP to be the more stable structure. When low-energy structures found in recent ab initio studies of Pt-13, Cu-13, and Au-13 other than Chang and Chou were optimized with SIESTA, those reported for Pt-13 and Cu-13 were found to be less stable than BBP, but the two-dimensional planar configuration reported for Au-13 proved to be more stable than BBP.