Structures of 13-atom clusters of fcc transition metals byab initioand semiempirical calculations

We report the results of ab initio calculations of the structures and magnetic moments of ${\mathrm{Ni}}_{13}$, ${\mathrm{Pd}}_{13}$, ${\mathrm{Pt}}_{13}$, ${\mathrm{Cu}}_{13}$, ${\mathrm{Ag}}_{13}$, and ${\mathrm{Au}}_{13}$ that were performed using a density-functional method that employs linear combinations of pseudoatomic orbitals as basis sets (SIESTA). Our structural results for ${\mathrm{Pt}}_{13}$, ${\mathrm{Cu}}_{13}$, ${\mathrm{Ag}}_{13}$, and ${\mathrm{Au}}_{13}$ 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 ${\mathrm{Ni}}_{13}$ and ${\mathrm{Pd}}_{13}$ 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 ${\mathrm{Pt}}_{13}$, ${\mathrm{Cu}}_{13}$, and ${\mathrm{Au}}_{13}$ other than Chang and Chou were optimized with SIESTA, those reported for ${\mathrm{Pt}}_{13}$ and ${\mathrm{Cu}}_{13}$ were found to be less stable than BBP, but the two-dimensional planar configuration reported for ${\mathrm{Au}}_{13}$ proved to be more stable than BBP.