Ab initio calculations of Ru, Pd, and Ag cluster structure with 55, 135, and 140 atoms

A massively parallel ab initio computer code, which uses Gaussian bases, pseudopotentials, and the local density approximation, permits the study of transition-metal systems with literally hundreds of atoms. We present total energies and relaxed geometries for Ru, Pd, and Ag clusters with N = 55, 135, and 140 atoms. The N = 55 and 135 clusters were chosen because of simultaneous cube-octahedral (fee) and icosahedral (ices) subshell closings, and we find ices geometries are preferred. Remarkably large compressions of the central atoms are observed for the ices structures (up to 6% compared with bulk interatomic spacings), while small core compressions (similar to 1%) are found for the fee geometry. In contrast, large surface compressive relaxations are found for the fee clusters (similar to 2%-3% in average nearest neighbor spacing), while the ices surface displays small compressions (similar to 1%). Energy differences between ices and fee are smallest for Pd, and for all systems the single-particle densities of states closely resembles bulk results. Calculations with N = 134 suggest slow changes in relative energy with N. Noting that the 135-atom fee has a much more open surface than the ices, we also compare N = 140 ices and fee, the latter forming an octahedron with close packed facets. These ices and fee clusters have identical average coordinations and the octahedron is found to be preferred for Ru and Pd but not for Ag. Finally, we compare Harris functional and LDA energy differences on the N = 140 clusters, and find fair agreement only for Ag.