Extending the cluster scaling technique to ruthenium clusters with hcp structures

Using density functional techniques at the level of the generalized gradient approximation, we addressed structural, energetic, and electronic properties of ruthenium clusters with hexagonal close-packed structural motifs and sizes between ~1 and ~2nm. We discuss the construction principles of model clusters with hcp structures and examine the evolution of various properties with respect to cluster size. We compare the scaling behavior with that of ruthenium clusters of similar sizes, but with face-centered cubic structures. Thus, we extended the scaling technique, well established for clusters of transition metals with face-centered cubic structures, to hexagonal closed-packed ones. For the model clusters explored, the examined properties scale well with cluster size. For example, a clear energy preference develops for hexagonal over cubic structures of ruthenium particles. Furthermore, we studied the differences in the scaling behavior as described by an all-electron treatment with localized basis functions and a projector augmented wave plane-wave method. [Display omitted] •Run clusters with hcp and fcc motifs were examined at the GGA-PBE level.•hcp clusters, scaling better than fcc clusters, extrapolate well to bulk values.•From Ru55/57 clusters, hcp structures are preferred over fcc, as in the bulk.•Results of all-electron scalar-relativistic and plane-wave PAW are very similar.