Electronic properties and magnetism of ruthenium clusters

Abstract

The electronic properties and magnetism of ${\mathrm{Ru}}_{\mathit{N}}$ clusters (N=4, 6, 10, 13, 19, 43, and 55) are studied using the discrete-variational local-spin-density-functional method. The bond lengths in the clusters with N\ensuremath{\le}13 are optimized, and the cluster binding energies are found to increase monotonically with the increase of cluster size. All clusters except ${\mathrm{Ru}}_{19}$ are shown to have magnetic ground states. The average magnetic moments per atom for the ${\mathrm{Ru}}_{\mathit{N}}$ are found to decrease rapidly with the increase of the cluster size, although small oscillation exists. The calculated moments per atom for ${\mathrm{Ru}}_{10}$ and ${\mathrm{Ru}}_{13}$ clusters are in good agreement with the experimental values. Multiple magnetic solutions are explored, and double magnetic solutions are found for the icosahedral (${\mathit{I}}_{\mathit{h}}$) ${\mathrm{Ru}}_{13}$ cluster which is used successfully to eliminate the contradiction between the previous theory and experiment on the moment of ${\mathrm{Ru}}_{13}$ cluster. The electronic structures of ${\mathrm{Ru}}_{\mathit{N}}$ clusters are calculated, and indicate that all clusters are metallic in behavior. The comparison between the ${\mathrm{Ru}}_{55}$ cluster and the bulk counterpart indicates that ${\mathrm{Ru}}_{55}$ has shown bulklike properties in the binding energy, magnetism, valence-band-width, and density of states. Based on electronic-structure results, the reactivity of ${\mathrm{Ru}}_{6}$, ${\mathrm{Ru}}_{19}$, and ${\mathrm{Ru}}_{43}$ clusters toward ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, and CO molecules is predicted. \textcopyright{} 1996 The American Physical Society.