First-principles calculations have been performed on the electronic structures for ${\mathrm{Ru}}_n$ $(n=2–14)$ clusters. The calculations show that square represents the basic unit in the growth of ${\mathrm{Ru}}_n$ clusters. For the stability, odd-even oscillation with respect to the cluster size is observed. Correspondingly, those clusters comprising integer number of square units are magic clusters with high stability. Simple cubic growth mode is detected with cluster size increasing, in line with latest publication. However, for some clusters, such as ${\mathrm{Ru}}_{13}$, more stable structures different from previous calculated results have been found. The calculated magnetic moment for the ground state of ${\mathrm{Ru}}_{13}$ ($0.15{\mu }_B$/atom) agrees better with experimental observation ($<0.29{\mu }_B$/atom) than those obtained before. The current optimized new structure is also found to be favored for some other 13-atom $4d$ transition metal clusters, such as ${\mathrm{Tc}}_{13}$. Our findings may thoroughly resolve a long standing discrepancy between theories and experiments and contribute basic data for design of novel catalysts.

• Received 11 March 2007

DOI:https://doi.org/10.1103/PhysRevB.76.045410