Electronic structures of 13-atom Rh clusters with three possible high-symmetry geometries are studied using the discrete variational local-spin-density-functional method. An anomalous symmetry dependence of the cluster magnetism is found: the total magnetic moment of the icosahedral ${\mathrm{Rh}}_{13}$ cluster is smaller than that of the other two lower-symmetry clusters in a wide range of interatomic spacings. An energy difference is identified to explain this anomalous relationship, which is found to be also useful for judging whether some techniques can or must be used in the local-spin-density-functional calculations. The calculated results are compared and discussed with those of previous theory and a recent experiment. The real geometry of the ${\mathrm{Rh}}_{13}$ cluster is suggested to be a distorted icosahedron.

• Received 25 March 1994

DOI:https://doi.org/10.1103/PhysRevB.50.7173