Structural, electronic, and magnetic properties of small rhodium clusters

Abstract

The structural, electronic, and magnetic properties of small ${\mathrm{Rh}}_{\mathit{N}}$ clusters (N=2--8,10,12,13, and 19) are studied using the discrete-variational local-spin-density-functional method. The ground-state structures of ${\mathrm{Rh}}_{2}$, ${\mathrm{Rh}}_{3}$, and ${\mathrm{Rh}}_{4}$ are obtained and found to exhibit a tendency toward higher-dimensional geometries with longer bond lengths and more nearest-neighbor bonds. The equilibrium bond lengths in the chosen geometry for the ${\mathrm{Rh}}_{5}$--${\mathrm{Rh}}_{8}$, ${\mathrm{Rh}}_{10}$, ${\mathrm{Rh}}_{12}$, and ${\mathrm{Rh}}_{13}$ clusters are determined and show 4--6 % bond length contractions compared with the bulk interatomic spacing. A complex size dependence of the magnetic properties of the ${\mathrm{Rh}}_{\mathit{N}}$ clusters is found to be consistent with a recent experiment. The average magnetic moment per atom of the ${\mathrm{Rh}}_{\mathit{N}}$ clusters varies from 0${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ to 2${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$. The clusters with magnetic ground states have ferromagnetic interactions, while the local moments of the 5s and 5p often align antiferromagnetically with that of the 4d. The calculated magnetic moments of the ${\mathrm{Rh}}_{10}$, ${\mathrm{Rh}}_{12}$, ${\mathrm{Rh}}_{13}$, and ${\mathrm{Rh}}_{19}$ clusters are compared and discussed with the experimental ones. Icosahedral growth is suggested for Rh clusters. The reactivity of the ${\mathrm{Rh}}_{\mathit{N}}$ clusters toward ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, and CO molecules is predicted. The densities of states, exchange splittings, valence band widths, and ground-state electronic configurations are presented for all the clusters. Finally, an energy difference is identified which may be used as the criterion for the existence of multiple magnetic solutions in local-spin-density-functional calculations.