We have used all-electron local (LDA) and nonlocal (GGA) approximations to the density-functional theory to determine binding energies, equilibrium geometries, vibrational frequencies, and magnetic properties of ${\mathrm{Rh}}_N$ clusters $(N<~6).$ We present careful tests on the ${\mathrm{Rh}}_2$ dimer that compare results as calculated with a large (18-single Gaussian) and a very large (23-single Gaussian) basis sets. While the smaller set of Gaussians leads to underconverged results, we find that the large basis set leads to converged results that are also in excellent agreement with the experimental data available for ${\mathrm{Rh}}_2.$ The ground state of ${\mathrm{Rh}}_2$ is confirmed to be a quintuplet, the trigonal ${\mathrm{Rh}}_3$ is predicted to be a sextuplet, ${\mathrm{Rh}}_4$ in its tetrahedral configuration is a singlet, ${\mathrm{Rh}}_5$ sextuplet is a square pyramid, and ${\mathrm{Rh}}_6$ septuplet is the octahedron. Results from several excited states are calculated and presented as well. It is found that LDA overestimates the binding energy but that GGA corrects this deficiency and predicts longer bond lengths.

• Received 23 January 1998

DOI:https://doi.org/10.1103/PhysRevA.58.2196