The electronic structure of cubo-octahedral and icosahedral ${\mathrm{Au}}_{13}$ clusters has been investigated by the self-consistent-field molecular-orbital Dirac scattered-wave method. Double-point-group–symmetry considerations indicate that the icosahedral cluster will undergo static Jahn-Teller distortion, while the cubo-octahedral cluster cannot distort because of a Kramers degeneracy in the ground state. Molecular Zeeman and hyperfine interactions are calculated for the cubo-octahedral ${\mathrm{Au}}_{13}$ cluster through a first-order perturbation to the Dirac Hamiltonian. The predicted g tensors and ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ hyperfine tensors are consistent with a nearly isotropic paramagnetic-resonance spectrum. The calculated density-of-states (DOS) curves for the ${\mathrm{Au}}_{13}$ clusters show similar features to those obtained in photoemission experiments of small clusters of gold. Relativistic effects increase the d-band width by more than 1 eV, and spin-orbit interaction splits the occupied d band by about 2 eV in both clusters. These calculated values are approximately 75% of the observed values for gold in the bulk metal. It is clearly shown that the overlap of the d band by the s-p band is mainly due to relativistic effects.

• Received 16 August 1988

DOI:https://doi.org/10.1103/PhysRevB.39.3005