SPIN-ORBIT EFFECTS ON HEAVY-METAL OCTAHEDRAL CLUSTERS

The relativistic electronic structure of octahedral Mo6, W6, Ag6 and A u6 clusters has been investigated using the self-consistent field Dira c scattered wave (SCF-DSW) method. It is shown that spin-orbit interac tion breaks the three-fold nonrelativistic Fermi (E(F)) level of each cluster into its four-fold and two-fold relativistic electronic states . The E(F) levels of the Mo6 and W6 clusters (of symmetry GAMMA8+) fal l in the d-band complex, the 2E+F level of the Ag6 cluster falls in th e s-band complex, and the E(F) level of the AU6 cluster (GAMMA8-) is l ocated in the hybridized s-d-band complex. The contour plots of the re lativistic highest occupied molecular orbital of the W6 and AU6 cluste rs support this view. We have folded the calculated spinor populations and the relativistic one-electron molecular orbital energies of the v alence band of each cluster with gaussians to obtain the convoluted to tal and partial local density of states (DOS). The partial DOS thus ob tained indicates that the d3/2 and d5/2 sub-bands of the Mo6 and W6 cl usters are overlapped, whereas in the Ag6 Cluster these sub-bands are separated by about 1.2 eV. In the AU6 cluster these sub-bands are almo st completely separated (by about 1.9 eV), in good agreement with phot oelectron data of high nuclearity gold-phosphine clusters. The calcula ted spin-orbit splitting of the valence d-band of the Ag6 and AU6 clus ters are in agreement with the observed d-band splitting of a series o f small clusters of gold and silver supported on carbon substrates.