The relativistic electronic structure of octahedral Mo6, W6, Ag6 and Au6 clusters has been investigated using the self-consistent field Dirac scattered wave (SCF-DSW) method. It is shown that spin-orbit interaction breaks the three-fold nonrelativistic Fermi (EF) level of each cluster into its four-fold and two-fold relativistic electronic states. The EF levels of the Mo6 and W6 clusters (of symmetry Γ8+) fall in the d-band complex, the 2E+F level of the Ag6 cluster falls in the s-band complex, and the EF level of the Au6 cluster (Γ8-) is located in the hybridized s-d-band complex. The contour plots of the relativistic highest occupied molecular orbital of the W6 and Au6 clusters support this view. We have folded the calculated spinor populations and the relativistic one-electron molecular orbital energies of the valence band of each cluster with gaussians to obtain the convoluted total and partial local density of states (DOS). The partial DOS thus obtained indicates that the d 3 2 and d 5 2 sub-bands of the Mo6 and W6 clusters 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 almost completely separated (by about 1.9 eV), in good agreement with photoelectron data of high nuclearity gold-phosphine clusters. The calculated spin-orbit splitting of the valence d-band of the Ag6 and Au6 clusters are in agreement with the observed d-band splitting of a series of small clusters of gold and silver supported on carbon substrates.
ASJC Scopus subject areas
- Condensed Matter Physics
- Physical and Theoretical Chemistry