Dirac scattered-wave calculations on an icosahedral Au13 cluster

Symmetry-adapted angular-momentum basis functions have been generated for the icosahedral double point group (Ih*). These basis functions are used to obtain the relativistic molecular orbitals for the icosahedral Au13 cluster via the self-consistent-field Dirac scattered-wave method. Nonrelativistic-limit calculations are also reported for the ground state of the Au13 cluster in order to ascertain the importance of relativistic effects in such heavy-atom systems. The ionization potential and the lowest dipole-allowed electronic transitions are predicted using the spin-restricted transition state formalism. The calculated density of states for the Au13 cluster shows similar features to those obtained in photoemission experiments of small clusters of gold on various substrates. Relativistic effects increase the d-bandwidth of Au13 to 3.9 eV, and spin-orbit interactions split the d band into the d3/2 and d5/2 subbands by 2.2 eV. These calculated results are in very good agreement with the values obtained from the x-ray photoemission spectra of the valence band of gold clusters. Due to relativity, an increased overlap of the s and d bands is observed, leading to appreciable s-d hybridization in the cluster-bonding molecular orbitals.