Dirac scattered-wave calculations on an icosahedral Au13 cluster.

Abstract

Symmetry-adapted angular-momentum basis functions have been generated for the icosahedral double point group (${I}_{h}^{\mathrm{*}}$). These basis functions are used to obtain the relativistic molecular orbitals for the icosahedral ${\mathrm{Au}}_{13}$ cluster via the self-consistent-field Dirac scattered-wave method. Nonrelativistic-limit calculations are also reported for the ground state of the ${\mathrm{Au}}_{13}$ 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 ${\mathrm{Au}}_{13}$ 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 ${\mathrm{Au}}_{13}$ to 3.9 eV, and spin-orbit interactions split the d band into the ${d}_{3/2}$ and ${d}_{5/2}$ 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.