Consistent size dependency of core-level binding energy shifts and single-electron tunneling effects in supported gold nanoclusters

Uniform Au-clusters supported on well-defined substrate [octanedithiol/Au(111)] were analyzed by tunneling and x-ray photoelectron spectroscopy. Single-electron tunneling effect and the binding-energy shift observed in these spectroscopies exhibit the consistent cluster-size dependency. Au $4f$ core-level shift of the supported clusters can be well explained by the charging energy e²/2C, where C is the capacitance between a cluster and its surroundings. The main contributions to this C are the self-capacitance of the cluster, the dielectric constant of the octanedithiol layer (ε~3) and the effect of the substrate. The other possible contributions are attributed to the effect of nearest-neighbor clusters and the electron spillout from the cluster and substrate due to the coupling between the molecular orbital and the conducting electrons.