Superatomic Orbitals under Spin-Orbit Coupling

The Au-25(SR)18(-) cluster has been the poster child of success in applying the superatom complex concept and remains the most studied system of all of the monolayer-protected metal clusters. In this Letter, we try to solve a mystery about this cluster: the low-temperature UV-vis absorption spectrum shows double peaks below 2.0 eV while simulation by scalar relativistic time-dependent density functional theory (TDDFT) shows only one peak in this region. Using a recently implemented two-component TDDFT, we show that spin-orbit coupling (SOC) leads to those two peaks by splitting the 1P superatomic HOMO orbitals. This work highlights the importance of SOC in understanding the electronic structure and optical absorption of thiolated gold nanoclusters, which has not been realized previously.