Ligand-Dependent Spin-Orbit Coupling Effects on Optical and Carrier Dynamics in M@Au₁₂ Nanoclusters

Spin-orbit coupling (SOC) plays a fundamental role in shaping the electronic structures, optical properties, and excited-state dynamics of nanoscale systems. However, in conventional quantum dots (e.g., CdSe and PbS), the observation and control of SOC effects are hindered by complex energy level structures and high densities of electronic states, which obscure the contributions of SOC and limit their tunability. In contrast, atomically precise superatomic metal nanoclusters (NCs), such as Au₁₃ and Au₂₅, offer a unique platform to isolate and systematically study SOC-driven phenomena, owing to their well-defined atomic configurations and discrete energy level distributions. In this work, we employed time-dependent density functional theory (TD-DFT) simulations to investigate the impact of SOC in ligand-protected Au₁₃ NCs. As a result, SOC lifts the degeneracy of the 1P superatomic orbitals, with the splitting patterns being strongly dependent on ligand identity. This ligand-specific SOC effect reshapes the optical absorption and magnetic circular dichroism (MCD) spectra, altering peak positions, intensities, and selection rules. Moreover, SOC significantly affects electronic transition channels, thereby influencing the relationship between electron-vibration interactions and carrier dynamics. These results provide a theoretical basis for designing metal nanoclusters with superior optoelectronic properties.