Understanding Excited States in Magic Series Au _{8 <i>n</i> +4} (SR) _{4 <i>n</i> +8} Nanoclusters: Role of Size, Ligands, and Theory Level

The excited-state properties of metal nanoclusters have attracted considerable attention for potential applications in optoelectronics and biomedicine. However, the theoretical exploration of these properties, particularly emission mechanisms, remains challenging due to the high computational cost of excited-state structure optimization. Herein, we investigate the geometric and electronic structural changes upon photoexcitation in the magic series gold nanocluster Au_8<i>n</i>+4(SR)_4<i>n</i>+8 (R = H or phenyl, <i>n</i> = 3-6) using time-dependent density functional theory (TDDFT) and its approximate variant, DFT plus tight binding (TD-DFT+TB). Our results demonstrate that approximate methods, which combine full DFT-ground-state descriptions with the tight-binding approximation in linear-response calculations, offer a cost-effective and reliable approach for predicting size and ligand effects on the excited-state properties of gold nanoclusters. Key parameters such as the Stokes shift, charge-transfer character, and energy gap between the first singlet (S₁) and triplet (T₁) states show strong dependence on cluster size and the nature of the ligand shell, and these trends are well captured by the approximate methods. These results emphasize their potential for the efficient design of gold nanoclusters with tailored optical functionalities.