We report a computational study via time-dependent density-functional theory (TDDFT) methods of the photo-absorption spectrum of an atomically precise monolayer-protected cluster (MPC), the Ag24Au(DMBT)18 single negative anion, where DMBT is the 2,4-dimethylbenzenethiolate ligand. The use of efficient simulation algorithms, i.e., the complex polarizability polTDDFT approach and the hybrid-diagonal approximation, allows us to employ a variety of exchange-correlation (xc-) functionals at an affordable computational cost. We are thus able to show, first, how the optical response of this prototypical compound, especially but not exclusively in the absorption threshold (low-energy) region, is sensitive to (1) the choice of the xc-functionals employed in the Kohn-Sham equations and the TDDFT kernel and (2) the choice of the MPC geometry. By comparing simulated spectra with precise experimental photoabsorption data obtained from room temperature down to low temperatures, we then demonstrate how a hybrid xc-functional in both the Kohn-Sham equations and the diagonal TDDFT kernel at the crystallographically determined experimental geometry is able to provide a consistent agreement between simulated and measured spectra across the entire optical region. Single-particle decomposition analysis tools finally allow us to understand the physical reason for the failure of non-hybrid approaches.
