Toward quantitative electronic structure in small gold nanoclusters

Ligand-protected gold nanoclusters (AuNCs) feature a dense but finite electronic structure that can be rationalized using qualitative descriptions such as the well-known superatomic model and predicted using quantum chemical calculations. However, the lack of well-resolved experimental probes of a AuNC electronic structure has made the task of evaluating the accuracy of electronic structure descriptions challenging. We compare electronic absorption spectra computed using time-dependent density functional theory to recently collected high resolution experimental spectra of Au₉(PPh₃)₈ ³⁺ and Au₈(PPh₃)₇ ²⁺ AuNCs with strikingly similar features. After applying a simple scaling correction, the computed spectrum of Au₈(PPh₃)₇ ²⁺ yields a suitable match, allowing us to assign low-energy metal-metal transitions in the experimental spectrum. No similar match is obtained after following the same procedure for two previously reported isomers for Au₉(PPh₃)₈ ³⁺, suggesting either a deficiency in the calculations or the presence of an additional isomer. Instead, we propose assignments for Au₉(PPh₃)₈ ³⁺ based off of similarities Au₈(PPh₃)₇ ²⁺. We further model these clusters using a simple particle-in-a-box analysis for an asymmetrical ellipsoidal superatomic core, which allows us to reproduce the same transitions and extract an effective core size and shape that agrees well with that expected from crystal structures. This suggests that the superatomic model, which is typically employed to explain the qualitative features of nanocluster electronic structures, remains valid even for small AuNCs with highly aspherical cores.