Optical spectra of the special Au₁₄₄ gold-cluster compounds: Sensitivity to structure and symmetry

This report concerns the remarkable fine structure reported recently in the optical absorption spectrum of the ubiquitous icosahedral Au₁₄₄(SR)₆₀ cluster compounds when measured under cryogenic conditions. The theoretical explanation of the spectrum relied upon an I-symmetrized variant of the conventional Pd₁₄₅-type structure-model; real-time TDDFT calculations revealed that, in contradistinction to the prior state of knowledge, the spectrum is profoundly structured and rich in quantum-state information.1 Reported herein is an investigation of the sensitivity of the theoretical electronic absorption spectra of this compound to variations in the structure. Both I-symmetric as well as asymmetric structure-models are considered; having the same core structure and connectivity, these differ in the mutual configurations about the pyramidal S atoms, which produce significant structure differences penetrating into the gold core. As R-groups, both methyl (R=CH₃) and hydrogen (R=H) are considered. The effects on the structure and spectra of local optimizations employing different exchange-correlation (xc-) functionals are also considered. The results may be summarized as follows: all computed spectra show a rich fine-structure when computed at a similar level of resolution (∼0.16 eV, transform limited); the I-symmetric structure with R=CH₃ has more pronounced features than the asymmetric structure with the same rest group. This is consistent with the high degree of symmetry-imposed degeneracy in the electronic states of the former. These spectral differences between the I-symmetric and the unsymmetrical models are reduced when the CH₃ R group is replaced by the smaller R=H. Many other systematic differences are noted. In particular, we show explicitly the differences caused by changing the R group, the exchange-correlation functional in the geometry relaxation, and the charge state. The present study contains clear indications as to what factors need to be well-controlled in order to achieve good agreement with available experiment. They will be useful for understanding ligand effects on the optical characteristics of thiolate-protected (and other) noble-metal clusters in this interesting size-range where the plasmon (LSPR) emerges.