Photoabsorption of Icosahedral Noble Metal Clusters: An Efficient TDDFT Approach to Large-Scale Systems

We apply a recently developed time-dependent density functional theory (TDDFT) algorithm based on the complex dynamical polarizability to calculate the photoabsorption spectrum of the following series of closed-shell icosahedral dusters of increasing size (namely, [M-13](5+), [M-55](3-), [M-147](-), and [M-309](3+) with M = Ag, Au), focusing in particular on their plasmonic response. The new method is shown to be computationally very efficient: it simultaneously retains information on the excited-state wave function and provides a detailed analysis of the optical resonances, e.g., by employing the transition contribution map scheme. For silver clusters, a very intense plasmon resonance is found for [Ag-55](3-), with strong coupling among-low-energy single-particle configurations. At variance, for gold clusters we do not find a single strong plasmonic peak but rather many features of comparable intensity, with partial plasmonic behavior present only for the lowest-energy transitions. Notably, we also find a much, greater sensitivity of the optical response of Ag clusters with respect to Au clusters to cluster charge, the exchange-correlation (xc) functional, and the basis set, as demonstrated via a detailed comparison between [Ag-55](q) and [Au-55](q). The results of the TDDFT algorithm obtained with the complex dynamical polarizability are finally compared with those produced by alternative (real-time evolution or Lanczos) approaches, showing that, upon proper choice of numerical parameters, overall nearly quantitative agreement is achieved among all of the considered approaches, in keeping with their fundamental equivalence.