Analytical Approaches To Identify Plasmon-like Excited States in Bare and Ligand-Protected Metal Nanoclusters

Abstract

Noble metal nanoclusters containing dozens to hundreds of metal atoms are of great interest because of their unique optical properties. Classical electrodynamics fails to describe the optical properties of clusters smaller than a few nanometers, so quantum-mechanical models are needed to describe these clusters. However, it is challenging to identify which features of the computed excited states indicate plasmon-like character, particularly in a way that is generalizable to the ligand-protected clusters that are commonly studied in experiments. We present an analytical method to identify plasmonlike excited states using three quantifiable indicators that must be considered in combination: (1) large superatomic character, (2) large collectivity among single-particle excitations, and (3) large additivity of contributions of these single-particle excitations to the transition dipole moment. Visualizing these three indicators on a single plot enables rapid classification of hundreds of excited states into plasmon-like, collective, single-particle, or interband categories or as intermediate between these categories. This method is used to identify excited states with plasmon-like character in both bare and ligand-protected Ag clusters at the TDDFT level. Using these three nearly orthogonal indicators in combination provides more information than any one criterion can provide.

Plasmon excitations in chemically heterogeneous nanoarrays

“…Molecular plasmons exhibit effects from finite-size quantum confinement, symmetry, and avoided crossings within nanosystems such as metallic clusters [18][19][20][21][22][23][24], arrays [16,25,26], chains [27][28][29], and conjugated and aromatic hydrocarbons [30][31][32][33][34]. As evidenced by previous computational studies [16,25,26], double-chain atomic arrays of metals, which we consider in this study, contain many of the physical and chemical phenomena which are central to any molecular plasmon.…”

“…The interference between the two first-order transition contributions is destructive in the antisymmetric combination and constructive in the symmetric combination. The constructive addition of dipoles has been used to gauge the coherence of an excitation [24]. While both excitations scale with λ, the very weak excitation at about 0.4 eV does not have the coherence required to be a plasmonic excitation.…”

Hydride- and Halide-Substituted Au9(PH3)83+ Nanoclusters: Similar Absorption Spectra Disguise Distinct Geometries and Electronic Structures

“…The superatomic character of each excited state was computed as the weighted percentage of the excitations contributing to the state that involve superatomic occupied MOs, consistent with our previous definitions. 79 The superatomic contributions to the absorption spectra were computed by scaling the oscillator strength of each excited state by its superatomic character.…”

“…To understand the absorption spectra, we have also computed the contribution of the superatomic MOs to each excited state. 79 The low-lying unoccupied MOs of most Au NCs have significant superatomic character, so the analysis is based solely on the occupied MOs in each excited state.…”

Plasmon Character Index: An Accurate and Efficient Metric for Identifying and Quantifying Plasmons in Molecules

“…6,14,17,[23][24][25][26] Nevertheless, the high degree of accuracy needed for fabrication and lithography places limitations on the practical implementation of these plasmonic materials. 14,27,28 Recently, plasmons in molecules have been reported by several groups, including in fewatom metal clusters [29][30][31][32][33] as well as in polycyclic aromatic hydrocarbon ions. 27,28,[34][35][36][37][38] Compared with nanomaterials, these molecules are cheaper to produce and easier to control due to the advantages of chemical synthesis.…”