Visualizing screening in noble-metal clusters: static vs. dynamic.

The localized surface-plasmon resonance of metal nanoparticles and clusters corresponds to a collective charge oscillation of the quasi-free metal electrons. The polarization of the more localized d electrons opposes the overall polarization of the electron cloud and thus screens the surface plasmon. By contrast, a static electric external field is well screened, as even very small noble-metal clusters are highly metallic: the field inside is practically zero except for the effect of the Friedel-oscillation-like modulations which lead to small values of the polarization of the d electrons. In the present article, we present and compare representations of the induced densities (i) connected to the surface-plasmon resonance and (ii) resulting from an external static electric field. The two cases allow for an intuitive understanding of the differences between the dynamic and the static screening.

Crucial Role of Conjugation in Monolayer-Protected Metal Clusters with Aromatic Ligands: Insights from the Archetypal Au144L60 Cluster Compounds.

Ligand-protected metal clusters are employed in a great many applications that include notably energy conversion and biomedical uses. The interaction between the ligands and the metallic cores, mediated by an often complex interface, profoundly influences the properties of small clusters, in particular. Nonetheless, the mechanisms of interaction remain far from fully understood. The Au144L60 class of cluster compounds has long played a central role in the study of monolayer-protected clusters, but total structure determination has been achieved only recently for a thiolated and an all-alkynyl cluster. Both ligands contain aromatic rings but differ in their ligation to the metal core: conjugation along a triple bond in the latter, saturation in the former. We demonstrate the paramount importance of the conjugation in the connection between aromatic ligand rings and metal cores for the electronic and optical properties and, by extension, the critical transport properties, providing a crucial element for the development of design-principle-based synthesis.

How metallic are noble-metal clusters? Static screening and polarizability in quantum-sized silver and gold nanoparticles.

Metallicity of nanoparticles can be defined in different ways. One possibility is to look at the degree to which external fields are screened inside the object. This screening would be complete in a classical perfect metal where surface charges arrange on the classical -i.e., abrupt - surface such that no internal fields exist. However, it is obvious that this situation is modified for very small clusters: the surface charges are "smeared out" at the surface, and the screening might be less complete. In the present work we ask the question as to how close small noble-metal clusters are to a classical metal. We show that, indeed, the screening is almost complete (≈96%) already for as little as one atomic layer of the coinage metals, silver and gold alike. At the same time, we show that quantum effects, viz., electronic shell closings and the Friedel-like oscillations of the density, play a role, meaning that the clusters cannot be described solely using the concept of screening in a classical metal.

Identifying Electronic Modes by Fourier Transform from δ-Kick Time-Evolution TDDFT Calculations.

Time-dependent density-functional theory (TDDFT) is widely used for calculating electron excitations in clusters and large molecules. For optical excitations, TDDFT is customarily applied in two distinct approaches: transition-based linear-response TDDFT (LR-TDDFT) and the real-time formalism (RT-TDDFT). The former directly provides the energies and transition densities of the excitations, but it requires the calculation of a large number of empty electron states, which makes it cumbersome for large systems. By contrast, RT-TDDFT circumvents the evaluation of empty orbitals, which is especially advantageous when dealing with large systems. A drawback of the procedure is that information about the nature of individual spectral features is not automatically obtained, although it is of course contained in the time-dependent induced density. Fourier transform of the induced density has been used in some simple cases, but the method is, surprisingly, not widely used to complement the RT-TDDFT calculations; although the reliability of RT-TDDFT spectra is now widely accepted, a critical assessment for the corresponding transition densities and a demonstration of the technical feasibility of the Fourier-transform evaluation for general cases is still lacking. In the present work, we show that the transition densities of the optically allowed excitations can be efficiently extracted from a single δ-kick time-evolution calculation even in complex systems like noble metals. We assess the results by comparison with the corresponding LR-TDDFT ones and also with the induced densities arising from RT-TDDFT simulations of the excitation process.