Extension of the Time-Dependent Density Functional Complex Polarizability Algorithm to Circular Dichroism: Implementation and Applications to Ag₈ and Au₃₈(SC₂H₄C₆H₅)₂₄

We detail the calculation of rotatory strengths as an extension of the complex polarizability algorithm of time dependent density functional theory (TDDFT) proposed in a recent publication (O. Baseggio, G. Fronzoni, M. Stener, <i>J. Chem. Phys.</i> <b>2015</b>, <i>143</i>, 024106). To demonstrate the generality and applicability of the proposed algorithm, we calculate the photoabsorption and circular dichroism (CD) spectra of Ag₈ (as a validation case), Au₃₈(SCH₃)₂₄, and Au₃₈(SCH₂CH₂Ph)₂₄ monolayer-protected gold clusters (as a system of great current interest for their optical properties). For Au₃₈(SCH₂CH₂Ph)₂₄, the computed CD spectrum agrees well with the experimental data from the literature. Furthermore, a comparison of the calculated CD spectra of the two thiolate-protected nanoclusters reveals that the most distinctive features of the spectra are rather insensitive to the nature of the thiolate tail groups, which, however, play a significant role in shaping optical and dichroic response of the systems, especially in the higher energy portion of the spectrum

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

7noWe 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 clusters of increasing size (namely, [M13]5+, [M55]3−, [M147]−, and [M309]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 [Ag55]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 [Ag55]q and [Au55]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.partially_openopenBaseggio, Oscar; De Vetta, Martina; Fronzoni, Giovanna; Stener, Mauro; Sementa, Luca; Fortunelli, Alessandro; Calzolari, ArrigoBaseggio, Oscar; De Vetta, Martina; Fronzoni, Giovanna; Stener, Mauro; Sementa, Luca; Fortunelli, Alessandro; Calzolari, Arrig

Au₃₈(SPh)₂₄: Au₃₈ Protected with Aromatic Thiolate Ligands

Au₃₈(SR)₂₄ is one of the most extensively investigated gold nanomolecules along with Au₂₅(SR)₁₈ and Au₁₄₄(SR)₆₀. However, so far it has only been prepared using aliphatic-like ligands, where <i>R</i> = −SC₆H₁₃, −SC₁₂H₂₅ and −SCH₂CH₂Ph. Au₃₈(SCH₂CH₂Ph)₂₄ when reacted with HSPh undergoes core-size conversion to Au₃₆(SPh)₂₄, and existing literature suggests that Au₃₈(SPh)₂₄ cannot be synthesized. Here, contrary to prevailing knowledge, we demonstrate that Au₃₈(SPh)₂₄ can be prepared if the ligand exchanged conditions are optimized, under delicate conditions, without any formation of Au₃₆(SPh)₂₄. Conclusive evidence is presented in the form of matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS), electrospray ionization mass spectra (ESI-MS) characterization, and optical spectra of Au₃₈(SPh)₂₄ in a solid glass form showing distinct differences from that of Au₃₈(S-aliphatic)₂₄. Theoretical analysis confirms experimental assignment of the optical spectrum and shows that the stability of Au₃₈(SPh)₂₄ is not negligible with respect to that of its aliphatic analogous, and contains a significant component of ligand−ligand attractive interactions. Thus, while Au₃₈(SPh)₂₄ is stable at RT, it converts to Au₃₆(SPh)₂₄ either on prolonged etching (longer than 2 hours) at RT or when etched at 80 °C

Ligand-Enhanced Optical Response of Gold Nanomolecules and Its Fragment Projection Analysis: The Case of Au₃₀(SR)₁₈

Here we investigate via first-principles simulations the optical absorption spectra of three different Au₃₀(SR)₁₈ monolayer-protected clusters (MPC): Au₃₀(S^tBu)₁₈, Au₃₀(SPh)₁₈, and Au₃₀(SPh-<i>p</i>NO₂)₁₈. Au₃₀(S^tBu)₁₈ is known in the literature, and its crystal structure is available. In contrast, Au₃₀(SPh)₁₈ and Au₃₀(SPh-<i>p</i>NO₂)₁₈ are two species that have been designed by replacing the <i>tert</i>-butyl organic residues of Au₃₀(S^tBu)₁₈ with aromatic ones so as to investigate the effects of ligand replacement on the optical response of Au nanomolecules. By analogy to a previously studied Au₂₃(SR)₁₆^– anionic species, despite distinct differences in charge and chemical composition, a substantial ligand enhancement of the absorption intensity in the optical region is also obtained for the Au₃₀(SPh-<i>p</i>NO₂)₁₈ MPC. The use of conjugated aromatic ligands with properly chosen electron-withdrawing substituents and exhibiting steric hindrance so as to also achieve charge decompression at the surface is therefore demonstrated as a general approach to enhancing the MPC photoabsorption intensity in the optical region. Additionally, we here subject the ligand-enhancement phenomenon to a detailed analysis based on the fragment projection of electronic excited states and on induced transition densities, leading to a better understanding of the physical origin of this phenomenon, thus opening avenues to its more precise control and exploitation

Crystal Structure and Theoretical Analysis of Green Gold Au₃₀(S‑<i>t</i>Bu)₁₈ Nanomolecules and Their Relation to Au₃₀S(S‑<i>t</i>Bu)₁₈

We report the complete X-ray crystallographic structure as determined through single-crystal X-ray diffraction and a thorough theoretical analysis of the green gold Au₃₀(S-<i>t</i>Bu)₁₈. While the structure of Au₃₀S­(S-<i>t</i>Bu)₁₈ with 19 sulfur atoms has been reported, the crystal structure of Au₃₀(S-<i>t</i>Bu)₁₈ without the μ₃-sulfur has remained elusive until now, though matrix-assisted laser desorption ionization mass spectrometry (MALDI-MS) and electrospray ionization mass spectrometry (ESI-MS) data unequivocally show its presence in abundance. The Au₃₀(S-<i>t</i>Bu)₁₈ nanomolecule not only is distinct in its crystal structure but also has unique temperature-dependent optical properties. Structure determination allows a rigorous comparison and an excellent agreement with theoretical predictions of structure, stability, and optical response

Crystal Structure and Theoretical Analysis of Green Gold Au₃₀(S‑<i>t</i>Bu)₁₈ Nanomolecules and Their Relation to Au₃₀S(S‑<i>t</i>Bu)₁₈

We report the complete X-ray crystallographic structure as determined through single-crystal X-ray diffraction and a thorough theoretical analysis of the green gold Au₃₀(S-<i>t</i>Bu)₁₈. While the structure of Au₃₀S­(S-<i>t</i>Bu)₁₈ with 19 sulfur atoms has been reported, the crystal structure of Au₃₀(S-<i>t</i>Bu)₁₈ without the μ₃-sulfur has remained elusive until now, though matrix-assisted laser desorption ionization mass spectrometry (MALDI-MS) and electrospray ionization mass spectrometry (ESI-MS) data unequivocally show its presence in abundance. The Au₃₀(S-<i>t</i>Bu)₁₈ nanomolecule not only is distinct in its crystal structure but also has unique temperature-dependent optical properties. Structure determination allows a rigorous comparison and an excellent agreement with theoretical predictions of structure, stability, and optical response