We probe the origin of photoluminescence of an atomically precise noble metal cluster, Ag24Au1(DMBT)18 (DMBT = 2,4-dimethylbenzenethiolate), and the origin of chirality in its chirally functionalized derivatives, Ag24Au1(R/S-BINAS) x (DMBT)18–2x , with x = 1–7 (R/S-BINAS = R/S-1,1′-[binaphthalene]-2,2′-dithiol), using chiroptical spectroscopic measurements and density functional theory (DFT) calculations. Combination of chiroptical and luminescence spectroscopies to understand the nature of electronic transitions has not been applied to such molecule-like metal clusters. In order to impart chirality to the achiral Ag24Au1(DMBT)18 cluster, the chiral ligand, R/S-BINAS, was incorporated into it. A series of clusters, Ag24Au1(R/S-BINAS) x (DMBT)18–2x , with x = 1–7, were synthesized. We demonstrate that the low-energy electronic transitions undergo an unexpected achiral to chiral and back to achiral transition from pure Ag24Au1(DMBT)18 to Ag24Au1(R/S-BINAS) x (DMBT)18–2x , by increasing the number of BINAS ligands. The UV/vis, luminescence, circular dichroism, and circularly polarized luminescence spectroscopic measurements, in conjunction with DFT calculations, suggest that the photoluminescence in Ag24Au1(DMBT)18 and its chirally functionalized derivatives originates from the transitions involving the whole Ag24Au1S18 framework and not merely from the icosahedral Ag12Au1 core. These results suggest that the chiroptical signatures and photoluminescence in these cluster systems cannot be solely attributed to any one of the structural components, that is, the metal core or the protecting metal–ligand oligomeric units, but rather to their interaction and that the ligand shell plays a crucial role. Our work demonstrates that chiroptical spectroscopic techniques such as circular dichroism and circularly polarized luminescence represent useful tools to understand the nature of electronic transitions in ligand-protected metal clusters and that this approach can be utilized for gaining deeper insights into the structure–property relationships of the electronic transitions of such molecule-like clusters.

A hybrid approach able to perform Time Dependent Density Functional Theory (TDDFT) simulations with the same accuracy as that of hybrid exchange-correlation (xc-) functionals but at a fraction of the computational cost is developed, implemented, and validated. The scheme, which we name Hybrid Diagonal Approximation (HDA), consists in employing in the response function a hybrid xc-functional (containing a fraction of the non-local Hartree-Fock exchange) only for the diagonal elements of the omega matrix, while the adiabatic local density approximation is employed for the off-diagonal terms. HDA is especially (but not exclusively) advantageous when using Slater type orbital basis sets and allows one to employ them in a uniquely efficient way, as we demonstrate here by implementing HDA in a local version of the Amsterdam Density Functional code. The new protocol is tested on NH 3 , C 6 H 6 , and the [Au 25 (SCH 3 ) 18 ] − cluster as prototypical cases ranging from small molecules to ligand-protected metal clusters, finding excellent agreement with respect to both full kernel TDDFT simulations and experimental data. Additionally, a specific comparison test between full kernel and HDA is considered at the Casida level on seven other molecular species, which further confirm the accuracy of the approach for all investigated systems. For the [Au 25 (SCH 3 ) 18 ] − cluster, a speedup by a factor of seven is obtained with respect to the full kernel. The HDA, therefore, promises to provide a quantitative description of the optical properties of medium-sized systems (nanoclusters) at an affordable cost, thanks to its computational efficiency, especially in combination with a complex polarization algorithm version of TDDFT.

We report the X-ray crystal structure of Au 36-x Ag x (SPh-tBu) 24 alloy nanomolecules, optical properties, and the substitutional disorder refinement protocol to obtain a reliable structural model. Single crystal X-ray crystallography (SC-XRD) revealed a composition of Au 33.17 Ag 2.83 (SPh-tBu) 24 with 2 Ag doped on the 28-atom face centered cubic core surface and 0.83 Ag distributed over metal atoms on dimeric staple motifs. Electrospray ionization mass spectrometry revealed a composition of Au 32.5 Ag 3.5 (SPh-tBu) 24 complementing the SC-XRD data. Optical properties were investigated by steady-state and transient absorption spectroscopies and computational studies, showing faster excited-state decay for Ag-doped clusters due to enhanced electronic coupling. A previously published SC-XRD based Au 36-x Ag x (SPh-tBu) 24 structure used positional disorder refinement and concluded that the structure is "solely motif-doped". But the structure has unusually large and small thermal ellipsoids indicating potential problems with the atom assignment. Here, we have modeled our SC-XRD data using both positional disorder and substitutional disorder. Subtitutional disorder modeling gave better R 1 and other refinement indicators, and similarly sized thermal ellipsoids. The resulting substitutional disorder model structure has Ag atoms not as "solely motif-doped" but is found both in the staple motifs and in the core. The substitutional disorder refinement for alloy nanomolecules must be performed at each metal site with independent free variables to determine the partial occupancy of hetero atoms. The positional disorder refinement should be performed for atoms or groups disordered over different positions typically found in disordered tBu group ligands.

We report a computational study via time-dependent density-functional theory (TDDFT) methods of the photo-absorption spectrum of an atomically precise monolayer-protected cluster (MPC), the Ag 24 Au(DMBT) 18 single negative anion, where DMBT is the 2,4dimethylbenzenethiolate ligand. The use of efficient simulation algorithms, i.e., the complex polarizability polTDDFT approach and the hybrid-diagonal approximation, allows us to employ a variety of exchange-correlation (xc-) functionals at an affordable computational cost. We are thus able to show, first, how the optical response of this prototypical compound, especially but not exclusively in the absorption threshold (low-energy) region, is sensitive to (1) the choice of the xc-functionals employed in the Kohn-Sham equations and the TDDFT kernel and (2) the choice of the MPC geometry. By comparing simulated spectra with precise experimental photoabsorption data obtained from room temperature down to low temperatures, we then demonstrate how a hybrid xc-functional in both the Kohn-Sham equations and the diagonal TDDFT kernel at the crystallographically determined experimental geometry is able to provide a consistent agreement between simulated and measured spectra across the entire optical region. Single-particle decomposition analysis tools finally allow us to understand the physical reason for the failure of non-hybrid approaches.

A new set of auxiliary basis function suitable to fit the induced electron density is presented. Such set has been optimized in order to furnish accurate absorption spectra using the complex polarizability algorithm of time‐dependent density functional theory (TDDFT). An automatic procedure has been set up, able, thanks to the definition of suitable descriptors, to evaluate the resemblance of the auxiliary basis‐dependent calculated spectra with respect to a reference. In this way, it has been possible to reduce the size of the basis set maximizing the basis set accuracy. Thanks to the choice to employ a collection of molecules for each element, such basis has proven transferable to molecules outside the collection. The final sets are therefore much more accurate and smaller than the previously optimized ones and have been already included in the database of the last release of the AMS suite of programs. The availability of the present new set will allow to improve drastically the applicability range of the polTDDFT method with higher accuracy and less computational effort.