A Resolution of Identity Technique to Speed up TDDFT with Hybrid Functionals: Implementation and Application to the Magic Cluster Series Au8n+4(SC6H5)4n+8 (n = 3-6).

The Resolution of Identity (RI) technique has been employed to speed up the use of hybrid exchange-correlation (xc) functionals at the TDDFT level using the Hybrid Diagonal Approximation. The RI has been implemented within the polTDDFT algorithm (a complex damped polarization method) in the AMS/ADF suite of programs. A speedup factor of 30 has been obtained with respect to a previous numerical implementation, albeit with the same level of accuracy. Comparison of TDDFT simulations with the experimental photoabsorption spectra of the cluster series Au8n+4(SR)4n+8(n = 3-6; R = C6H5) showed the excellent accuracy and efficiency of the method. Results were compared with those obtained via the more simplified and computationally cheaper TDDFT+TB and sTDDFT methods. The present method represents an accurate as well as computationally affordable approach to predict photoabsorption spectra of complex species, realizing an optimal compromise between accuracy and computational efficiency, and is suitable for applications to large metal clusters with sizes up to several hundreds of atoms.

Optimization of density fitting auxiliary Slater-type basis functions for time-dependent density functional theory.

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.

Coupling between Plasmonic and Molecular Excitations: TDDFT Investigation of an Ag-Nanorod/BODIPY-Dye Interaction.

A time-dependent density functional theory (TDDFT) computational approach is employed to study the optical coupling between a plasmonic system (a Ag50 nanorod) and a fluorescent dye (BODIPY). It is found that the BODIPY dye can interact with a plasmonic system in a rather different and selective way according to the mutual orientation of the fragments. Indeed, (i) the plasmon excitation turns out to be sensitive to the presence of the BODIPY transition and (ii) this can lead to amplify or suppress the resonance accordingly to the relative orientation of the corresponding transition dipoles. To understand the coupling mechanism, we analyze the shape of the induced density in real space and the Individual Component Map of the Oscillator Strength (ICM-OS) plots and achieve a simple rationalization and insight on the origin and features of the coupling. The resulting possibility of understanding plasmon/fluorophore interactions by simple qualitative arguments opens the way to a rational design of hybrid (plasmon + dye) systems with the desired optical behavior.

Predictive optical photoabsorption of Ag24Au(DMBT)18 - via efficient TDDFT simulations.

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 Ag24Au(DMBT)18 single negative anion, where DMBT is the 2,4-dimethylbenzenethiolate 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.

Plasmonic Circular Dichroism in Chiral Gold Nanowire Dimers.

We report a computational study at the time-dependent density functional theory (TDDFT) level of the chiro-optical spectra of chiral gold nanowires coupled in dimers. Our goal is to explore whether it is possible to overcome destructive interference in single nanowires that damp chiral response in these systems and to achieve intense plasmonic circular dichroism (CD) through a coupling between the nanostructures. We predict a huge enhancement of circular dichroism at the plasmon resonance when two chiral nanowires are intimately coupled in an achiral relative arrangement. Such an effect is even more pronounced when two chiral nanowires are coupled in a chiral relative arrangement. Individual component maps of rotator strength, partial contributions according to the magnetic dipole component, and induced densities allow us to fully rationalize these findings, thus opening the way to the field of plasmonic CD and its rational design.

Chiral Functionalization of an Atomically Precise Noble Metal Cluster: Insights into the Origin of Chirality and Photoluminescence.

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.

An efficient hybrid scheme for time dependent density functional theory.

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 NH3, C6H6, and the [Au25(SCH3)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 [Au25(SCH3)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.