An efficient hybrid scheme for time dependent density functional theory

Combined experimental and computational study of the photoabsorption of the monodoped and nondoped nanoclusters Au24Pt(SR)18, Ag24Pt(SR)18, and Ag25(SR)18

Assessing the accuracy of first-principles computational approaches is instrumental to predict electronic excitations in metal nanoclusters with quantitative confidence. Here we describe a validation study on the optical response of a set of monolayer-protected clusters (MPC). The photoabsorption spectra of Ag25(DMBT)18-, Ag24Pt(DMBT)182- and Au24Pt(SC4H9)18, where DMBT is 2,4-dimethylbenzenethiolate and SC4H9 is n-butylthiolate, have been obtained at low temperature and compared with accurate TDDFT calculations. An excellent match between theory and experiment, with typical deviations of less than 0.1 eV, was obtained, thereby validating the accuracy and reliability of the proposed computational framework. Moreover, an analysis of the TDDFT simulations allowed us to ascribe all relevant spectral features to specific transitions between occupied/virtual orbital pairs. The doping effect of Pt on the optical response of these ultrasmall MPC systems was identified and discussed.

Sparse-Stochastic Fragmented Exchange for Large-Scale Hybrid Time-Dependent Density Functional Theory Calculations

We extend our recently developed sparse-stochastic fragmented exchange formalism for ground-state near-gap hybrid DFT to calculate absorption spectra within linear-response time-dependent generalized Kohn-Sham DFT (LR-GKS-TDDFT) for systems consisting of thousands of valence electrons within a grid-based/plane-wave representation. A mixed deterministic/fragmented-stochastic compression of the exchange kernel, here using long-range explicit exchange functionals, provides an efficient method for accurate optical spectra. Both real-time propagation as well as frequency-resolved Casida-equation-type approaches for spectra are presented, and the method is applied to large molecular dyes.

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.

The Conformational Dynamics of the Ligands Determines the Electronic Circular Dichroism of the Chiral Au38(SC2H4Ph)24 Cluster

Effects of the conformational dynamics of 2-PET protective ligands on the electronic circular dichroism (ECD) of the chiral Au₃₈(SC₂H₄Ph)₂₄ cluster are investigated. We adopt a computational protocol in which ECD spectra are calculated via the first principle polTDDFT approach on a series of conformations extracted from MD simulations by using Essential Dynamics (ED) analysis, and then properly weighted to predict the final spectrum. We find that the experimental spectral features are well reproduced, whereas significant discrepancies arise when the spectrum is calculated using the experimental X-ray structure. This result unambiguously demonstrates the need to account for the conformational effects in the ECD modeling of chiral nanoclusters. The present procedure proved to be able of capturing the essential conformational features of the dynamic Au₃₈(SC₂H₄Ph)₂₄ system, opening the possibility to model the ECD of soluble chiral nanoclusters in a realistic way.

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.

Optical Activity of Metal Nanoclusters Deposited on Regular and Doped Oxide Supports from First-Principles Simulations

We report a computational study and analysis of the optical absorption processes of Ag20 and Au20 clusters deposited on the magnesium oxide (100) facet, both regular and including point defects. Ag20 and Au20 are taken as models of metal nanoparticles and their plasmonic response, MgO as a model of a simple oxide support. We consider oxide defects both on the oxygen anion framework (i.e., a neutral oxygen vacancy) and in the magnesium cation framework (i.e., replacing Mg++ with a transition metal: Cu++ or Co++). We relax the clusters' geometries via Density-Functional Theory (DFT) and calculate the photo-absorption spectra via Time-Dependent DFT (TDDFT) simulations on the relaxed geometries. We find that the substrate/cluster interaction induces a broadening and a red-shift of the excited states of the clusters, phenomena that are enhanced by the presence of an oxygen vacancy and its localized excitations. The presence of a transition-metal dopant does not qualitatively affect the spectral profile. However, when it lies next to an oxygen vacancy for Ag20, it can strongly enhance the component of the cluster excitations perpendicular to the surface, thus favoring charge injection.

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.

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.