Isomerism and structural fluxionality in the Au26 and Au26(-) nanoclusters

Isomeric Effects of Au28(S-c-C6H11)20 Nanoclusters on Photoluminescence: Roles of Electron-Vibration Coupling and Higher Triplet State

The exploration of near-infrared photoluminescence (PL) from atomically precise nanoclusters is currently a prominent area of interest owing to its importance in both fundamental research and diverse applications. In this work, we investigate the near-infrared (NIR) photoluminescence mechanisms of two structural isomers of atomically precise gold nanoclusters of 28 atoms protected by cyclohexanethiolate (CHT) ligands, i.e., Au28i(CHT)20 and Au28ii(CHT)20. Based on their structures, analysis of 3O2 (triplet oxygen) quenching of the nanocluster triplet states, temperature-dependent photophysical studies, and theoretical calculations, we have elucidated the intricate processes governing the photoluminescence of these isomeric nanoclusters. For Au28i(CHT)20, its emission characteristics are identified as phosphorescence plus thermally activated delayed fluorescence (TADF) with a PL quantum yield (PLQY) of 0.3% in dichloromethane under ambient conditions. In contrast, the Au28ii(CHT)20 isomer exhibits exclusive phosphorescence with a PLQY of 3.7% in dichloromethane under ambient conditions. Theoretical simulations reveal a larger singlet (S1)-triplet (T1) gap in Au28ii than that in Au28i, and the higher T2 state plays a critical role in both isomers' photophysical processes. The insights derived from this investigation not only contribute to a more profound comprehension of the fundamental principles underlying the photoluminescence of atomically precise gold nanoclusters but also provide avenues for tailoring their optical properties for diverse applications.

Principles of isomer stability in small clusters

In this work we study isomers of several representative small clusters to find principles for their stability. Our conclusions about the principles underlying the structure of clusters are based on a huge database of 44 000 isomers generated for 58 different clusters on the density functional theory level by Minima Hopping. We explore the potential energy surface of small neutral, anionic and cationic isomers, moving left to right across the third period of the periodic table and varying the number of atoms n and the cluster charge state q (X ^q _n , with X = {Na, Mg, Al, Si, Ge}, q = -1, 0, 1, 2). We use structural descriptors such as bond lengths and atomic coordination numbers, the surface to volume ratios and the shape factor as well as electronic descriptors such as shell filling and hardness to detect correlations with the stability of clusters. The isomers of metallic clusters are found to be structure seekers with a strong tendency to adopt compact shapes. However certain numbers of atoms can suppress the formation of nearly spherical metallic clusters. Small non-metallic clusters typically also do not adopt compact spherical shapes for their lowest energy structures. In both cases spherical jellium models are not any more applicable. Nevertheless for many structures, that frequently have a high degree of symmetry, the Kohn-Sham eigenvalues are bunched into shells and if the available electrons can completely fill such shells, a particularly stable structure can result. We call such a cluster whose shape gives rise to shells that can be completely filled by the number of available electrons an optimally matched cluster, since both the structure and the number of electrons must be special and match. In this way we can also explain the stability trends for covalent silicon and germanium cluster isomers, whose stability was previously explained by the presence of certain structural motifs. Thus we propose a unified framework to explain trends in the stability of isomers and to predict their structure for a wide range of small clusters.

New Insights into Adsorption Properties of the Tubular Au26 from AIMD Simulations and Electronic Interactions

Recently, we revealed the electronic nature of the tubular Au₂₆ based on spherical aromaticity. The peculiar structure of the Au₂₆ could be an ideal catalyst model for studying the adsorptions of the Au nanotubes. However, through Google Scholar, we found that no one has reported connections between the structure and reactivity properties of Au₂₆. Here, three kinds of molecules are selected to study the fundamental adsorption behaviors that occur on the surface of Au₂₆. When one CO molecule is adsorbed on the Au₂₆, the σ-hole adsorption structure is quickly identified as belonging to a ground state energy, and it still maintains integrity at a temperature of 500 K, where σ donations and π-back donations take place; however, two CO molecules make the structure of Au₂₆ appear with distortions or collapse. When one H₂ is adsorbed on the Au₂₆, the H-H bond length is slightly elongated due to charge transfers to the anti-bonding σ* orbital of H₂. The Au₂₆-H₂ can maintain integrity within 100 fs at 300 K and the H₂ molecule starts moving away from the Au₂₆ after 200 fs. Moreover, the Au₂₆ can act as a Lewis base to stabilize the electron-deficient BH₃ molecule, and frontier molecular orbitals overlap between the Au₂₆ and BH₃.

Probing Anion-Molecule Complexes of Atmospheric Relevance Using Anion Photoelectron Detachment Spectroscopy

Bimolecular reaction and collision complexes that drive atmospheric chemistry and contribute to the absorption of solar radiation are fleeting and therefore inherently challenging to study experimentally. Furthermore, primary anions in the troposphere are short lived because of a complicated web of reactions and complex formation they undergo, making details of their early fate elusive. In this perspective, the experimental approach of photodetaching mass-selected anion-molecule complexes or complex anions, which prepares neutrals in various vibronic states, is surveyed. Specifically, the application of anion photoelectron spectroscopy along with photoelectron-photofragment coincidence spectroscopy toward the study of collision complexes, complex anions in which a partial covalent bond is formed, and radical bimolecular reaction complexes, with relevance in tropospheric chemistry, will be highlighted.

Large-Sized Aun- Core-Shell Clusters (n = 61-66): Enduring Structure of the Icosahedral Au13 Core

Large-sized gold Au_n^- anion clusters exhibit structural characteristics drastically different from other coinage metals. Typically, coinage metal nanoclusters exhibit a 13-atom icosahedral core at the cluster size of 55. Gold clusters, contrarily, do not entail this core until the size reaches 60. Here, we investigated the robustness of the icosahedral core within the large-sized Au_n^- anion clusters. We found that the icosahedral core persists over the size of range of n = 61-66. To adapt the exceptional robustness of the icosahedral core, the shells of the clusters tend to undergo notable structural deformations with polygonal defects. As the cluster size increases from 61 to 66, the core starts to become distorted at n = 64 and the space between the core and shell becomes enlarged. To our knowledge, this is the first theoretical study that provides the simulated photoelectron spectra of the two largest sized gold clusters: Au₆₅^- and Au₆₆^-.

How Many Isomers Do Metallic Clusters Have? Case of Magnesium Clusters of up to 55 Atoms

About 9000 structures of magnesium clusters Mg_n (n = 2-13) generated via different methods were optimized at the DFT levels in order to estimate the number of all possible stable structures that can exist for the given cluster size (∼820,000 PES points were explored in total). It was found that the number of possible cluster isomers N quickly grows with a number of atoms n; however, it is significantly lower than the number of possible nonisomorphic graph structures, which can be drawn for the given n. At the DFT potential energy surface, we found only 543 local minima corresponding to the isomers of Mg₂-Mg₁₃. The number of isomers obtained in the DFT optimizations grows with n approximately as n⁴, whereas the N values extrapolated to the infinite generation process grow as n⁸. The cluster geometries obtained from the global DFT optimization were then used to adjust two empirical potentials of Gupta type (GP) and modified Sutton-Chen type (SCG3) describing the interactions between the magnesium atoms. Using these potentials, the extensive sets of structures Mg₂-Mg₅₅ (up to 30,000 clusters for each n) were optimized to obtain the dependence of the cluster isomer count on n in the continuous range of n = 2-30 and for selected n up to n = 55. It was found that the SCG3 potential, which is closer to the DFT results, gives a number of possible isomers growing as approximately n^8.9, whereas GP potential results in the n^4.3 dependence.

How O2-Binding Affects Structural Evolution of Medium Even-Sized Gold Clusters Aun- (n = 20-34)

We report the first joint anion photoelectron spectroscopy and theoretical study on how O₂-binding affects the structures of medium even-sized gold clusters, Au_n^- (n = 20-34), a special size region that entails a variety of distinct structures. Under the temperature conditions in the current photoelectron spectroscopy experiment, O₂-bound gold clusters were observed only for n = 22-24 and 34. Nevertheless, O₂ binding with the clusters in the size range of n = 20-34 can be still predicted based on the obtained global-minimum structures. Consequently, a series of structural transitions, from the pyramidal to fused-planar to core-shell structures, are either identified or predicted for the Au_nO₂^- clusters, where the O₂-binding is in either superoxo or peroxo fashion. The identified global-minimum structures of Au_nO₂^- (n = 20-34) also allow us to gain improved understanding of why the clusters Au_n^- (n = 26-32) are less reactive with O₂ in comparison to others.

Adsorption and reactions of NO molecules on anionic gold clusters in the size range below 1 nm: effects of clusters' global electronic properties

We systemically studied adsorption and reactions of NO on Au_n^- (n≤ 80) using a mini flow-tube reactor running at 150 K. For Au_n^- (n≤ 11), their reactions with NO mainly formed cluster complexes containing various numbers of NO units; for Au_n^- (n≥ 12), most active sizes eventually formed specific complexes Au_n(NO)₃^-. The relative rates of the reactions with the first NO were measured. Correlations between these relative rates and the adiabatic detachment energies (ADEs) of Au_n^- revealed the dominant effect of the clusters' spins and a more complicated electron transfer mechanism than that of reactions with O₂. Au₂₀^- as well as previously reported Au_4,6,8^- is an exceptional size, which eventually formed the disproportionate product Au₂₀NO₂^-, and all these four sizes have very low ADEs. The effects of the clusters' global electronic properties on adsorption and reactions of NO on anionic gold are helpful to understand catalytic mechanisms of gold-based catalysts in NO removal reactions.

Distance makes a difference in crystalline photoluminescence

Crystallization-induced photoluminescence weakening was recently revealed in ultrasmall metal nanoparticles. However, the fundamentals of the phenomenon are not understood yet. By obtaining conformational isomer crystals of gold nanoclusters, we investigate crystallization-induced photoluminescence weakening and reveal that the shortening of interparticle distance decreases photoluminescence, which is further supported by high-pressure photoluminescence experiments. To interpret this, we propose a distance-dependent non-radiative transfer model of excitation electrons and support it with additional theoretical and experimental results. This model can also explain both aggregation-induced quenching and aggregation-induced emission phenomena. This work improves our understanding of aggregated-state photoluminescence, contributes to the concept of conformational isomerism in nanoclusters, and demonstrates the utility of high pressure studies in nanochemistry.

Structural Evolution and Stability Trend of Small-Sized Gold Clusters Aun (n = 20-30)

Structural evolution and stability pattern of pure neutral gold clusters Au_n in the small size range of n = 20-30 are examined using density functional theory (DFT) calculations. The equilibrium geometries are either confirmed or determined, and some new ground state structures are identified. The most stable configurations of Au₂₁-Au₂₃ sizes are formed by adding extra gold atoms to the highly stable pyramidal structure of Au₂₀, while flat-cage shapes are the best candidates for the global minima of both Au₂₄ and Au₂₅. For larger sizes of n = 26-30, pyramidal motifs tend to dominate the lower-lying population rather than tubular conformations as previously reported. The energy gaps, excitation energies, and exciton binding energies are also computed to test out the performance of the computational methods employed. Accordingly, a density functional with long-range exchange effects is highly recommended to quantitatively investigate both the ground and excited states of pure gold clusters.

Electronic shells of a tubular Au26 cluster: a cage-cage superatomic molecule based on spherical aromaticity

Gold clusters, which display a variety of unusual geometric structures due to their strong relativistic effects, have attracted much attention. Among them, Au₂₆ has a high-symmetry tubular structure (D_6d) with a large HOMO-LUMO energy gap, but its electronic stability still remains unclear. In this paper, the electronic nature of the Au₂₆ cluster is investigated using the density functional theory method. Depending on the super valence bond model, the tubular Au₂₆ cluster with 26 valence electrons could be viewed as a superatomic molecule composed of two open cages based on spherical aromaticity, and its molecule-like electronic shell closure is achieved via a super triple bond (σ, 2π) between the two cages. Based on this new cage-cage superatomic structural model, a series of similar tubular clusters are predicted from the Au₂₆ skeleton. The two capped Au atoms are replaced by Cu, Ag and In atoms, respectively, to form tubular D_6d Au₂₄Cu₂ and Au₂₄Ag₂ (26e) and Au₂₄In₂ (30e) clusters, where the super triple bonds also exist. Moreover, tubular D_5d Au₂₀In₂ (26e) is obtained by replacing hexatomic Au₆ rings in the bulk of Au₂₄In₂ with pentagonal Au₅ rings. Chemical bonding analysis reveals that there is a super quintuple bond (σ, 2π, 2δ) between two open (Au₁₀In) cages, in accordance with the 26e Li₂₀Mg₃ superatomic molecule composed of two icosahedral superatoms. Our study proposes the new cage-cage structural model of superatomic molecules based on spherical aromaticity, which extends the range of the super valence bonding pattern and gives inferences for further study of superatomic clusters.

Determination of CO Adsorption Sites on Gold Clusters Au n- ( n = 21-25): A Size Region That Bridges the Pyramidal and Core-Shell Structures

We perform a joint photoelectron spectroscopy and theoretical study to investigate CO adsorption sites on midsized gold clusters, Au _n^- ( n = 21-25), a special size region that bridges the highly symmetric pyramidal cluster Au₂₀^- (Li et al. Science 2003, 299, 864) and the prevailing core-shell clusters starting from Au₂₆^- (Schaefer et al. ACS Nano 2014, 8, 7413). Particular attention is placed on whether the CO binding can significantly change structures of the host clusters in view of the fact that the size-dependent structural change already occurs for bare gold clusters in this size range. A transition from hollow-tubular to fused-planar structures is identified for the Au _nCO^- clusters even though the CO molecule mostly binds to an apex gold atom. The computed CO adsorption energy and HOMO-LUMO gap of the gold clusters suggest that among the five gold clusters the Au₂₃^- cluster exhibits the strongest CO binding and thereby could be a good catalytic model system.

Toward Solution Syntheses of the Tetrahedral Au20 Pyramid and Atomically Precise Gold Nanoclusters with Uncoordinated Sites

A long-standing objective of cluster science is to discover highly stable clusters and to use them as models for catalysts and building blocks for cluster-assembled materials. The discovery of catalytic properties of gold nanoparticles (AuNPs) has stimulated wide interests in gaseous size-selected gold clusters. Ligand-protected AuNPs have also been extensively investigated to probe their size-dependent catalytic and optical properties. However, the need to remove ligands can introduce uncertainties in both the structures and sizes of ligand-protected AuNPs for catalytic applications. Ideal model catalysts should be atomically precise AuNPs with well-defined structures and uncoordinated surface sites as in situ active centers. The tetrahedral ( T_d) Au₂₀ pyramidal cluster, discovered to be highly stable in the gas phase, provided a unique opportunity for such an ideal model system. The T_d-Au₂₀ consists of four Au(111) faces with all its atoms on the surface. Bulk synthesis of T_d-Au₂₀ with appropriate ligands would allow its catalytic and optical properties to be investigated and harnessed. The different types of its surface atoms would allow site-specific chemistry to be exploited. It was hypothesized that if the four corner atoms of T_d-Au₂₀ were coordinated by ligands the cluster would still contain 16 uncoordinated surface sites as potential in situ catalytically active centers. Phosphine ligands were deemed to be suitable for the synthesis of T_d-Au₂₀ to maintain the integrity of its pyramidal structure. Triphenyl-phosphine-protected T_d-Au₂₀ was first observed in solution, and its stability was confirmed both experimentally and theoretically. To enhance the synthetic yield, bidentate diphosphine ligands [(Ph)₂P(CH₂) _nP(Ph)₂ or L ⁿ] with different chain lengths were explored. It was hypothesized that diphosphine ligands with the right chain length might preferentially coordinate to the T_d-Au₂₀. Promising evidence was initially obtained by the formation of the undecagold by the L³ ligand. When the L⁸ diphosphine ligand was used, a remarkable Au₂₂ nanocluster with eight uncoordinated Au sites, Au₂₂(L⁸)₆, was synthesized. With a tetraphosphine-ligand (PP₃), a new Au₂₀ nanocluster, [Au₂₀(PP₃)₄]Cl₄, was isolated with high yield. The crystal structure of the new Au₂₀ core did not reveal the expected pyramid but rather an intrinsically chiral gold core. The surface of the new chiral-Au₂₀ was fully coordinated, and it was found to be highly stable chemically. The Au₂₂(L⁸)₆ nanocluster represents the first and only gold core with uncoordinated gold atoms, providing potentially eight in situ catalytically active sites. The Au₂₂ nanoclusters dispersed on oxide supports were found to catalyze CO oxidation and activate H₂ without ligand removal. With further understanding about the formation mechanisms of gold nanoclusters in solution, it is conceivable that T_d-Au₂₀ can be eventually synthesized, allowing its novel catalytic and optical properties to be explored. More excitingly, it is possible that a whole family of new atomically precise gold nanoclusters can be created with different phosphine ligands.

Neural network potentials for dynamics and thermodynamics of gold nanoparticles

For understanding the dynamical and thermodynamical properties of metal nanoparticles, one has to go beyond static and structural predictions of a nanoparticle. Accurate description of dynamical properties may be computationally intensive depending on the size of nanoparticle. Herein, we demonstrate the use of atomistic neural network potentials, obtained by fitting quantum mechanical data, for extensive molecular dynamics simulations of gold nanoparticles. The fitted potential was tested by performing global optimizations of size selected gold nanoparticles (Au_n, 17 ≤ n ≤ 58). We performed molecular dynamics simulations in canonical (NVT) and microcanonical (NVE) ensembles on Au₁₇, Au₃₄, Au₅₈ for a total simulation time of around 3 ns for each nanoparticle. Our study based on both NVT and NVE ensembles indicate that there is a dynamical coexistence of solid-like and liquid-like phases near melting transition. We estimate the probability at finite temperatures for set of isomers lying below 0.5 eV from the global minimum structure. In the case of Au₁₇ and Au₅₈, the properties can be estimated using global minimum structure at room temperature, while for Au₃₄, global minimum structure is not a dominant structure even at low temperatures.

Adsorption of O2 on Anionic Gold Clusters in the 0-1 nm Size Range: An Insight into the Electron Transfer Dynamics from Kinetic Measurements

We systematically studied the adsorption of O₂ on Au _n^- in the size range of 0-1 nm at low temperatures and determined new active sizes with n = 22, 24, 34, and 36. The kinetic measurements more clearly showed the correlation between the reactivity of Au _n^- with O₂ and their electronic properties: the sizes with a closed electron shell are always inert, and the sizes with an unpaired electron can chemically adsorb one O₂ molecule if their adiabatic detachment energies (ADEs) are lower than a threshold around 3.5 eV. This ADE threshold dividing the active and inert Au _n^- is independent of the clusters' sizes, global geometries, and local adsorption sites. According to the widely accepted electron transfer mechanism, this threshold could stand for the case in which the total energy of the Au _n^- and an O₂ roughly equals that of the spin crossover point of the potential surfaces of Au _n-O₂^- and Au _n^-···O₂.

Au26: a case of fluxionality/co-existence

BOMD simulations are performed on experimentally identified conformations of the fluxional Au26 cluster at finite temperature. Comprehensive analysis of structural, electronic and thermal properties indicates that the highest energy tubular cage conformation (till 500 K) outperforms the ground state conformation (till 400 K) in terms of thermal stability.

First-Principles Study of Structural, Electronic and Magnetic Properties of Metal-Centered Tetrahexahedral V15⁺ Cluster

The V-centered bicapped hexagonal antiprism structure (A), as the most stable geometry of the cationic V₁₅⁺ cluster, is determined by using infrared multiple photo dissociation (IR-MPD) in combination with density functional theory computations. It is found that the A structure can be stabilized by 18 delocalized 3c-2e σ-bonds on outer V₃ triangles of the bicapped hexagonal antiprism surface and 12 delocalized 4c-2e σ-bonds on inner trigonal pyramidal V₄ moiety, and the features are related to the strong p-d hybridization of the cluster. The total magnetic moments on the cluster are predicted to be 2.0 µ_B, which come mainly from the central vanadium atom.

The effect of ligand–ligand interactions on the formation of photoluminescent gold nanoclusters embedded in Au(i)–thiolate supramolecules

Photoluminescence of cysteine-capped gold nanoclusters obtained via the reduction of –[Cys–Au(i)]_n– supramolecules is highly dependent on the degree of supramolecular aggregation.

CO oxidation on Rh-doped hexadecagold clusters

Exploring the unique catalytic properties of gold clusters associated with specific nano-architectures is essential for designing improved catalysts with a high mass-specific activity.

Structural Evolution of Core-Shell Gold Nanoclusters: Aun- (n = 42-50)

Gold nanoclusters have attracted great attention in the past decade due to their remarkable size-dependent electronic, optical, and catalytic properties. However, the structures of large gold clusters are still not well-known because of the challenges in global structural searches. Here we report a joint photoelectron spectroscopy (PES) and theoretical study of the structural evolution of negatively charged core-shell gold nanoclusters (Au_n^-) for n = 42-50. Photoelectron spectra of size-selected Au_n^- clusters are well resolved with distinct spectral features, suggesting a dominating structural type. The combined PES data and density functional calculations allow us to systematically identify the global minimum or candidates of the global minima of these relatively large gold nanoclusters, which are found to possess low-symmetry structures with gradually increasing core sizes. Remarkably, the four-atom tetrahedral core, observed first in Au₃₃^-, continues to be highly robust and is even present in clusters as large as Au₄₂^-. Starting from Au₄₃^-, a five-atom trigonal bipyramidal core appears and persists until Au₄₇^-. Au₄₈^- possesses a six-atom core, while Au₄₉^- and Au₅₀^- feature seven- and eight-atom cores, respectively. Notably, both Au₄₆^- and Au₄₇^- contain a pyramidal Au₂₀ motif, which is stacked with another truncated pyramid by sharing a common 10-atom triangular face. The present study sheds light on our understanding of the structural evolution of the medium-sized gold nanoclusters, the shells and core as well as how the core-shell structures may start to embrace the golden pyramid (bulk-like) fragment.

Structural isomerism in gold nanoparticles revealed by X-ray crystallography. [Corrected]

Revealing structural isomerism in nanoparticles using single-crystal X-ray crystallography remains a largely unresolved task, although it has been theoretically predicted with some experimental clues. Here we report a pair of structural isomers, Au_38T and Au_38Q, as evidenced using electrospray ionization mass spectrometry, X-ray photoelectron spectroscopy, thermogravimetric analysis and indisputable single-crystal X-ray crystallography. The two isomers show different optical and catalytic properties, and differences in stability. In addition, the less stable Au_38T can be irreversibly transformed to the more stable Au_38Q at 50 °C in toluene. This work may represent an important advance in revealing structural isomerism at the nanoscale.

Revealing structural isomerism in nanoparticles remains a largely unresolved task. Here, the authors use several techniques, including single-crystal X-ray crystallography, to characterize two structural isomers of Au₃₈, and report their different optical and catalytic properties and differences in stability.

Magic-number gold nanoclusters with diameters from 1 to 3.5 nm: relative stability and catalytic activity for CO oxidation

Relative stability of geometric magic-number gold nanoclusters with high point-group symmetry ((Ih), D(5h), O(h)) and size up to 3.5 nm, as well as structures obtained by global optimization using an empirical potential, is investigated using density functional theory (DFT) calculations. Among high-symmetry nanoclusters, our calculations suggest that from Au(147) to Au(923), the stability follows the order Ih > D(5h) > Oh. However, at the largest size of Au(923), the computed cohesive energy differences among high-symmetry I(h), D(5h) and O(h) isomers are less than 4 meV/atom (at PBE level of theory), suggesting the larger high-symmetry clusters are similar in stability. This conclusion supports a recent experimental demonstration of controlling morphologies of high-symmetry Au(923) clusters ( Plant, S. R.; Cao, L.; Palmer, R. E. J. Am. Chem. Soc. 2014, 136, 7559). Moreover, at and beyond the size of Au(549), the face-centered cubic-(FCC)-based structure appears to be slightly more stable than the Ih structure with comparable size, consistent with experimental observations. Also, for the Au clusters with the size below or near Au(561), reconstructed icosahedral and decahedral clusters with lower symmetry are slightly more stable than the corresponding high-symmetry isomers. Catalytic activities of both high-symmetry and reconstructed I(h)-Au(147) and both Ih-Au(309) clusters are examined. CO adsorption on Au(309) exhibits less sensitivity on the edge and vertex sites compared to Au(147), whereas the CO/O2 coadsorption is still energetically favorable on both gold nanoclusters. Computed activation barriers for CO oxidation are typically around 0.2 eV, suggesting that the gold nanoclusters of ∼ 2 nm in size are highly effective catalysts for CO oxidation.

Perspectives on the energy landscape of Au–Cl binary systems from the structural phase diagram of AuxCly (x + y = 20)

Structural phase diagram (SPD) of Au_xCl_y (x + y = 20) clusters.

Structure identification of endohedral golden cage nanoclusters

The endohedral structures of MAu₁₆⁻ (M = Y, Zr and Nb) nanoclusters.