Ellipsoidal shell structure in free-electron metal clusters

Gas Phase Reactions of Pristine and Single-Atom-Doped Copper and Silver Clusters: Probing Size-Dependent Stability and Novel Superatoms

Gas phase reactions have been a subject of research interest, enabling reliable strategies to explore the stability and reactivity of metal clusters as well as to probe novel superatoms that form the building blocks to assemble new materials with tailored properties. Coinage metal clusters have attracted great research attention due to their simple electronic shell structures and rich photochemical and catalytic properties at relatively low cost. This perspective focuses on the recent progress made in studying the gas phase reactions of undamaged and single-atom-doped Cun±,0 and Agn±,0 clusters with O2, CO, and NO molecules. It covers various aspects, such as reaction mechanisms, relationships between structure and activity, control of reactivity by changing cluster size and composition, and the identification of novel superatoms (Cu18-, Ag13-, Ag17-, and Ag15O+). Lastly, we provide a detailed account of the obstacles and prospective avenues for future research in order to establish a connection between these findings and nanocluster systems that have practical applications.

Accelerating Global Search of Large-Sized Silver Clusters Using Cluster Graph Attention Network

Great efforts have been devoted to understanding the stability and reactivity of silver clusters, which usually depend on geometric structures, electronic configuration, and cluster size. Despite the fact that the jellium model and Wulff construction rule have successfully rationalized the stable clusters with "magic number" behavior, some experiments imply that silver clusters with 48 valence electrons also possess puzzling enhanced stability. In this work, using a recently developed deep learning technology, i.e., cluster graph attention network (CGANet), combined with a homemade comprehensive genetic algorithm (CGA) program, we searched the global minimum (GM) structures of Agn (n = 30-60) clusters with graphics processing unit acceleration, whose efficiency is about 2 orders of magnitude higher than that of the conventional density functional theory (DFT) calculations. GM structures and some representative isomers are reported at each size, revealing the competitive structural patterns based on truncated octahedra and icosahedra as well as the icosahedra-based layer-by-layer growth mode of large-sized Ag clusters. Most importantly, the size-dependent evolution behavior of structural and electronic properties of Agn (n = 30-60) clusters can successfully explain the observed stability at Ag48. Therefore, CGANet provides a powerful tool for rapidly exploring the potential energy surface of atoms with an accuracy comparable to that of DFT.

The smallest triple-ring tubular gold clusters M2@Au15 with M = Mo, W: stability, electronic properties and nonlinear optical response

The smallest triple ring tube-like gold clusters M2@Au15q with M = Mo, W and q = 1, 0, -1 are reported for the first time. Incorporation of an M2 dimer results in a remarkable modification of both atomic and electronic structures of the gold host. While the bare Au15 cluster exhibits a 3D cage shape, the doubly doped clusters M2@Au15 in all charge states are found to prefer a tubular form composed of three five-membered Au rings in an anti-prism arrangement and stabilized by an M2 unit placed inside the tube-like Au15 gold framework. The equilibrium geometry of both M2@Au15 and M2@Au15- is not much modified upon electron detachment from or attachment to their pure gold counterpart. The anion M2@Au15- with 28 itinerant electrons establishes an electron shell configuration of 1S21P61D102S21F8, in which the 1F shell splits into four different sub-levels. These stable clusters are thus not magic. Computed results on the first and second hyper-polarizability parameters of the doped clusters show a strong dependence on the charge. Overall, the neutral M2@Au15 is found to exhibit a particularly strong nonlinear optical (NLO) response. These clusters can also be extended to 1D nanowires, providing helpful guidance for the design of novel gold-based nanowires with rich optoelectronic properties.

Ca n neutral clusters: a two-step G 0 W 0 and DFT benchmark

Electronic and structural properties of calcium clusters with a varying size range of 2-20 atoms are studied using a two-step scheme within the GW and density functional theory (DFT) with generalized gradient approximation (GGA). The GGA overestimates the binding energies, optimized geometries, electron affinities, and ionization potentials reported in the benchmark. The ground-state structure geometry and binding energy were obtained from the DFT for the ground-state structure of each cluster. The binding energy of the neutral clusters of the calcium series follows an increasing trend, except for a few stable even and odd clusters. The electronic properties of the calcium cluster were studied with an all-electron FHI-aims code. In the G 0 W 0 calculation, the magic cluster Ca10 has relatively high ionization potential and low electron affinity. The obtained ionization potentials from the G 0 W 0 @PBE calculation showed that the larger cluster has less variation, whereas the electron affinities of the series have an increasing trend. The ionization potentials from the G 0 W 0 benchmark for the calcium cluster series have not yet been described in the literature.

Thiacalix[4]arene-Protected Silver Nanoclusters Encapsulating Different Two-Electron Superatom Oligomers

The subvalent silver kernel represents the nascent state of silver cluster formation, yet the growth mechanism has long been elusive. Herein, two silver nanoclusters (Ag30 and Ag34) coprotected by TC4A4- (H4TC4A = p-tert-butylthiacalix[4]arene) and TBPMT- (TBPMTH = 4-tert-butylbenzenemethanethiol) containing 6e and 4e silver kernels are synthesized and characterized. The trimer of the 2e superatom Ag14 kernel in Ag30 is built from a central Ag6 octahedron sandwiched by two orthogonally oriented Ag5 trigonal bipyramids through sharing vertexes, whereas a double-octahedral Ag10 kernel in Ag34 is a dimer of 2e superatoms. They manifest disparate polyhedron fusion growth patterns at the beginning of the silver cluster formation. Their excellent solution stabilities are contributed by the multisite and multidentate coordination fashion of TC4A4- and the special valence electron structures. This work demonstrates the precise control of silver kernel growth by the solvent strategy and lays a foundation for silver nanocluster application in photothermal conversion.

Structural Determination and Hierarchical Evolution of Transition Metal Clusters Based on an Improved Self-Adaptive Differential Evolution with Neighborhood Search Algorithm

Determining the optimal structures and clarifying the corresponding hierarchical evolution of transition metal clusters are of fundamental importance for their applications. The global optimization of clusters containing a large number of atoms, however, is a vastly challenging task encountered in many fields of physics and chemistry. In this work, a high-efficiency self-adaptive differential evolution with neighborhood search (SaNSDE) algorithm, which introduced an optimized cross-operation and an improved Basin Hopping module, was employed to search the lowest-energy structures of CoN, PtN, and FeN (N = 3-200) clusters. The performance of the SaNSDE algorithm was first evaluated by comparing our results with the parallel results collected in the Cambridge Cluster Database (CCD). Subsequently, different analytical methods were introduced to investigate the structural and energetic properties of these clusters systematically, and special attention was paid to elucidating the structural evolution with cluster size by exploring their overall shape, atomic arrangement, structural similarity, and growth pattern. By comparison with those results listed in the CCD, 13 lower-energy structures of FeN clusters were discovered. Moreover, our results reveal that the clusters of three metals had different magic numbers with superior stable structures, most of which possessed high symmetry. The structural evolution of Co, Pt, and Fe clusters could be, respectively, considered as predominantly closed-shell icosahedral, Marks decahedral, and disordered icosahedral-ring growth. Further, the formation of shell structures was discovered, and the clusters with hcp-, fcc-, and bcc-like configurations were ascertained. Nevertheless, the growth of the clusters was not simply atom-to-atom piling up on a given cluster despite gradual saturation of the coordination number toward its bulk limit. Our work identifies the general growth trends for such a wide region of cluster sizes, which would be unbearably expensive in first-principles calculations, and advances the development of global optimization algorithms for the structural prediction of clusters.

Metal nanoclusters: from fundamental aspects to electronic properties and optical applications

Monolayer-protected noble metal clusters, also called nanoclusters, can be produced with the atomic precision and in large-scale quantity and are playing an increasingly important role in the field of nanoscience. To outline the origin and the perspectives of this new field, we overview the main results obtained on free metal clusters produced in gas phase including mainly electronic properties, the giant atom concept, the optical properties, briefly the role of the metal atom (alkali, divalent, noble metal) and finally the atomic structure of clusters. We also discuss the limitations of the free clusters. Then, we describe the field of monolayer-protected metal clusters, the main results, the new offered perspectives, the added complexity, and the role of the ligand beyond the superatom concept.

The global minimum of Ag30: a prolate spheroidal structure predicted using a genetic algorithm with incomplete local optimizations at the DFT level

Genetic algorithms have been widely used to explore global minimum points of atomic clusters, and their incorporation with ab initio calculations (including density functional theory methods) as local optimization approaches increases their ability to accurately locate the global minimum points on complicated potential energy surfaces. However, the local optimizations using ab initio calculations significantly increase the computational cost relative to those based on empirical or semi-empirical calculations. Herein, we develop a genetic algorithm program with an incomplete local optimization strategy at the DFT level. Using several representative clusters as test examples, this program showed high efficiency in locating their global minimum points. The low-lying isomers of Ag₃₀ were explored using this program, and the determined global minimum is a prolate spheroidal structure. The elongated spheroidal shape causes degeneracy lifting of the free electron shells, and endows Ag₃₀ with a large HOMO-LUMO gap. The sharp increase of silver clusters' reactivity around the sizes with 30 valence electrons observed in our previous experiments could be correlated with this theoretical figure.

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.

Single atom alloy clusters Agn-1X- (X = Cu, Au; n = 7-20) reacting with O2: Symmetry-adapted orbital model

Single atom alloy AgCu catalysts have attracted great attention, since doping the single Cu atom introduces narrow free-atom-like Cu 3d states in the electronic structure. These peculiar electronic states can reduce the activation energies in some reactions and offer valuable guidelines for improving catalytic performance. However, the geometric tuning effect of single Cu atoms in Ag catalysts and the structure-activity relationship of AgCu catalysts remain unclear. Here, we prepared well-resolved pristine Ag_n ^- as well as single atom alloy Ag_n-1Cu^- and Ag_n-1Au^- (n = 7-20) clusters and investigated their reactivity with O₂. We found that replacing an Ag atom in Ag_n ^- (n = 15-18) with a Cu atom significantly increases the reactivity with O₂, while replacement of an Ag with an Au atom has negligible effects. The adsorption of O₂ on Ag_n ^- or Ag_n-1Cu^- clusters follows the single electron transfer mechanism, in which the cluster activity is dependent on two descriptors, the energy level of α-HOMO (strong correlation) and the α-HOMO-LUMO gap (weak correlation). Our calculation demonstrated that the cluster arrangements caused by single Cu atom alloying would affect the above activity descriptors and, therefore, regulates clusters' chemical activity. In addition, the observed reactivity of clusters in the representative sizes with n = 17-19 can also be interpreted using the symmetry-adapted orbital model. Our work provides meaningful information to understand the chemical activities of related single-atom-alloy catalysts.

The Proxy-SU(3) Symmetry in Atomic Nuclei

The microscopic origins and the current predictions of the proxy-SU(3) symmetry model of atomic nuclei were reviewed. Beginning with experimental evidence for the special roles played by nucleon pairs with maximal spatial overlap, the proxy-SU(3) approximation scheme is introduced; its validity is demonstrated through Nilsson model calculations and its connection to the spherical shell model. The major role played by the highest weight-irreducible representations of SU(3) in shaping up the nuclear properties is pointed out, resulting in parameter-free predictions of the collective variables β and γ for even–even nuclei in the explanation of the dominance of prolate over oblate shapes in the ground states of even–even nuclei, in the prediction of a shape/phase transition from prolate to oblate shapes below closed shells, and in the prediction of specific islands on the nuclear chart in which shape coexistence is confined. Further developments within the proxy-SU(3) scheme are outlined.

An Open-Shell Superatom Cluster Ta10- with Enhanced Stability by United d-d π Bonds and d-Orbital Superatomic States

We carried out a comprehensive study on the gas-phase reactions of Ta_n^- (n = 5-27) with nitrogen using a customized reflection time-of-flight mass spectrometer coupled with a velocity map imaging apparatus (Re-TOFMS-VMI). Among the studied tantalum clusters, Ta₁₀^- exhibits prominent mass abundance indicative of its unique inertness. DFT calculation results revealed a D_4d bipyramidal prolate structure of the most stable Ta₁₀^-, which was verified by photoelectron spectroscopy experiments. The calculations also unveiled that Ta₁₀^- has the largest HOMO-LUMO gap and second-order difference of binding energy among the studied clusters. This is associated with its well-organized superatomic orbitals, which consist of both 6s and 5d orbitals of tantalum atoms, allowing for splitting of superatomic 1D and 2P orbitals and an enlarged gap between the singly occupied molecular orbital (SOMO) and unoccupied β counterpart, which brings forth stabilization energy pertaining to Jahn-Teller distortion. Also, the SOMO exhibits a united d-d π orbital pattern that embraces the central Ta₈^- moiety.

Electrical devices designed based on inorganic clusters

The idea of exploring the bottom brink of material science has been carried out for more than two decades. Clusters science is the frontmost study of all nanoscale structures. Being an example of 0-dimensional quantum dot, nanocluster serves as the bridge between atomic and conventionally understood solid-state physics. The forming mechanism of clusters is found to be the mutual effects of electronic and geometric configuration. It is found that electronic shell structure influences the properties and geometric structure of the cluster until its size becomes larger, where electronic effects submerge in geometric structure. The discrete electronic structures depend on the size and conformation of clusters, which can be controlled artificially for potential device applications. Especially, small clusters with a size of 1-2 nm, whose electronic states are possibly discrete enough to overcome thermal fluctuations, are expected to build a single-electron transistor with room temperature operation. However, exciting as the progress may be seen, cluster science still falls within the territory of merely the extension of atomic and molecular science. Its production rate limits the scientific and potential application research of nanoclusters. It is suggested in this review that the mass-produce ability without losing the atomic precision selectivity would be the milestone for nanoclusters to advance to material science.

Superatomic Orbital Splitting in Coinage Metal Nanoclusters

The superatomic orbital splitting (SOS) method is developed to understand the electronic structures of coinage metal nanoclusters, in which delocalized electron counts are not magic numbers. Because the symmetry of a metal core can significantly affect the electronic structure of a nanocluster, this method takes the shape of the core into account in determining the order of group orbital levels. By taking nanoclusters as superatoms, a highly positively charged core is established by removing the ligands and staples. The superatomic orbitals split into group orbitals at different energy levels because of the nonspherical shape of the cluster core. Therefore, the electron configuration of the nonmagic-number nanocluster can be qualitatively analyzed without quantum chemical calculations, which is very important for understanding the stability of the cluster.

The binary boron lithium clusters B12Lin with n = 1-14: in search for hydrogen storage materials

Molecular structures and properties of the binary clusters containing twelve boron atoms mixed with n lithium atoms, B₁₂Li_n with n = 1-14, were investigated using density functional theory with the TPSSh functional and the 6-311+G(d) basis set. Energetic parameters including relative energies, average binding energies and second-order energies of the entire series were predicted using the coupled-cluster theory (U)CCSD(T) in conjunction with the cc-pVTZ basis set. Several lowest-lying isomers were determined for each size B₁₂Li_n whose energies differ from each other by <3 kcal mol^-1, except for n = 1, 2 and 4 (≤5 kcal mol^-1), and particularly n = 8 (∼13 kcal mol^-1). Electronic structure and chemical bonding in some specific sizes such as B₁₂Li₄, B₁₂Li₈ and B₁₂Li₁₄ were analyzed in detail. We established the electron shells of some magic clusters such as the B₁₂Li₄ cone for which we proposed a mixed cone-disk electron shell model. Thanks to both the phenomenological shell and Clemenger-Nilsson models, B₁₂Li₈ which contains a specific set of shells of 44 valence electrons is a high stability species. The arrangement of Li atoms around a fullerene B₁₂ framework shows that the mixed B₁₂Li₈ emerges as the most suitable of this cluster series to adsorb molecular hydrogen. Up to 32 H₂ molecules can strongly be attached to the B₁₂Li₈ cluster which is thus predicted to be a realistic candidate for hydrogen storage material with gravimetric density reaching up to a theoritical limit of 26 wt%. Attachment of the fifth H₂ molecule to each Li atom of B₁₂Li₈ results in weaker average bonds but can give rise to a total of 40 H₂ molecules, corresponding to 30 wt% of hydrogen.

Molecular Gold Nanocluster Au156 Showing Metallic Electron Dynamics

The boundary between molecular and metallic gold nanoclusters is of special interest. The difficulty in obtaining atomically precise nanoclusters larger than 2 nm limits the determination of such a boundary. The synthesis and total structural determination of the largest all-alkynyl-protected gold nanocluster (Ph₄P)₆[Au₁₅₆(C≡CR)₆₀] (R = 4-CF₃C₆H₄-) (Au₁₅₆) are reported. It presents an ideal platform for studying the relationship between the structure and the metallic nature. Au₁₅₆ has a rod shape with the length and width of the kernel being 2.38 and 2.04 nm, respectively. The cluster contains a concentric Au₁₂₆ core structure (Au₄₆@Au₅₀@Au₃₀) protected by 30 linear RC≡C-Au-C≡CR staple motifs. It is interesting that Au₁₅₆ displays multiple excitonic peaks in the steady-state absorption spectrum (molecular) and pump-power-dependent excited-state dynamics as revealed in the transient absorption spectrum (metallic), which indicates that Au₁₅₆ is a critical crossover cluster for the transition from molecular to metallic state. Au₁₅₆ is the smallest-sized gold nanocluster showing metal-like electron dynamics, and it is recognized that the cluster shape is one of the important factors determining the molecular or metallic nature of a gold nanocluster.

The superatomic state beyond conventional magic numbers: Ligated metal chalcogenide superatoms

The field of cluster science is drawing increasing attention due to the strong size and composition-dependent properties of clusters and the exciting prospect of clusters serving as the building blocks for materials with tailored properties. However, identifying a unifying central paradigm that provides a framework for classifying and understanding the diverse behaviors is an outstanding challenge. One such central paradigm is the superatom concept that was developed for metallic and ligand-protected metallic clusters. The periodic electronic and geometric closed shells in clusters result in their properties being based on the stability they gain when they achieve closed shells. This stabilization results in the clusters having a well-defined valence, allowing them to be classified as superatoms-thus extending the Periodic Table to a third dimension. This Perspective focuses on extending the superatomic concept to ligated metal-chalcogen clusters that have recently been synthesized in solutions and form assemblies with counterions that have wide-ranging applications. Here, we illustrate that the periodic patterns emerge in the electronic structure of ligated metal-chalcogenide clusters. The stabilization gained by the closing of their electronic shells allows for the prediction of their redox properties. Further investigations reveal how the selection of ligands may control the redox properties of the superatoms. These ligated clusters may serve as chemical dopants for two-dimensional semiconductors to control their transport characteristics. Superatomic molecules of multiple metal-chalcogen superatoms allow for the formation of nano-p-n junctions ideal for directed transport and photon harvesting. This Perspective outlines future developments, including the synthesis of magnetic superatoms.

Stability of Two-Dimensional Ionic Clusters at Solid-Liquid Interfaces

The stability of two-dimensional clusters (2DCs) at the interface between ionic crystals and their solutions was investigated by molecular dynamics simulations. We found that 2DCs show a remarkable feature of odd-even alternation in stability. In NaCl and NaBr systems, the clusters containing an odd number of ions are more stable than those with an even number of ions, while in KCl systems, it is the other way round. Accordingly, the stability of water molecules in the first hydration shell of 2DCs also shows an odd-even alternation, which is consistent with the associated 2DCs. The odd-even alternation is discussed based on a competition mechanism between two factors: the Coulomb repulsion in charged 2DCs and the interaction between charges and water dipoles. Our discussion indicates that this odd-even alternation should be a universal feature in similar systems and would be important for understanding the nucleation and crystallization of solutions on ionic crystal surfaces.

Stability of cationic silver doped gold clusters and the subshell-closed electronic configuration of AgAu14. J Chem Phys 2020;153:244304. [PMID: 33380086 DOI: 10.1063/5.0033487]

Silver doping is a valuable route to modulate the structural, electronic, and optical properties of gold clusters. We combine photofragmentation experiments with density functional theory calculations to investigate the relative stability of cationic Ag doped Au clusters, AgAu_N-1 ⁺ (N ≤ 40). The mass spectra of the clusters after photofragmentation reveal marked drops in the intensity of AgAu₈ ⁺, AgAu₁₄ ⁺, and AgAu₃₄ ⁺, indicating a higher relative stability of these sizes. This is confirmed by the calculated AgAu_N-1 ⁺ (N ≤ 17) dissociation energies peaking for AgAu₆ ⁺, AgAu₈ ⁺, and AgAu₁₄ ⁺. While the stability of AgAu₆ ⁺ and AgAu₈ ⁺ can be explained by the accepted electronic shell model for metal clusters, density of states analysis shows that the geometry plays an important role in the higher relative stability of AgAu₁₄ ⁺. For this size, there is a degeneracy lifting of the 1D shell, which opens a relatively large HOMO-LUMO gap with a subshell-closed 1S²1P⁴1P²1D⁶ electronic configuration.

A method for predicting basins in the global optimization of nanoclusters with applications to AlxCuy alloys

The problem of obtaining the geometrical configuration of a molecule that minimizes its potential energy is a very complicated one for a series of applications, ranging from determining the structure of biological macromolecules to nanoclusters of atoms. Global optimization tools are available for this task, and many of them are based in performing successive local optimizations, where the starting geometries for these steps are determined by an intelligent algorithm. Here we develop a method to save computing time in the optimization of nanoclusters by predicting if a given minimum has been previously visited during local optimization steps. Our application to Cu-Al nanoalloys indicates that it is possible to save a substantial amount of computational cost. The application also reveals new promising Al_xCu_y clusters and explain their stabilities in terms of the jellium model.

Structure, stability, absorption spectra and aromaticity of the singly and doubly silicon doped aluminum clusters Al n Si m 0/+ with n = 3-16 and m = 1, 2

Structures of the binary Al n Si m clusters in both neutral and cationic states were investigated using DFT and TD-DFT (B3LYP/6-311+G(d)) and (U)CCSD(T)/cc-pvTZ calculations. Silicon-doped aluminum clusters are characterized by low spin ground states. For small sizes, the Si dopant prefers to be located at vertices having many edges. For larger sizes, the Si atom prefers to be endohedrally doped inside an Al n cage. Relative stability, adiabatic ionization energy and dissociation energies of each cluster size were evaluated. A characteristic of most Si doped Al clusters is the energetic degeneracy of two lowest-lying isomers. Calculated results confirm the high stability of the sizes Al4Si2, Al12Si and Al11Si2 + as "magic" clusters, that exhibit 20 or 40 shell electrons and are thermodynamically more stable as compared to their neighbors. Electronic absorption spectra of isoelectronic magic clusters Al13 -, Al12Si, and Al11Si2 + that have two pronounced bands corresponding to blue and violet lights, have been rationalized by using the electron shell model. The magnetically included ring current density (MICD) analyses suggest that they are also aromatic structures as a result of the "magic" 40 shell electrons.

Thermal Kinetics of Aln- + O2 (n = 2-30): Measurable Reactivity of Al13. J Phys Chem A 2019;123:6123-6129. [PMID: 31251615 DOI: 10.1021/acs.jpca.9b03552]

Mass-selected aluminum anion clusters, Al_n^-, were reacted with O₂. Rate constants (300 K) for 2 < n < 30 and product branching fractions for 2 < n < 17 are reported. Reactivity is strongly anticorrelated to Al_n^- electron binding energy (EBE). Al₁₃^- reacts more slowly than predicted by EBE but notably is not inert, reacting at a measurable 0.05% efficiency (2.5 ± 1.5 × 10^-13 cm³ s^-1). Al₆^- is also an outlier, reacting more slowly than expected after accounting for other factors, suggesting that high symmetry increases stability. Implications of observed Al₁₃^- reactivity, contributions of both electronic shell-closing and geometric homogeneity to Al_n^- resistance to O₂ etching, and future directions to more fully unravel the reaction mechanisms are discussed.

[Au18(dppm)6Cl4]4+: a phosphine-protected gold nanocluster with rich charge states

A diphosphine-protected 18-gold-atom nanocluster was isolated via a facile reduction of an Au^I precursor by NaBH₄.

Application of Electronic Counting Rules for Ligand-Protected Gold Nanoclusters

Understanding special stability of numerous ligand-protected gold nanoclusters has always been an active area of research. In the past few decades, several theoretical models, including the polyhedral skeletal electron pair theory (PSEPT), superatom complex (SAC), and superatom network (SAN), among others, have been developed for better understanding the stabilities and structures of selected ligand-protected gold nanoclusters. This Account overviews the recently proposed grand unified model (GUM) to offer some new insights into the structures and growth mechanism of nearly all crystallized and predicted ligand-protected gold nanoclusters. The main conceptual advancement of the GUM is identification of the duet and octet rules on the basis of the "big data" of 70+ reported ligand-protected gold nanoclusters. According to the two empirical rules, the cores of the gold nanoclusters can be regarded as being composed of two kinds of elementary blocks (namely, triangle Au₃ and tetrahedron Au₄), each having 2 e closed-shell valence electrons (referred as Au₃(2 e) and Au₄(2 e)), as well as the secondary block (icosahedron Au₁₃) with 8 e closed-shell valence electrons (referred as Au₁₃(8 e)). The two elementary blocks (Au₃(2 e) and Au₄(2 e)) and the secondary block (Au₁₃(8 e)), from electron counting point of view, can be regarded as an analogy of the highly stable noble-gas atoms of He and Ne, respectively. In each elementary block, the Au atoms exhibit three different valence-electron states (i.e., 1 e, 0.5 e, and 0 e), depending on the type of ligands bonded with these Au atoms. Such three valence-electron states are coined as three "flavors" of gold (namely, bottom, middle, and top "flavor"), a term borrowed from the quark model in the particle physics. Upon application of the duet and octet rules with accounting the three valence states of gold atoms, the Au₃(2 e), Au₄(2 e), and Au₁₃(8 e) blocks can exhibit 10 (denoted as Δ₁-Δ₁₀), 15 (denoted as T₁-T₁₅), and 91 (denoted as I₁-I₉₁) variants of valence states, respectively. When packing these blocks (with distinct electronic states) together, it forms the gold core of ligand-protected gold nanocluster. As such, the special stabilities of the ligand-protected gold nanoclusters are explained based on the local stability of each block. With GUM, rich and complex structures of ligand-protected gold nanoclusters have been analyzed through structure anatomy. Moreover, the growth of these clusters can be simply viewed as sequential addition of the blocks, rather than as addition of the gold atoms. Another useful application of the GUM is to analyze the structural isomerism. The three types of isomerism for the gold nanoclusters, i.e., core, staple, and complex isomerism, can be considered as an analogy of chain, point, and functional isomerism (known in organic chemistry), respectively. GUM can be applied to predict new clusters, thereby guiding experimental synthesis. Indeed, a number of ligand-protected gold nanoclusters with high stabilities were rationally designed based on the GUM.

Elucidation of the molecular and electronic structures of some magic silver clusters Agn (n = 8, 18, 20)

Density functional theory (DFT) calculations were carried out to explore the geometric, spectroscopic, and electronic properties of three magic silver clusters Ag_n (n = 8, 18, and 20) in detail. The computed results show that the global minima of these clusters are compact, near-spherical structures, while other low-lying isomers exhibit oblate or prolate shapes. Vertical ionization energies for the low-lying isomers were also computed and assigned with respect to available experimental values. Although several isomers were predicted to have similar energies, their electronic and vibrational signatures were quite distinctive, meaning that they could be used as fingerprint signals to distinguish between isomers. In addition, the electronic structures of these systems were explored using the phenomenological shell model. Calculations for the coinage metal clusters M₂₀ (M = Cu, Ag, Au) indicated that the structures and properties of the Ag cluster are similar to those of the Cu cluster in that both Cu₂₀ and Ag₂₀ prefer a compact structure whereas Au₂₀ prefers to adopt a tetrahedral form. Graphical abstract Shell Orbitals of Ag₈ Cluster.

Evolution of the Spin Magnetic Moments and Atomic Valence of Vanadium in VCux+, VAgx+, and VAux+ Clusters (x = 3-14)

The atomic structures, bonding characteristics, spin magnetic moments, and stability of VCu_x⁺, VAg_x⁺, and VAu_x⁺ (x = 3-14) clusters were examined using density functional theory. Our studies indicate that the effective valence of vanadium is size-dependent and that at small sizes some of the valence electrons of vanadium are localized on vanadium, while at larger sizes the 3d orbitals of the vanadium participate in metallic bonding eventually quenching the spin magnetic moment. The electronic stability of the clusters may be understood through a split-shell model that partitions the valence electrons in either a delocalized shell or localized on the vanadium atom. A molecular orbital analysis reveals that in planar clusters the delocalization of the 3d orbital of vanadium is enhanced when surrounded by gold due to enhanced 6s-5d hybridization. Once the clusters become three-dimensional, this hybridization is reduced, and copper most readily delocalizes the vanadium's valence electrons. By understanding these unique features, greater insight is offered into the role of a host material's electronic structure in determining the bonding characteristics and stability of localized spin magnetic moments in quantum confined systems.

First-principles calculations of the electronic structure and bonding in metal cluster-fullerene materials considered within the superatomic framework

Inspired by recent success of synthesizing cluster assembled compounds we address the question to what extent the three new materials [Co₆Se₈(PEt₃)₆][C₆₀]₂, [Cr₆Te₈(PEt₃)₆][C₆₀]₂, and [Ni₉Te₆(PEt₃)₈]C₆₀, upon forming bulk compounds, imitate atomic analogues. Although experimental results suggest the latter, a theoretical approach is the method of choice for offering a conclusive answer and for studying the actual superatomic character. The concept of superatoms for describing atom-imitating clusters is very intriguing since it allows chemists to apply their chemical intuition - a useful tool for predicting new materials - when it comes to inter-cluster reactions. Thus, we systematically study the lattice structure, the intercluster binding, and the electronic structure by density functional theory and assess them in terms of their superatomic features. We show that collective properties arise upon bulk formation, which promotes arguments for the formation of solids in which the constituent clusters have a superatomic character that determines some form of chemical bonding. Additionally, we find evidence for the formation of superatomic states. Unfortunately, however, due to the mixing of electronic states of transition metals and chalcogen atoms, no typical electronic shell closing in the cluster cores can be identified.

Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots

We consider a droplet of electrons confined within an external harmonic potential well of elliptical or ellipsoidal shape, a geometry commonly encountered in work with semiconductor quantum dots and other nanoscale or mesoscale structures. For droplet sizes exceeding the effective Bohr radius, the dominant contribution to average system parameters in the Thomas-Fermi approximation comes from the potential energy terms, which allows us to derive expressions describing the electron droplet's shape and dimensions, its density, total and capacitive energy, and chemical potential. The analytical results are in very good agreement with experimental data and numerical calculations, and make it possible to follow the dependence of the properties of the system on its parameters (the total number of electrons, the axial ratios and curvatures of the confinement potential, and the dielectric constant of the material). An interesting feature is that the eccentricity of the electron droplet is not the same as that of its confining potential well.

From isosuperatoms to isosupermolecules: new concepts in cluster science

As an extension of the superatom concept, a new concept "isosuperatom" is proposed, reflecting the physical phenomenon that a superatom cluster can take multiple geometrical structures with their electronic structures topologically invariant. The icosahedral and cuboctahedral Au13(5+) units in the Au25(SCH2CH2Ph)18(-), Au23(SC6H11)16(-) and Au24(SAdm)16 nanoclusters are found to be examples of this concept. Furthermore, two isosuperatoms can combine to form a supermolecule. For example, the structure of the {Ag32(DPPE)5(SC6H4CF3)24}(2-) nanocluster can be understood well in terms of a Ag22(12+) supermolecule formed by two Ag13(8+) isosuperatoms. On the next level of complexity, various combinations of isosuperatoms can lead to supermolecules with different geometrical structures but similar electronic structures, i.e., "isosupermolecules". We take two synthesized nanoclusters Au20(PPhpy2)10Cl4(2+) and Au30S(StBu)18 to illustrate two Au20(6+) isosupermolecules. The proposed concepts of isosuperatom and isosupermolecule significantly enrich the superatom concept, give a new framework for understanding a wide range of nanoclusters, and open a new door for designing assembled materials.

Electronic structure of the boron fullerene B14 and its silicon derivatives B13Si(+), B13Si(-) and B12Si2: a rationalization using a cylinder model

Geometric and electronic structures of the boron cluster B14 and its silicon derivatives B13Si(+), B13Si(-), and B12Si2 were determined using DFT calculations (TPSSh/6-311+G(d)). The B12Si2 fullerene, which is formed by substituting two B atoms at two apex positions of the B14 fullerene by two Si atoms, was also found as the global minimum structure. We demonstrated that the electronic structure and orbital configuration of these small fullerenes can be predicted by the wavefunctions of a particle on a cylinder. The early appearance of high angular node MOs in B14 and B12Si2 can be understood by this simple model. Replacement of one B atom at a top position of B14 by one Si atom, followed by the addition or removal of one electron does not lead to a global minimum fullerene structure for the anion B13Si(-) and cation B13Si(+). The early appearance of the 5σ1 orbital in B13Si(+) causes a lower stability for the fullerene-type structure.