From isosuperatoms to isosupermolecules: new concepts in cluster science

Doping-mediated excited state dynamics of diphosphine-protected M@Au12 (M = Au, Ir) superatom nanoclusters

Doping heterometal atoms into ligand-protected gold superatom nanoclusters (Aun NCs) is proposed to further diversify their geometrical and electronic structures and enhance their photoluminescence properties, which is attributed to the mixing and effects between atoms. However, the fundamental principles that govern the optoelectronic properties of the doped Aun NCs remain elusive. Herein, we systematically explored two prototypical 8-electron Aun (n = 11 and 13) NCs with and without Ir dopant atoms using comprehensive ab initio calculations and real-time nonadiabatic molecular dynamics simulations. These doped Aun NCs maintain their parent geometrical structures and 8-electron superatomic configuration (1S21P6). Strong core-shell (Ir-Aun) electronic coupling significantly expands the energy gap, resulting in a weak nonadiabatic coupling matrix element, which in turn increases the carrier lifetime. This increase is mainly governed by the low-frequency vibration mode. We uncovered the relationship between electronic structures, electron-vibration, and carrier dynamics for these doped Aun NCs. These calculated results provide crucial insights for the atomically precise design of metal NCs with superior optoelectronic properties.

Dual External Field Strategy in Regulating the Superhalogen Characteristics of the Non-Noble Metal Constituted Tantalum Oxide Clusters

The identification of the non-noble metal constituted TaO cluster as a potential analogue to the noble metal Au is significant for the development of tailored materials. It leverages the superatom concept to engineer properties with precision. However, the impact of incrementally integrating TaO units on the electronic configurations and properties within larger TaO-based clusters remains to be elucidated. By employing the density functional theory calculations, the global minima and low-lying isomers of the TanOn (n = 2-5) clusters were determined, and their structural evolution was disclosed. In the cluster series, Ta5O5 was found to possess the highest electron affinity (EA) with a value of 2.14 eV, based on which a dual external field (DEF) strategy was applied to regulate the electronic property of the cluster. Initially, the electron-withdrawing CO ligand was affixed to Ta5O5, followed by the application of an oriented external electric field (OEEF). The CO ligation was found to be able to enhance the Ta5O5 cluster's electron capture capability by adjusting its electron energy levels, with the EA of Ta5O5(CO)4 peaking at 2.58 eV. Subsequently, the introduction of OEEF further elevated the EA of the CO-ligated cluster. Notably, OEEF, when applied along the +x axis, was observed to sharply increase the EA to 3.26 eV, meeting the criteria for superhalogens. The enhancement of EA in response to OEEF intensity can be quantified as a functional relationship. This finding highlights the advantage of OEEF over conventional methods, demonstrating its capacity for precise and continuous modulation of cluster EAs. Consequently, this research has adeptly transformed tantalum oxide clusters into superhalogen structures, underscoring the effectiveness of the DEF strategy in augmenting cluster EAs and its promise as a viable tool for the creation of superhalogens.

Synthesis of N2-Type Superatomic Molecules

Exploration of multiple bonds between superatoms remains an uncharted territory. In this study, we present the synthesis and characterization of N2-type superatomic molecules featuring triple bonds between two superatoms. The successful synthesis of M2Au17 (M = Pd, Pt) nanoclusters hinged upon the photoinduced fusion of MAu12 superatoms, achieved through sequential electron transfer and detachment of [AuPR3]+ species. Solid-state structures were confirmed via X-ray crystallography, while their electronic structures were elucidated through density functional theory (DFT) calculations. Analysis of electronic absorption properties, coupled with time-dependent DFT calculations, unveiled a symmetry-dependent electron transition nature between superatomic molecular orbitals, akin to that observed in conventional molecules.

Intermediate Intercluster Bond Orders. Electronic Communication in Au38(SR)24 Superatomic Molecules

Ligand-protected gold clusters remain potential building blocks for envisaged molecular materials. The archetypal Au38(SR)24 cluster can be viewed as a robust template for the fusion of two Au25(SR)18 - cluster units, retaining a bi-icosahedral Au23 core. Via electrochemical properties, the overall charge state can be selectively tuned, enabling the access of 14 valence electron (ve) species featuring a single intercluster bond and nearby charge from -1 to +3, achieving related species bearing 15- to 11-ve with variable intercluster bond orders. Here, we explore the characteristics of intermediate intercluster bond orders in order to provide insights into the plausible electron communication between the constituent building blocks, with Au38(SR)24, as a representative template. Our results denote a small structural variation along -1 to +3 charge states, provided by the core-protecting ligand interaction, which is enhanced towards more oxidized species. The remaining unpaired electron from intermediate intercluster bond orders of 1.5 for Au38(SR)24 1-, 1.5 for Au38(SR)24 1+, and 2.5 for Au38(SR)24 3+, holds delocalized characteristics between the building block units, favoring electron communication for conductive and cooperative cluster aggregates. Such features are relevant for the formation of molecular electronic device applications, favoring the rationalization prior to engaging in explorative synthesis of larger ligand-protected cluster aggregates.

Chiroptical Activity Amplification of Chiral Metal Nanoclusters via Surface/Interface Solidification

It remains a grand challenge to amplify the chiroptical activity of chiral metal nanoclusters (NCs) although it is desirable for fundamental research and practical application. Herein, we report a strategy of surface/interface solidification (SIS) for enhancing the chiroptical activity of gold NCs. Structural analysis of [Au19(2R,4R/2S,4S-BDPP)6Cl2]3+ (BDPP is 2,4-bis(diphenylphosphino)pentane) clusters reveals that one of the interfacial gold atoms is flexible between two sites and large space is present on the surface, thus hampering chirality transfer from surface chiral ligands to metal core and leading to low chiroptical activity. Following SIS by filling the flexible sites and replacing chlorides with thiolate ligands affords another pair of [Au20(2R,4R/2S,4S-BDPP)6(4-F-C6H4S)2]4+, which shows a more compact and organized structure and thus an almost 40-fold enhancement of chiroptical activity. This work not only provides an efficient approach for amplifying the chiroptical activity of metal nanoclusters but also highlights the significance of achiral components in shaping chiral nanostructures.

Superatomic Aromaticity in Cyclic Superatomic Molecules: Ligand-Protected Penta-Icosahedral [M@Au11]5 (M = Au, Pt) Clusters

Pure or doped gold icosahedra, which can be generally viewed as superatoms, are promising candidates for cluster-assembled structures. As the first large-scale ring-like gold cluster, the report of [Au60Se2(Ph3P)10(SeR)15]+ has arisen much interest, where its Au60 core is composed of five vertex-sharing gold icosahedra in a cyclic way. From electronic characters, this Au60 core is a 40e cyclic penta-superatom network formed by five 8e closed-shell superatoms (S2P6). When more valence electrons are introduced into the penta-superatom network by atomic doping, global delocalized bonds are induced in its bonding framework. In the 42e Au60 core of the [Au60Se2Cl15]- cluster, two extra electrons occupy one delocalized π-bonding orbital formed by super D orbitals of five superatoms, resulting in superatomic π aromaticity. In the 46e [Pt@Au11]5 core of [(Pt@Au11)5Ga2Cl15] cluster, three delocalized super-π bonds are formed, which are organized in the similar way as the aromatic C5H5- molecule. The unveiling of superatomic aromaticity promotes our understanding of the stability of cyclic superatom assemblies and extends the family of superatomic bonding patterns.

Staggered Assembly of a Dimeric Au13 Cluster: Impacts on Coupling of Geometric Isomerism

The specific states of aggregation of metal atoms in sub-nanometer-sized gold clusters are related to the different quantum confinement volumes of electrons, leading to novel optical and electronic properties. These volumes can be tuned by changing the relative positions of the gold atoms to generate isomers. Studying the isomeric gold core and the electron coupling between the basic units is fundamentally important for nanoelectronic devices and luminescence; however, appropriate cases are lacking. In this study, the structure of the first staggered di-superatomic Au25 -S was solved using single-crystal X-ray diffraction. The optical properties of Au25 -S were studied by comparing with eclipsed Au25 -E. From Au25 -E to Au25 -S, changes in the electronic structures occurred, resulting in significantly different optical absorptions originating from the coupling between the two Au13 modules. Au25 -S shows a longer electron decay lifetime of 307.7 ps before populating the lowest triplet emissive state, compared to 1.29 ps for Au25 -E. The experimental and theoretical results show that variations in the geometric isomerism lead to distinct photophysical processes owing to isomerism-dependent electronic coupling. This study offers new insights into the connection between the geometric isomerism of nanosized building blocks and the optical properties of their assemblies, opening new possibilities for constructing function-specific nanomaterials.

Ligand-free supermolecules: [Pd2@Ge18]4- and [Pd2@Sn18]4- as multiple-bonded Zintl-ion clusters based on Pd@Ge9 and Pd@Sn9 assembled units

Understanding intercluster bonding interactions is important in the rational synthesis of building blocks for molecular materials. Such characteristics have been developed for coinage metal clusters resembling single-, double-, and triple-bonded species, coined as supermolecules. Herein, we extend such an approach for understanding main-group clusters, thus evaluating [Pd2@E18]4- clusters (E = Ge, Sn) involving the fusion of parent spherical aromatic [Pd@E12]2- building units. Our results indicate intercluster bonding provided by contribution from 2P and 1G shells centered at each building motif, leading to an overall bond order of 2.70 and 2.31 for [Pd2@Ge18]4- and [Pd2@Sn18]4-, respectively. In addition, 119Sn-NMR patterns were evaluated to complement the experimental characterization of a single peak owing to the insolution fluxional behavior of [Pd2@Sn18]4- as three peaks owing to the three sets of unique Sn atoms within the structure. Magnetic response properties revealed that spherical aromatic characteristics from parent [Pd@E12]2- building units are retained in the overall [Pd2@E18]4- oblate cluster as two spherical aromatic units. Hence, the notion of superatomic molecules is extended to Zintl-ion clusters, favoring further rationalization for the fabrication of cluster-assembled solids.

Second-order superatoms: Au52-PAP featuring a three-dimensional cluster-of-clusters core

The recent characterization of Au52-PAP cluster can be viewed as a three-dimensional arrangement featuring four Au13 motifs. As a result, a new set of superatomic orbitals are built up from the superatomic shell of each constituent unit, denoted by 1S'21P'62S'21D'102P'61F'6 and, thus, referred to as a second-order superatomic shell structure. This favors the rationalization of larger species toward the formation of cluster-assembled materials of different sizes.

Electron delocalization of robust high-nuclear bismuth-oxo clusters for promoted CO2 electroreduction

The integration of high activity, selectivity and stability in one electrocatalyst is highly desirable for electrochemical CO2 reduction (ECR), yet it is still a knotty issue. The unique electronic properties of high-nuclear clusters may bring about extraordinary catalytic performance; however, construction of a high-nuclear structure for ECR remains a challenging task. In this work, a family of calix[8]arene-protected bismuth-oxo clusters (BiOCs), including Bi4 (BiOC-1/2), Bi8Al (BiOC-3), Bi20 (BiOC-4), Bi24 (BiOC-5) and Bi40Mo2 (BiOC-6), were prepared and used as robust and efficient ECR catalysts. The Bi40Mo2 cluster in BiOC-6 is the largest metal-oxo cluster encapsulated by calix[8]arenes. As an electrocatalyst, BiOC-5 exhibited outstanding electrochemical stability and 97% Faraday efficiency for formate production at a low potential of -0.95 V vs. RHE, together with a high turnover frequency of up to 405.7 h-1. Theoretical calculations reveal that large-scale electron delocalization of BiOCs is achieved, which promotes structural stability and effectively decreases the energy barrier of rate-determining *OCHO generation. This work provides a new perspective for the design of stable high-nuclear clusters for efficient electrocatalytic CO2 conversion.

Self-isomerization of nearly planar superatoms formed by actinide embedded gold clusters

First-principles calculations show a self-isomerization process of the nearly planar superatom, in which the maximum energy difference between different extreme points is below 0.1 eV and a crossing between singlet and triplet states is also involved. Further UV-Vis spectra reveal a correlation between the spectra and structures caused by self-isomerization.

Fabricating sub-nanometer materials through cluster assembly

The self-assembly of clusters provides a feasible approach for the bottom-up fabrication of functional materials with tailored properties. Sub-nanometer cluster assembly with a well-defined construction presents a precisely controllable structure and extraordinary properties, which provides an ideal model for the investigation of structures and properties at the molecular level. Non-covalent interactions between clusters may dominate the assembly behavior, appearing as tunable structures different from their nano-counterparts. Interactions between clusters and their superatom orbitals can significantly influence the electronic structures, because of which exceptional properties may emerge. In this paper, recent progress on cluster-based assemblies is introduced, including sub-nanometer building blocks of noble metal and polyoxometalate (POM) clusters. The structures, formation mechanism and properties of these cluster assemblies are discussed from experimental and theoretical aspects. This perspective aims to provide a new insight into the design and manufacture of sub-nanometer materials based on clusters.

Visible Light Induced Ag-Polyoxometalate Coassembly into Single-Cluster Nanowires

1D superlattices with long-ranged periodicity present extraordinary application properties due to their unique electronic structures. Here, the visible light driven synthesis of 1D single-cluster chains constructed by polyoxometalate (POM) and Ag clusters is reported, where two types of clusters align alternatively along the nanowire. Low symmetrical POM clusters of [P₂ W₁₇ O₆₁ ]^10- , [P₂ W₁₅ O₅₆ ]^12- , and [EuW₁₀ O₃₆ ]^9- can be used as building blocks. The directly bonding cluster units result in interactive electronic structures of Ag and POM clusters, as well as the greatly promoted electron transfer during the redox reaction. The Ag-P₂ W₁₇ nanowires perform significantly enhanced activities in both electrochemical sensing and catalytic gasoline desulfurization compared with individual building blocks, demonstrating the extraordinary application properties and promising potentials of cluster-based heteroconstructions.

Self-assembly of polyoxometalate clusters into two-dimensional clusterphene structures featuring hexagonal pores

Two-dimensional (2D) structures have been shown to possess interesting and potentially useful properties. Because of their isotropic structure, however, clusters tend to assemble into 3D architectures. Here we report the assembly of polyoxometalate clusters into layered structures that feature uniform hexagonal pores and in-plane electron delocalization properties. Because these structures are 2D and visually reminiscent of graphene, they are referred to as 'clusterphenes'. A series of multilayer and monolayer clusterphenes have been constructed with 13 types of polyoxometalate cluster. The resulting clusterphenes were shown to exhibit substantially improved stability and catalytic efficiency towards olefin epoxidation reactions, with a turnover frequency of 4.16 h^-1, which is 76.5 times that of the unassembled clusters. The catalytic activity of the clusterphenes derives from the electron delocalization between identical clusters within the 2D layer, which efficiently reduces the activation energy of the catalytic reaction.

Controlling the Chemistry of Nanoclusters: From Atomic Precision to Controlled Assembly

Metal nanoclusters have gained prominence in nanomaterials sciences, owing to their atomic precision, structural regularity, and unique chemical composition. Additionally, the ligands stabilizing the clusters provide great opportunities for linking the clusters in higher order dimensions, eventually leading to the formation of a repertoire of nanoarchitectures. This makes the chemistry of atomic clusters worth exploring. In this mini review, we aim to focus on the chemistry of nanoclusters. Firstly, we summarize the important strategies developed so far for the synthesis of atomic clusters. For each synthetic strategy, we highlight the chemistry governing the formation of nanoclusters. Next, we discuss the key techniques in the purification and separation of nanoclusters, as the chemical purity of clusters is deemed important for their further chemical processing. Thereafter which we provide an account of the chemical reactions of nanoclusters. Then, we summarize the chemical routes to the spatial organization of atomic clusters, highlighting the importance of assembly formation from an application point of view. Finally, we raise some fundamentally important questions with regard to the chemistry of atomic clusters, which, if addressed, may broaden the scope of research pertaining to atomic clusters.

Electron counting and bonding patterns in assemblies of three and more silver-rich superatoms

DFT calculations were carried out on a series of cluster cores, the framework of which was made of the condensation of several Pt@Ag12-centered icosahedra. Icosahedral condensations through vertex-sharing, face-sharing, and interpenetration were considered and their favored electron counts were determined from their stable closed-shell configurations. A large number of the computed assemblies of n icosahedral superatomic units can be considered as isolobal analogs of stable, closed-shell n-atom molecules, most of them obeying the octet rule. The larger the degree of fusion between icosahedra, the stronger the interaction between them. For example, it was possible to design 3-icosahedral supermolecular cores analogous to CO2, SF2, or [I3]-, but also to the not-yet-isolated cyclic O3. Supermolecules equivalent to non-stable molecules can also be designed. Indeed, differences exist between atoms and superatoms, and original icosahedra assemblies with no "molecular" analogs are also likely to exist, especially with compact structures and/or systems made of a large number of fused superatoms.

Triple 1D[triple bond, length as m-dash]1D superatomic bonding. Au22(dppo)6 as a Π4- and Δ2-triply bonded cluster based on Au11 assembled units

δ-Bonds have been intimately related to metal-metal bonds of d-elements since the archetypal d⁴-d⁴ [Re₂Cl₈]^2- ion with a σ²π⁴δ² bond. Currently, the notion of multiple superatom arrangements as initial steps toward molecular materials within the building-up approach is dominated by P-shell characteristics, as given in the well-described Au₂₅(SR)₁₈ ligand protected cluster. In this work we rationalize the Au₂₂(dppo)₆ cluster as a triple-bonded 22-valence electron (ve) supermolecule, featuring a bonding scheme based on 1D + 1D shell combinations, which largely contrasts with the 14-ve Au₃₈(SR)₂₄ with mainly 1P + 1P patterns mimicking a F₂ molecule. The resulting Π⁴Δ²-bonding pattern shows an unprecedented superatomic counterpart of a d-shell based bond inherently related to transition-metal dimers, adding useful key aspects to the understanding of species based on cluster-assembly.

Polymeric tungsten carbide nanoclusters: structural evolution, ligand modulation, and assembled nanomaterials

Seeking novel superatoms with tunable electronic and magnetic properties has attracted much interest due to their potential application in cluster assembly nanomaterials. By employing density functional theory (DFT) calculations, the recently observed superatomic WC cluster was adopted as the basic unit to construct larger polymeric clusters, namely (WC)_n (n = 2-7), and their structural evolution was explored to understand the growth pattern of these superatomic clusters into nanoscale materials. An unusual odd-even pattern in structural evolution was disclosed, in which the (WC)₂ unit is considered as the basic building block. Moreover, W₄C₄ is found to possess a cubic structure, based on which the CO and PH₃ ligands were attached to examine their ligation effects on W₄C₄. Theoretical results show that the electronic properties of W₄C₄ can be dramatically altered during the ligation process. Intriguingly, the continuous attachment of CO and PH₃ ligands strongly increases and decreases the electron affinities (EA) and ionization potentials (IP) of the ligated W₄C₄ clusters, respectively, leading to the formation of superhalogen and superalkali species with high magnetic moments. The observed ligand induced strategy highlighted here could serve as an effective way to tune the electronic and magnetic properties of clusters resulting in the formation of novel superatoms. Finally, studies on the geometrical and electronic structures of the W₄C₄ cluster solid unveil its special 3-D cubic honeycomb geometry and metallic properties with predominant contribution from the 5d of W, which may have potential applications in electro-catalysis.

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.

Face-Sharing Homo- and Hetero-Bitetrahexahedral Superatomic Molecules M1M2@Li20 (M1/M2 = Ti and W)

Superatoms, being a class of clusters with chemical behavior similar to atoms, can be used as building blocks for constructing novel functional materials. Here, superatomic molecules M₁M₂@Li₂₀ (M₁/M₂ = Ti and W) are built with our recently discovered tetrahexahedral superatoms Ti@Li₁₄ and W@Li₁₄. A low-energy face-sharing bi-tetrahexahedral structure with a high symmetry of D_{6 h} is identified by global minimum structure search and frequency calculations. The number of shared Li atoms amounts to 6, which is rarely seen before. Molecular orbital and chemical bonding analyses reveal that although isolated superatoms Ti@Li₁₄ and W@Li₁₄ are nonmagnetic, Ti₂@Li₂₀ is an open-shell superatomic molecule with a magnetic moment of 2 μ_B, whereas for W₂@Li₂₀, the electronic shell remains closed. In both Ti₂@Li₂₀ and W₂@Li₂₀, a quadruple superbonding between superatoms is found. Interestingly, an assembly of two hetero-tetrahexahedral superatoms Ti@Li₁₄ and W@Li₁₄ also gives a face-sharing bi-tetrahexahedral structure but with a notable dipole moment. This study provides a basic understanding for the superatomic bonding of Ti@Li₁₄ and W@Li₁₄, which may aid their application in developing multi-superatom molecules or even bulk crystals.

Single, double, and triple intercluster bonds: analyses of M2Au36(SR)24 (M = Au, Pd, Pt) as 14-, 12- and 10-ve superatomic molecules

Single, double, and triple-bonds can be found in fused superatomic clusters.

Evidence for the Superatom-Superatom Bonding from Bond Energies

Metal clusters with specific number of valence electrons are described as superatoms. Super valence bond (SVB) model points out that superatoms could form the superatomic molecules through SVBs by sharing nucleus and electrons. The existence of superatom-superatom bonding was verified by the shape of their orbitals in former studies. In this paper, another important evidence-bond energy is studied as the criterion for the SVBs using the density functional theory method. In order to get the reliable values of bond energies, the series of Zn-Cu and Mg-Li superatomic molecules composed of two tetrahedral superatoms which do not share their nucleus are designed. Considering the number of the valence electrons in one tetrahedral superatomic unit, (Zn₄)₂/(Mg₄)₂, (Zn₃Cu)₂/(Mg₃Li)₂, (Zn₂Cu₂)₂/(Mg₂Li₂)₂, and (ZnCu₃)₂/(MgLi₃)₂ clusters are 8e-8e, 7e-7e, 6e-6e, and 5e-5e binary superatomic molecules with super nonbond, single bond, double bond, and triple bond, respectively, which are verified by chemical bonding analysis depending on the SVB model. Further calculations reveal that the bond energies increase and the bond lengths decrease along with the bond orders in Zn-Cu and Mg-Li systems which is in accordance with the classical nonbond, single bond, double bond, and triple bond in C-H systems. Thus, these values of bond energies confirm the existence of the SVBs. Moreover, electron localization function analysis is also carried on to describe the similarity between the superatomic bonds and atomic bonds in simple molecules directly. This study reveals the new evidence for the existence of the superatom-superatom bonding depending on the bond energies, which gives the new insight for the further investigation of the superatomic clusters.

New insights into the stability and structural evolution of some gold nanoclusters

Revealing the stability and structural patterns is important for precisely synthesizing or assembling ligand protected nanoclusters, and even their applications as functional nanomaterials. Investigations on structural evolutional patterns and structural stability are very challenging, because structures change with the nanocluster size and the structural stability depends on both the electron structures of cores and ligand type. Herein, we propose a hybrid superatom network (hSAN) model to understand the stability of some gold nanoclusters with different kinds of ligands. In this model, 4c-2e superatom Au₄ can form conjugated superatom networks by vertex sharing, and ligands further connect the conjugated superatom networks together to form a bigger complex network, i.e. a hSAN. The stability of the clusters, including [Au₂₄(C[triple bond, length as m-dash]CPh)₁₄(PPh₃)₄]²⁺, Au₂₈(S-c-C₆H₁₁)₂₀, Au₃₆(SCH₂Ph-tBu)₈Cl₂₀, Au₄₀(O-MBT)₂₄ and Au₅₂(TBBT)₃₂ can be explained uniformly by the hSAN model. Beyond that, a new heuristic structural pattern named the Au₁₃ topological rule is proposed. In the light of this heuristic rule, every Au₇ bi-tetrahedral kernel is included in an Au₁₃ structure with quasi-O_h symmetry, i.e. as long as the Au₇ bi-tetrahedral kernel is formed, it will be surrounded by six Au atoms to form an Au₁₃ structure topologically. According to this understanding, a new nanocluster [Au₄₄(C[triple bond, length as m-dash]CH₃)₂₆(PCH₃)₄]²⁺ and a new nanowire with the structural evolutional formula [Au_(20n+4)(C[triple bond, length as m-dash]CH₃)_(12n+2)(PCH₃)₄]²⁺ (n = 1, 2, 3, 4, …) are predicted. Both the understanding of the stability and the structure rule are free from the type of ligand, and will be useful for the structural predictions and determinations of ligand protected gold nanoclusters.

The nature of the multicenter bonding in π-[TCNE]22− dimer: 4c/2e, 12c/2e, or 20c/2e?

Composition of the 20c–2e bonding orbital in the π-[TCNE]₂²⁻ dimer, and the partial occupancy numbers C1, C2 and N in the 20c–2e bond.