Recent advances in atomic cluster synthesis: a perspective from chemical elements

Abstract

Despite its potential significance, “cluster chemistry” remains a somewhat marginalized topic within the chemistry field. However, atomic clusters with their unusual and unique structures and properties represent a novel material group situated between molecules and nanoparticles or solid matter, judging from both scientific standpoints and historical backgrounds. Surveying an entire material group, including all substances that can be regarded as a cluster, is essential for establishing cluster chemistry as a more prominent chemistry field. This review aims to provide a comprehensive understanding by categorizing, summarizing, and reviewing clusters, focusing on their constituent elements in the periodic table. However, because numerous disparate synthetic processes have been individually developed to date, their straightforward and uniform classification is a challenging task. As such, comprehensively reviewing this field from a chemical composition viewpoint presents significant obstacles. It should be therefore noted that despite adopting a synthetic method-based classification in this review, the discussions presented herein could entail inaccuracies. Nevertheless, this unorthodox viewpoint unfolds a new scientific perspective which accentuates the common ground between different development processes by emphasizing the lack of a definitive border between their synthetic methods and material groups, thus opening new avenues for cementing cluster chemistry as an attractive chemistry field.

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Takamasa Tsukamoto

Takamasa Tsukamoto received his PhD degree in Eng. from Tokyo Metropolitan University in 2015. After being a research fellow of the Japan Society for the Promotion of Science (2014–2016), a visiting researcher at the University of Miami (2014), a doctoral research fellow at the University of Tokyo (2015–2016), and a postdoctoral researcher and an assistant professor at the Tokyo Institute of Technology (2016–2023), he joined the Institute of Industrial Science at the University of Tokyo as a lecturer (2023) and the Japan Science and Technology Agency as a PRESTO researcher (2020–2023). His current research interests include developing organic–inorganic hybrid compounds for cluster synthesis, theoretical studies on clusters involving superatoms, the interpretation of the super-degeneracy phenomenon, and proposing a higher-order periodic table of superatoms.

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1. Introduction

Atomic clusters comprising a few, a few dozen, or hundred atoms, with particle diameters of typically ∼1 nm and reaching up to ∼3 nm fall under an ultrasmall particulate material group (Fig. 1).

Fig. 1 Classification of materials based on the size scale.

Compared to conventional nanoparticles (5–500 nm), their atypical smallness exhibits certain eccentric properties not found in nanoparticles, originating from the remarkable quantum size effect. Regarding general nanoparticles, physical properties and chemical reactivities are determined by their surface structures and geometrical shapes.^1–3 On the other hand, their electronic states of clusters resemble more closely those of molecules than bulk materials (including nanoparticles), leading to their unique characteristics.^4–8 Such clusters contribute to the manifestation of highly efficient and sophisticated biological functions in nature, such as water oxidation in photosynthesis, electron transfer, nitrogen fixation, and breathing.^9–13 Moreover, clusters possess various structural characteristics that are not observed in other chemicals, including the number of constituent atoms, types of constituent elements, elemental ratios, atomic arrangements, and geometrical symmetry. Such a feature affords a great degree of freedom in terms of material design. Furthermore, their steric and electronic structures on a molecular scale offer significant potential for achieving novel properties and functions. Therefore, this sub-nanometer material group has attracted worldwide attention as a candidate for next-generation post-nanotechnology materials.

However, the desired progress in the cluster chemistry field has been hindered by the inherent challenges entailed in synthesizing clusters, as compared to nanoparticles. This issue originates from the critical factors differentiating the properties of nanoparticles and clusters. Particularly, in contrast to nanoparticles, the structures, properties, and stabilities of clusters depend significantly on the number of constituent atoms. Since precise atom manipulation techniques (within 1 nm of the space in cluster particles) are necessary for the synthesis of clusters, applying conventional synthetic methods lacking atomic-level precision is unsuitable for forming such sub-nanosized materials. Therefore, developing new clustering techniques that are independent of these methods is essential. Atomic-level synthesis is significantly influenced by the nature of the constituent elements; however, in many cases, the types of elements that can be treated using a single method tend to be limited. By considering this aspect, synthetic methods dedicated to certain elements or elemental groups have been established, with the regions of the corresponding elements distributed on the periodic table like islands (Fig. 2). Notable developments in cluster chemistry have been achieved using these methods as starting points.

Fig. 2 A rough sketch of a map for the classification of suitable methods for atomic cluster synthesis depending on the chemical element composition.

As noted above, synthetic methods for clusters, unlike those for nanoparticles, tend to be inflexible in terms of element selectivity and applicability, despite their high efficacy for a certain region in the periodic table. This limitation has hindered cross-cutting discussions focusing on constituent elements in the topic of cluster synthesis. In this review, with the aim of providing a comprehensive discussion and understanding of the entire field of cluster synthesis, we categorize, summarize, and review these methods by focusing on the constituent elements of clusters in the periodic table.

2. Methods for cluster synthesis

Metal carbonyl clusters composed of single or multiple transition metal elements and carbonyl ligands represent one of the most well-established material groups among chemical clusters. They possess the most fundamental structures in coordination chemistry and serve as precursors in various chemistry fields, typified by organometallic chemistry.¹⁴ These clusters are synthesized by common chemical reactions and their reaction formulas are relatively simple. Moreover, borane clusters are also well synthesized mainly by the pyrolysis of diborane, and their atomicity and shape are classified as obeying the Wade–Mingos rule^15,16 or the Jemmis mno rule.¹⁷

However, in such cases, the degrees of freedom of design and synthesis are reduced and limited from the perspective of expanding the applicable elements. For example, in thermodynamically stable clusters obtained as metal carbonyls, the number of metal atoms, carbonyl ligands, and structures (hapticity) are uniquely determined by the electronic state of the transition metals. Therefore, the introduction of new factors that can be actively added or modified into the synthesis process of clusters is key for obtaining clusters composed of the desired number of atoms and element types. Based on this concept, various synthetic approaches using gas-, liquid-, and solid-phase reactions have been investigated.

3. Gas-phase synthesis

Fullerenes stand as the most well-known clusters synthesized in the gas-phase.^18–20 In an arc reactor or through laser vaporization in vacuum, fullerenes, typified by commercially available C₆₀, C₇₀, and C₈₄ are obtained from carbon sources as a mixture and subsequently separated and purified by chromatography.

Endohedral fullerenes in which other elements are constrained in their cages, such as [Li@C₆₀]⁺, can also be prepared using carbon mixed with metal sources.^21,22

Although gas-phase synthesis is also effective in the case of heavier metal elements,²³ metal clusters tend to easily undergo aggregation and particle enlargement after production, in contrast to lighter elements. Therefore, techniques for separating clusters from mixtures directly after synthesis are crucial. In particular, gas-phase reaction systems combined with mass-separation units are often employed, leading to numerous reports on metal clusters typified by Na_x.²⁴ This method not only effectively yields single elemental clusters such as superatomic [Al₁₃]⁻,²⁵ stannaspherene [Sn₁₂]²⁻,²⁶ borospherene [B₄₀]⁻,²⁷ and tetrahedral Au₂₀,²⁸ but also heteroelemental clusters such as M@Sn₁₂²⁶ and M@Si₁₆.²⁹ On the other hand, stable extraction of clusters produced from the gas phase has recently been investigated, including the soft-landing method, in which clusters are deposited intact on a self-assembled monolayer (SAM) of alkyl groups formed on a substrate.³⁰

As mentioned above, gas-phase preparation techniques offer the merit of involving the use of many elements, including both metal and nonmetal elements, but are fundamentally not conducive to mass production. Therefore, although these methods are significantly effective for analyzing physical properties, including electronic states, they are not suitable for investigations requiring large amounts of clusters, such as chemical reactivity. Additionally, because it is necessary to provide a positive or negative charge to clusters for mass separation, the properties of charged clusters are preferentially observed. The latter can be addressed by establishing a neutralization method for obtaining neutral clusters after mass separation.³¹

4. Liquid-phase synthesis

Various liquid-phase synthesis methods have been explored due to their practicality. The principal approaches for stabilizing clusters involve methods adopting ligand protection, employing polyoxometalate anions, and applying the Zintl phase. Each method targets specific regions of elements in the periodic table, leading to differences in the properties of the obtained clusters. These disparities often arise from variations in the chemical states of the clusters’ surface or interior. Therefore, given the present circumstances, a suitable synthetic method should be carefully selected that not only considers the employed elements, but that can also induce the desired properties.

4.1. Clusters stabilized by ligand protection

In this method, the clusters are chemically stabilized by the steric and electronic protection effect of the organic ligands, which cover their surface atoms with functional groups. Applicable metal elements vary depending on the functional groups of the ligands. Negatively charged alkylthiolate-type (SR⁻) ligands typically used for group 11 element clusters (Au, Ag, Cu) are among the most well-investigated representatives of this method.^32–36 Alkyl selenide-type analog structures (SeR⁻) have also been reported.³⁷ The steric structure of ligands modifies the number of constituent atoms and their geometric arrangements, which are often based on highly symmetric core structures.³⁸ In this regard, Au₁₀₂(SR)₄₄,³⁹ Au₁₄₄(SR)₆₀,^40,41 [Ag₁₈₀(SR)₉₀(CH₃SO₃)₄₄]⁴⁶⁺,⁴² and Ag₃₇₄(SR)₁₁₃Br₂Cl₂⁴³ stand as the largest well-known clusters with numerous constituent atoms (Fig. 3A). Recent reports have revealed that this method is also applicable to the synthesis of alloy clusters composed of group 11 elements, such as [Au₁₂Ag₃₂(SR)₃₀]⁴⁻ (ref. 44) (Fig. 3B), despite the composition and arrangement of multiple elements in these clusters tending to be uncontrollable because of the preferential generation of energetically stable clusters. Additionally, an alloying method for doping with other metal elements has been developed by utilizing the stability of ligand-protected Au or Ag clusters.⁴⁵ This approach enables the use of metals that do not achieve ligand stabilization, such as [M@Au₂₅(SR)₁₈]⁻ (M = Pd, Pt, Cd, Hg)⁴⁶ and Pd@Ag₂₀(S₂PR₂)₁₂ ⁴⁷ (S₂P(OR)₂⁻ = dialkoxyldithiophosphinate). A recently reported anion-templated synthesis method of such clusters (especially for Ag clusters) also provides various geometric structures containing non-metallic elements or anionic species (atomic anion: H⁻, D⁻, F⁻, Cl⁻, Br⁻, I⁻, S²⁻, Se²⁻, and Te²⁻; oxoanion: CO₃²⁻, C₂O₄²⁻, C₄O₄²⁻, C₅O₅²⁻, NO₃⁻, AsO₄³⁻, SO₃²⁻, SO₄²⁻, SeO₃²⁻, SeO₄²⁻, TeO₃²⁻, TeO₆⁶⁻, ClO₄⁻, VO₄³⁻, CrO₄²⁻, MoO₄²⁻, and WO₄²⁻; polyoxometalate anion: [V₁₀O₂₈]⁶⁻, [Mo₆O₂₂]⁸⁻, [EuW₁₀O₃₆]⁹⁻, etc.) in the center of the structure,⁴⁸ such as [X@Ag₈(S₂P(OR)₂)₆]^+/0 (X = F, Cl, Br, S).^49,50 Other elements in group 11 have also been investigated, such as [Cl@Cu₁₄(S(CH₃)₂(CH₂NH₂))₁₂]⁷⁺.⁵¹ Thiolate-type ligands have also been used to stabilize metal sulfide clusters. For example, group 10 elements (Ni, Pd, Pt) form tiara-shaped cluster complexes, such as [M(SR)₂]_n (M = Ni, Pd, Pt)^52–54 (Fig. 3C), that often encapsulate guest metal ions or molecules in their ring centers (I₂, Ag⁺).^55,56 In the case of other group elements typified by Mn, Co, Zn, and Cd, a combination of monoanionic SR⁻ and dianionic S²⁻ provides sulfide clusters including tetrahedral [Mn₈Se(SePh)₁₆]²⁻,⁵⁷ octahedral [Co₈S₆(SPh)₈]⁴⁻,⁵⁸ tetrahedral [Zn₁₀S₄(SPh)₁₆]⁴⁻,⁵⁹ and [Cd₅₄S₃₂(SPh)₄₈(DMF)₄]⁴⁻ (ref. 60) (Fig. 3D).

Fig. 3 Crystal structures of: (A) Ag₃₇₄(SR)₁₁₃Br₂Cl₂ (R = 4-tert-butylphenyl),⁴³ Ag: gray, S: yellow, Cl: green, Br: brown, and C: grayish bone; (B) [Au₁₂Ag₃₂(SR)₃₀]⁴⁻ (R = 4-fluorophenyl),⁴⁴ Au: orange-yellow, Ag: gray, S: yellow, C: gray bone, and F: pale blue bone; (C) Ni₁₀(SR)₂₀ (R = 2-pyridylethyl),⁵² Ni: gray, S: yellow, C: grayish bone, and N: pale blue bone; (D) [Mn₈Se(SePh)₁₆]²⁻,⁵⁶ Mn: violet, Se: yellow-green, C: gray bone; (E) [Au₁₃(Ph₂PCH₂PPh₂)₆]⁵⁺,⁶⁶ Au: orange-yellow, P: grayish pink, and C: grayish bone; (F) [Pd₈(Ph₂P(CH₂PPh)₂CH₂PPh₂)₄]⁴⁺,⁷⁰ Pt: gray, P: grayish pink, C: grayish bone; and (G) [Be₄(NH₂)₆(NH₃)₄]²⁺,⁷⁵ Be: green, N: pale blue, and H: white. Figures are reproduced from (A) CCDC 1496141, (B) CCDC 953881, (C) CCDC 743607, (D) CCDC 612696, (E) CCDC 1577669, (F) CCDC 1023572, and (G) CCDC 1982295.

Among other functional groups used for ligand protection, various neutral, cationic, and anionic ligands have been investigated. Neutral ligands typically include monodentate or multidentate organophosphines (PR₃), amines (NR₃), and imines (NR(=R)). Analogs with heavier atoms, such as organostibines (SbR₃), have recently been reported.⁶¹ In the case of phosphines, clusters with group 11 elements, especially gold^62–65 (sometimes group 10 elements, such as Ni₃(PPh)(PPh₂)₂(PPh₃)₃⁶⁶), typified by commercially available [Au₃O(PPh₃)₃]⁺ and icosahedral [Au₁₃(Ph₂PCH₂PPh₂)₆]⁵⁺ (ref. 67) are principally explored in the same manner as alkylthiolate (Fig. 3E). In particular, precisely designed multidentate phosphine ligands provide and control unique arrangements of metal atoms in a cluster, such as icosahedron-based [Au₂₀(P(CH₂CH₂PPh₂)₃)]⁴⁺,⁶⁸ linear [Au₄(Ph₂P(CH₂PPh)₂CH₂PPh₂)₂]⁴⁺ (ref. 69) and linear [Pd₈(Ph₂P(CH₂PPh)₂CH₂PPh₂)₄]⁴⁺ with tetraphosphines⁷⁰ (Fig. 3F). Anion-templated synthesis is also used for clusters with phosphine ligands such as Cl@Ag₁₂@Ag₄₈(Ph₂PCH₂PPh₂)₁₂.⁷¹ Another example is transition-metal chalcogenide clusters with protective ligands, such as Co₆Te₈(PR₃)₆.⁷² The clusters were stabilized by amine or imine ligands: cubic Cu₄I₄(C₅H₅N)₄ with pyridine ligands,⁷³ rhombic [In₄(C₁₀H₈N₂)₆]⁴⁺ with bipyridyl ligands,⁷⁴ and [Be₄(NH₂)₆(NH₃)₄]²⁺ with ammonia ligands⁷⁵ (Fig. 3G).

Anionic ligands, including carboxylate (OCOR⁻), represent a well-known example, especially for clusters with low atomicity. Examples include dinuclear clusters such as M₂(OCOR)₄(L)₂ (where M = Cr, Mo, Rh, Cu, Bi)⁷⁶ and trinuclear clusters such as [M₃O(OCOR)₆(L)₃]⁺ (where M = V, Cr, Fe, Ru, Co, Rh, Ir).^77,78 Notably, such clusters are often commercially available. For the formation of these complex clusters, the oxidation number of the transition metal ions is an important factor; for example, dinuclear and trinuclear carboxylate clusters require metal ions with stable valences of +II and +III, respectively. In this regard, square-planar V₄(OCOCH₃)₄(OH)₄(H₂O)₈,⁷⁷ tetrahedral Zn₄O(OCOCH₃)₆, Zn₁₀O₄(OCOCH₃)₁₂⁷⁹ and In₃₇P₂₀(OCOCH₂Ph)₅₁ ⁸⁰ have been successfully reported. Alkoxides (OR⁻), amides (NR₂⁻), and methides (CR₃⁻) have also been used as simple protecting ligands. In particular, research has primarily focused on group 13 and 14 elements (Al, Ga, In, and Sn).⁸¹ Examples include [Al₇₇(N(SiMe₃)₂)₂₀]²⁻ (ref. 82) and Sn₁₅(NR₂)₆,⁸³ while transition metal elements with structures resembling oxides are often crucial for alkoxides, as seen in compounds like W₄(OR)₁₆.⁸⁴

Organometallic approaches are also effective in stabilizing clusters, with the formation of tetrahedral Li₄R₄ or octahedral Li₆R₆ clusters standing as a typical example.⁸⁵ In particular, cyclopentadienyl-type or pentamethylcyclopentadienyl-type ligands (C₅H₅⁻ or C₅Me₅⁻) have been extensively investigated for the stabilization of clusters composed of various elements. Typically, clusters of group 11, 12, and 13 elements (Cu, Zn, Al, Ga, and In) tend to have structures with large atomicity compared to transition metal elements (Co, Rh, Ir, etc.),⁸⁶ such as trigonal-bipyramidal Zn₉(C₅Me₅)₆ ⁸⁷ and tetrahedral Al₄(C₅Me₅)₄ ⁸⁸ (Fig. 4A). Alloy clusters have also been obtained using this method, such as trigonal-bipyramidal Cu₃Zn₄(C₅Me₅)₅,⁸⁹ with icosahedral Cu₄₃Al₁₂(C₅Me₅)₁₂ being one of the largest clusters reported to date⁹⁰ (Fig. 4B and C). Moreover, some transition metal halides, chalcogenides, and pnictogenides are also stabilized by cyclopentadienyl ligands like pseudo-tridecahedral La₉I₁₈(C₅Me₅)₉,⁹¹ trigonal-bipyramidal Rh₃Se₂(C₅EtMe₄)₉,⁹² and tetrahedral Cr₄P₄(C₅Me₅)₄ ⁹³ or Mn₄P₄(C₅H₅)₄ ⁹⁴ (Fig. 4D and E). Using this synthetic approach, model clusters mimicking the biochemical functions associated with nitrogen fixation were recently created (e.g., FeMo₃S₄(C₅H₄SiR₃)₃).⁹⁵ Additionally, the aromatic rings with large π-conjugated systems also serve as a planar protection ligand and often provide sophisticated highly-symmetric clusters such as cuboctahedral [Pd₁₃(C₇H₇)₆]²⁺ stabilized by cycloheptatrienylium (C₇H₇⁺)⁹⁶ and square-planar [Pd₄(C₈H₈)(C₉H₉)]⁺ stabilized by cyclooctatetraene (C₈H₈) and cyclononatetraenyl (C₉H₉⁻)⁹⁷ (Fig. 5A). Conversely, bridged aromatic ligands can effectively stabilize group 11 elements (Au, Ag, and Cu), yielding star-shaped clusters typified by pentagonal planar Au₅(C₆H₃Me₃)₅, Cu₅(C₆H₃Me₃)₅, and square-planar Ag₄(C₆H₃Me₃)₄ with mesityl anions (C₆H₂Me₃⁻)^98,99 (Fig. 5B). Additionally, tetramesityl diiron Fe₂(C₆H₃Me₃)₄ has also been reported, albeit not among group 11 elements.¹⁰⁰ Recently, by utilizing such bridged aromatic ligands, other atomic arrangements including alloys are obtained, like octahedral [Au₄Ag₂(C₆H₄PR₂)₄]²⁺.¹⁰¹ In contrast, aromatic ligands with bulky substituents also stabilize unique cluster structures by the steric protection effect, such as adamantane-shaped Al₄(PH)₆(2,6-C₆H₄(C₆Me₃H₂)₂)₄.¹⁰²

Fig. 4 Crystal structures of (A) Zn₉(C₅Me₅)₆.⁸⁷ (B) Cu₃Zn₄(C₅Me₅)₅,⁸⁹ (C) Cu₄₃Al₁₂(C₅Me₅)₁₂,⁹⁰ (D) La₉I₁₈(C₅Me₅)₉,⁹¹ and (E) Cr₄P₄(C₅Me₅)₄.⁹³ Zn: gray, Cu: blue, Al: light blue, La: green, I: violet, Cr: dark blue, P: grayish pink, and C: grayish bone. Figures are reproduced from (A) CCDC 1434844, (B) CCDC 1854852, (C) CCDC 1845365, (D) CCDC 1992039, and (E) CCDC 984791.

Fig. 5 Crystal structures of (A) [Pd₁₃(C₇H₇)₆]²⁺,⁹⁶ (B) Au₅(C₆H₃Me₃)₅,⁹⁸ (C) Pd₄(SiPh₂)₃((CH₂PMe₂)₂)₃,¹⁰³ (D) Ge₅Ph₁₀,¹⁰⁹ and (E) Ir₄Au₂(CO)₁₁(PPh₃)₂.¹¹⁸ Pd: gray, Au: orange-yellow, Si: blue-violet, P: grayish pink, Ge: grayish blue-violet, Ir: light green-yellow, C: gray bone, and O: red bone. Figures are reproduced from (A) CCDC 1813458, (B) CCDC 1119882, (C) CCDC 702935, (D) CCDC 1137518, and (E) CCDC 924993.

Other organometallic approaches for controlling the number and arrangement of metal atoms in clusters have also been developed. For example, organosilicon or organogermanium ligands containing Si and Ge as metalloid elements yield group 10 metal clusters with unusual geometric structures, such as hexagonal planar Pd₄(SiPh₂)₃((CH₂PH₂)₂)₃ and hexagonal-bipyramidal Pd₆(GePh₂)₂(CNC₆H₃Me₂)₁₀ ^103–106 (Fig. 5C). Otherwise, the organometallic ligands form clusters, such as cyclic (GeMes₂)₃, (GePh₂)₄, and (GePh₂)₅ with Ge–Ge bonds^107–109 (Fig. 5D). Organic or organosilicon ligands have also been employed to synthesize clusters comprising nonmetallic C and semimetallic Si. For example, employing a low-temperature photochemical process or a pure organometallic process in a solvent can yield tetrahedral structures such as C₄(CR₃)₄ ¹¹⁰ and Si₄(SiR₃)₄.¹¹¹

In other cases, methods for achieving both the stabilization and alloying of metal clusters using transition metal carbonyl complexes as ligands have been reported, such as octahedral [Ag₁₃Fe₈(CO)₃₂]⁴⁻ (ref. 112) and three pentagonal-antiprismatic [Sb₃Rh₂₀(CO)₃₆]³⁻ (ref. 113) complexes. It is worth mentioning that as a technique for clustering certain metals or mixing different metal elements in a cluster, the method using multiple ligands with different functional groups has been investigated, such as Fe₈(N[o-H₂NC₆H₄NH(CH₂)₂]₃)₂(PMe₂Ph)₂ with tetraamine and phosphine ligands,¹¹⁴ Ga₆(C₆Me₃H₂)₄(C₃N₂Me₂Pr₂)₂ with mesityl and tetraalkylimidazol-2-ylidene ligands,¹¹⁵ [Mg₁₆(C₅Me₅)₈(NEt₃)₂Br₄]²⁻ with cyclopentadienyl and amine ligands,¹¹⁶ Cu₁₀Zn₂(C₆Me₃H₂)₆(C₅Me₅)₂ with mesityl and cyclopentadienyl ligands,¹¹⁷ Ir₄Au₂(CO)₁₁(PPh₃)₂,¹¹⁸ Pt₁₃Au₄(CO)₁₀(PPh₃)₈,¹¹⁹ and Pd₁₄₅(CO)_x(PEt₃)₃₀ (x ≈ 60)¹²⁰ with carbonyl and phosphine ligands (Fig. 5E), and co-crystalized [(AuAg)₂₆₇(SPhMe₂)₈₀]·[(AuAg)₄₅(SPhMe₂)₂₇(PPh₃)₆] with thiolate and phosphine ligands.¹²¹ This approach has recently led to the development of model clusters for photosynthetic systems (Mn₃Ca clusters with carboxylate and pyridine ligands).¹²²

By surveying ligand protection methods, we can broadly summarize the tendencies of the applicable elements for each method. The most extensively studied elements in ligand protection methods are noble metals (Pd, Pt, Au, and Ag). Following closely are other late transition metal elements (Fe, Co, Rh, Ni, Cu) and post-transition elements (Zn, Cd, Al, Ga, and In). Remarkably, the bond type between the metal atoms directly influences the diversity of the cluster structures. The fact that the most varied cluster structures were found for the metal elements in group 11 could be rationalized by their valence s-electrons forming relatively free bonds and resistance to oxidation. In contrast, other elements tend to be in charged states with the ligands. Although there are relatively few reports on minor elements, a few atoms are often implemented in a cluster by doping the surrounding environment where the stabilization effect of cluster structures composed of major elements is dominant. The types of elements stabilized as a cluster significantly differ by and depend on the functional groups of the organic ligands, which are frequently observed in the case of clusters with single-bond-mediated ligand protection. However, only cyclopentadienyl ligands differ from these ligands and are utilized for applying a broad range of elements by stabilizing clusters with both electrostatic and steric effects. Therefore, such an approach, without obvious single-bond-mediated ligand protection, is expected to be effective for developing versatile synthetic methods from the viewpoint of applicable elements.

Although simple functional groups such as thiolates, carboxylates, and phosphines are used in conventional methods, suitable ligands for this approach are being explored and developed. In particular, new ligands with more complicated structures and compositions containing multidentate ligands afford unique stability to cluster structures.¹²³ Such a method to stabilize a certain geometric structure using custom-designed multidentate ligands is similar to the approach for controlling crystal polymorphs of nanoparticles, in which modification of the surface of a nanoparticle by multidentate ligands induces unusual crystal structures in the whole nanoparticle.¹²⁴ These reports also indicated that an approach that induces multipoint interactions between a cluster and its ligands is effective for developing versatile synthetic methods.

4.2. Clusters stabilized as ionic compounds

Clusters solely stabilized without protecting ligands have also been reported. They are generally obtained as ionic compounds that undergo electronic stabilization by bonding with pnictogens, chalcogens, halides, and metals with lower electronegativity. Polyoxometalate (POM) clusters are well-known materials. These clusters are almost negatively charged metal oxides and tend to be composed of metal atoms with high oxidation numbers.^125–127 In many cases, group 5 and 6 elements (V, Nb, Ta, Mo, and W) in the +V or +VI state prefer a six-coordination state. Some species such as paramolybdate [Mo₇O₂₄]⁶⁻, decatungstate [W₁₀O₃₂]⁴⁻, metatungstate [W₁₂O₄₀]⁸⁻, paratungstate [W₁₂O₄₂]¹²⁻, molybdenum blue reagents [Mo₁₅₄O₄₆₂H₁₄(H₂O)₇₀]¹⁴⁻ and [Mo₁₅₂O₄₅₇H₁₄(H₂O)₆₈]¹⁶⁻ are commercially available.¹²⁸ [H_xMo₃₆₈O₁₀₃₂(H₂O)₂₄₀(SO₄)₄₈]⁴⁸⁻ was one of the largest POM clusters¹²⁹ (Fig. 6A). Similarly, group 3 superheavy elements (U, Np, Pu, and partially Am) in the +V or +VI state also form POM structures, such as [U₆₀O₂₄₀(OH)₆₀]⁶⁰⁻ with fullerene topologies^130–132 (Fig. 6B). The atomicity and arrangement of POM clusters can often be tuned by introducing other elements as the central core. For example, 4-coordinating species mainly in group 13, 14, and 15 elements (B, Al, Ga, C, Si, Ge, P, and As), such as PO₄⁻, SiO₄²⁻, and AlO₄³⁻ species, form unique structures typified by tungstophosphate [PMo₁₂O₄₀]³⁻ called Keggin-type structures.^125,126 Fe, Co, Cu, and Zn in the +II or +III state, and S and Se in the +VI state have also been reported as tetrahedral centers. In the case of 6-coordinating species of elements (Cr, Mn, Fe, Co, Rh, Ir, Ni, Pd, Pt, Cu, Zn, Al, Ga, Sb, Te, I), more planar Anderson–Evans-type POM clusters are constructed by a central EO₆ unit that is often in highly oxidized states, such as [CoMo₆O₁₈(OH)₆]⁶⁻ with Co(+III), [PtW₆O₂₄]⁸⁻ with Pt(+IV), and [IMo₆O₂₄]⁸⁻ with I(+VII).^124,133 Moreover, icosahedrally 12-coordinating EO₁₂ central units containing group 3 and 4 heavy elements (Ce, Th, U, Np, and Zr in the +IV or +V state) provide unique Dexter–Silverton-type structures such as pyritohedral [CeMo₁₂O₄₂]⁸⁻.¹³⁴ By introducing two or more core units, POMs lead to the construction of more complicated structures called Wells–Dawson-type or Preyssler–Pope–Jeannin-type structures.¹²⁵ Additionally, multiple POMs form sandwich-type or capsule-type structures intercalating group 1, 2, and 3 elements and low valent transition metals as a cation,^125,135 and they are also found in natural minerals, typified by the [Zn₂Mn₂(H₂O)₂(FeW₉O₃₄)₂]¹²⁻ cluster in ophirite.¹³⁶ By applying this unique property that partially incorporates other elements in or between POMs, it is possible to synthesize rarer, larger and more complicated structures, such as tetrapod-shaped [Ti₄Cl(OH)₁₂(P₂W₁₅Ti₃O₆₂)₄]⁴⁵⁻ where Ti atoms are sandwiched by four POM cluster units,¹³⁷ wheel-shaped [Cu₂₀Cl(OH)₂₄(H₂O)₁₂(P₈W₄₈O₁₈₄)]²⁵⁻ where Cu atoms are encapsulated in a circular POM cluster host,¹³⁸ and a tetrahedral layered superstructure of [La₁₀Ni₄₈W₁₄₀Sb₁₆P₁₂O₅₆₈(OH)₂₄(H₂O)₂₀]⁸⁶⁻.¹³⁹ Recently, it was reported that large capsule-like POM clusters can also incorporate other small metal clusters into their centers, such as [Ag₂₇@(Si₂W₁₈O₆₆)₃]³¹⁻.¹⁴⁰

Fig. 6 Crystal structures of (A) a unit in [H_xMo₃₆₈O₁₀₃₂(H₂O)₂₄₀(SO₄)₄₈]⁴⁸⁻ with a structure showing molybdenum oxide polyhedra,¹²⁹ (B) a unit in [U₆₀O₂₄₀(OH)₆₀]⁶⁰⁻ with a structure showing uranium oxide polyhedra,¹³⁰ and (C) a unit in [Fe₁₃O₁₆(OH)₁₂(OCOR)₁₂]¹⁷⁻ with a structure showing iron oxide polyhedra (below).¹⁴² Mo: reddish gray polyhedron, O: red, U: bluish gray polyhedron, Fe: brown, and O: red. Figures are reproduced from (A) CCDC 1727624, (B) CCDC 1732644, and (C) CCDC 1525080.

With the exception of V, Mo, and W, advanced synthesis techniques have been developed. In particular, the polycationic Keggin-type structures of aluminum [Al₃₀O₈(OH)₅₆(H₂O)₂₄]¹⁸⁺ containing 6-coordinating AlO₆ sites and central 4-coordinating AlO₄ sites are well known.¹⁴¹ However, in such cases, co-adoption of the concept of ligand protection in these clusters is also effective in synthesizing POMs composed of minor elements, such as Keggin-type [Fe₁₃O₁₆(OH)₁₂(OCOR)₁₂]¹⁷⁻ containing an Fe(+II) center and Fe(+III) shells with carboxylate ligands¹⁴² (Fig. 6C), Keggin-type [Mn₁₃O₆(OH)₂(OMe)₄L₆]⁴⁺ containing a Mn(+III) center and Mn(+IV) shells with alkoxylate and imine ligands (L = 2,6-bis[N-(2-hydroxyethyl)iminomethyl]-4-methylphenol),¹⁴³ Ti₁₇O₂₄(OiPr)₂₀ with alkoxylate ligands,¹⁴⁴ and octahedral [(BuSn)₁₂O₁₄(OH)₆]²⁺ with alkyl ligands.¹⁴⁵ In contrast, a few POMs composed of only four-coordinating units are reported including [Mn₃₉O₅₅]²⁶⁻ (ref. 146) (Fig. 7A). Interestingly, the anion-templated synthesis described in the section on ligand-protected noble metal clusters is also effective for the synthesis of POM clusters. The geometries and charges of the template anion provide clusters with various sophisticated core–shell structures, such as [(SCN)@HV₂₂O₅₄]⁶⁻, [(CH₃COO)@H₂V₂₂O₅₄]⁷⁻,¹⁴⁷ [Cl@Eu₁₅(OH)₂₀]²⁴⁺,¹⁴⁸ and [(SO₄)@As₄Mo₆V₇O₃₉]⁴⁻.¹⁴⁹ Even electronically neutral chemical species, such as solvent molecules, often serve as templates. For example, water and acetonitrile molecules compose [(H₂O)@V₁₈O₄₂]¹²⁻ (ref. 150) and [(CH₃CN)@V₁₂O₃₂]⁴⁻,¹⁵¹ respectively.

Fig. 7 Crystal structures of (A) a unit in [Mn₃₉O₅₅]²⁶⁻ with a structure showing manganese oxide polyhedra (right),¹⁴⁶ (B) [Nb₆Cl₁₈]²⁻,¹⁵² (C) a unit in [In₃₅S₄₈O₈(Im)₂]⁹⁻,¹⁵³ and (D) [AsNi₁₂As₂₀]³⁻.¹⁵⁵ Mn: reddish violet, O: red, Nb: bluish green, Cl: light green, In: pale magenta, S: yellow, Ni: gray, As: green, C: grayish bone, and N: light blue bone. Figures are reproduced from (A) CCDC 1728352, (B) CCDC 654117, (C) CCDC 1862551, and (D) CCDC 206301.

Except for the stabilization of clusters, such as the oxides mentioned above, other pnictogenides, chalcogenides, and halides can induce such stabilization. Polyhalometalate clusters, especially of early transition metals (Zr, Hf, Nb, Ta, Mo, W, Re), are well-known, such as [Nb₆Cl₁₈]²⁻ (ref. 152) (Fig. 7B). The compound clusters also often have larger layered structures, such as tetrahedral [In₃₅S₄₈O₈(Im)₂]⁹⁻,¹⁵³ tetrahedral [Sn₁₀O₄S₂₀]⁸⁻,¹⁵⁴ icosahedral [AsNi₁₂As₂₀]³⁻,¹⁵⁵ and tetrahedral Sc₄C₁₀Sc₂₀I₃₀ ¹⁵⁶ (Fig. 7C and D). Additionally, it has been reported that the cation-templated synthesis of some chalcogenide clusters provides rare geometric structures, such as [(NH₄)@Pd₂S₂₈]⁴⁻ (ref. 157) and [Na₂@Fe₁₈S₃₀]⁸⁻.¹⁵⁸

In summary, in the case of clusters obtained as ionic compounds, the oxide clusters of the early transition metals (V, Mo, and W) are the most investigated, and the runner-up is another base metal element with a relatively high valence (Al, Ti, Mn, Fe, and U). Halide clusters of early transition metals (Zr, Nb, Mo, Hf, Ta, W, and Re) are the main compounds used in this field. Similar to ligand-protected clusters, the introduction of minor elements is achieved by doping a few atoms into the cluster structure composed of major elements. Particularly for POM clusters, it appears that metal elements in remarkably high oxidation states play an important role in diversifying their steric structures. One factor is that metals with high oxidation states maintain the charge balance of the entire cluster structure by reducing the negative charge on their own metalate units. If the metalate anion is represented as {MⁿO₆}^(12−n)−, its total negative charge is smaller when oxidation state n is higher. On the other hand, because the stability of these clusters is significantly associated with the affinity of the metal elements for pnictogens, chalcogens, and halogens, clusters composed of noble metals have rarely been reported. As represented by POMs, these clusters often have unique symmetric structures, whereas in the case of different metal elements, these metal oxide units tend to undergo atomic-level phase separation in a cluster and do not form true complex oxides with a uniform atomic co-arrangement. This suggests that the variety of ionic compound clusters can be expanded by improving the synthetic schemes.

4.3. Naked elementary clusters

In contrast, naked clusters composed only of icosagens, tetrels, pnictogens, chalcogens, and halogens (groups 13, 14, 15, 16, and 17) are also well known. Although white phosphorus (tetrahedral P₄) is the most famous example, it is generally an ionic species called Zintl clusters or Zintl ions that is stabilized in crystals.¹⁵⁹ In particular, there are many reports of Zintl clusters of group 13, 14, 15, and 16 metal elements with various polyhedral structures, such as icosahedral [Tl₁₃]¹⁰⁻,¹⁶⁰ trigonal-bypyramidal [Sn₅]²⁻,¹⁶¹ bicapped-square-antiprismatic [Pb₁₀]²⁻,¹⁶² square antiprismatic [Bi₈]²⁺,¹⁶³ square-planar [Te₄]²⁺, and barrel-shaped [Te₈]²⁺ (ref. 164) (Fig. 8A–C). In other cases, examples of clusters made of group 11, 12, and 17 elements are slightly known like icosahedral [Ag₁₃]⁴⁺ (ref. 165) or polyhalogen cations and anions typified by rectangular [Cl₄]⁺ (ref. 166) and trigonal-pyramidal [I₇]⁻ (ref. 167) (Fig. 8D and E). Similar to other methods, Zintl clusters also form molecular alloys (intermetalloids) of such elements including [BiIn₈Bi₁₂]^3−/5− (ref. 168) and [K₂Zn₂₀Bi₁₆]⁶⁻,¹⁶⁹ or clusters incorporating a few other transition metal elements¹⁷⁰ including [Sn₉Pt₂(PPh₃)]²⁻, [Sn₉Ni₂(CO)]³⁻ (ref. 171) and [Th@Bi₁₂]⁴⁻ (ref. 172) with and without protecting ligands, respectively (Fig. 8F and G).

Fig. 8 Crystal structures of (A) [Pb₁₀]²⁻,¹⁶² (B) [Bi₈]²⁺,¹⁶³ (C) [Te₈]²⁺,¹⁶⁴ (D) [Ag₁₃]⁴⁺,¹⁶⁵ (E) [Cl₄]⁺,¹⁶⁶ (F) [K₂Zn₂₀Bi₁₆]⁶⁻,¹⁶⁹ and (G) [Th@Bi₁₂]⁴⁻.¹⁷² Pb: black, Bi: purple, Te: grayish yellow, Ag: pale gray, Cl: light green, K: violet, Zn: gray, and Th: bluish green. Figures are reproduced from (A) CCDC 288640, (B) CCDC 1728864, (C) CCDC 1471867, (D) CCDC 1728248, (E) CCDC 1726993, (F) CCDC 1969162, and (G) CCDC 1983072.

As mentioned above, these clusters are mainly composed of post-transition elements with many valence electrons, and in many cases, they are positively or negatively charged structures. This tendency is rationalized by the thermodynamic stability based on the electronic configurations unique to clusters typified by superatoms.^{6–8,25,32,36,47,90} These clusters generally have relatively rigid structures with large bond angles of up to 90° originating from p-electrons and the ability to contain a few atoms of other group elements in electronically stabilized skeletons. In particular, the endohedral structures typified by stannaspherenes mentioned in the gas-phase synthesis section enable the incorporation of other groups of elements without ligands. It should be noted that the accurate choice of counter ions is an important factor in the stable design of these clusters because most clusters are obtained only in the crystal form.

4.4. Clusters obtained by nanospace-assisted template synthesis

The third method utilizes nanospace as reaction fields for cluster synthesis. Because the aforementioned synthetic methods depend on the thermodynamic stability of the cluster structure, only certain clusters with energetically suitable atomicity, atomic arrangement, and composition ratios were obtained. However, in this method, the reaction field is confined within a nanosized space using various approaches, and unique clusters in metastable states that are not found using other methods are forcibly obtained. The pores of zeolites serve as typical capsules for cluster synthesis, such as tetrahedral [Ag₄(H₂O)₄]²⁺ in their cages.^173–177 Metal–organic frameworks (MOFs) are also used for nanosized cages, and templated synthesis of various clusters, including Pt quasi-linear [Pd₄]²⁺,¹⁷⁸ tetrahedral Ir₄,¹⁷⁹ Pt_12±x,¹⁸⁰ and triple-decker trigonal [Au₃L₃-Ag-Au₃L₃-Ag-Au₃L₃]²⁺,¹⁸¹ has been reported. Recently, MOFs have been used to cluster carbon as a nonmetal element through selective template synthesis of polyacenes using reactants.¹⁸² Flexible supramolecular capsules realize the synthesis of such metastable clusters, including some allotropes of nonmetal elements, such as phosphorus P₄ ¹⁸³ and sulfur S₆ or S₁₂,¹⁸⁴ where the catenation behavior is controlled. In other cases, cages of crystalline proteins and nanospaces of macromolecules have been used as templates and protectors for clusters.^185,186 In such cases, because the precision of cluster synthesis depends on the operation of the atomic assembly, it is expected that only one method will allow us to use a broad range of elements by adopting the same chemical principle for the assembly. Indeed, the atom hybridization method utilizing multimetallic multinuclear complexes of dendrimers as macromolecular templates for cluster synthesis affords the highest degrees of freedom in the design of multielemental clusters.^187–191 Because it adopts the coordination behavior of guests for metal assembly based on the simple principle of acid–base chemistry, all elements can be treated under the same conditions during cluster synthesis. This approach led to the first synthesis of multimetallic clusters containing five or six metal elements like GaInAu₃Bi₂Sn₆.¹⁸⁷

In contrast to other liquid-phase synthesis methods, template synthesis provides clusters with relatively metastable structures, which are also regarded as intermediates in the process producing more stable clusters. Capsules need to be individually designed for each chemical element, while this approach, which reduces the direct influence originating from the properties of the elements, enables the use of a broad range of elements. Alternatively, in this method, the interaction between the capsules and precursor compounds, such as electrostatic interactions, acid–base reactions (including coordination), and hydrophobic interactions, is a key factor for accumulating atoms. However, it is important to stabilize such clusters in order to hold them in capsules or fix them on/in support materials. Moreover, in many cases, it is difficult to conduct the usual identification analyses, such as single-crystal X-ray diffraction and direct observation by STEM, SPM, and MS, which are often effective.

5. Solid-phase synthesis

Several methods have been reported for the synthesis of clusters in the solid phase. The mechanochemical synthesis of general nanoparticles has already been established, but that of clusters remains limited.¹⁹² For instance, Keggin-type POM of aluminum [Al₁₃O₄(OH)₂₄(H₂O)₁₂]⁷⁺ can be obtained by a mechanochemical reaction between the [Al(H₂O)₆]Cl₃ and (NH₄)₂CO₃ reactants.¹⁹³ Dimensional reduction of solid-state precursors is effective for the precise synthesis of clusters. Some metal chalcogenide or halide clusters typified by [Re₆S₆Cl₈]²⁻ are stoichiometrically synthesized by dimensional reduction of an extended solid-state structure.^194,195 As an ultimate physical method, a technique for the mechanical synthesis of clusters by directly manipulating atoms using scanning probe microscopy was recently developed. Indeed, metal clusters such as Au₁₂, Ag₁₂, and Au₅Pb have been synthesized directly on Si surfaces.¹⁹⁶

As mentioned previously, the advantages of synthetic methods involving solid-phase processes are extremely limited in terms of the selectability of elements. However, bottom–up synthesis involving mechanochemical reactions and top–down synthesis involving dimensional reduction are significantly more effective for mass production than liquid-phase synthesis. This suggests that expanding the applicable elements in solid-phase synthesis will contribute to promoting clusters as more general and valuable materials in the future.

6. Conclusions and perspectives

As discussed above, the optimal method for synthesizing clusters varies significantly depending on the chemical element involved. Consequently, research on cluster synthesis has been pursued individually, with each method serving as a starting point. Notably, in liquid-phase processes, doping other group elements using the stable structures and atomic-level space obtained by each method has proven highly effective. Recently, these methods have been increasingly interconnected based on this approach.

However, according to the classification of clusters based on chemical elements, it is evident that there is no accurate border between cluster structures, even though each adopts a different synthetic method. For example, certain representatives among ligand-protected clusters and ionic compound clusters, namely [Be₄(NH₂)₆(NH₃)₄]²⁺,⁷⁵ [Zn₁₀S₄(SR)₁₆]⁴⁻,⁵⁹ Zn₁₀O₄(OCOR)₁₂,⁷⁹ In₃₇P₂₀(OCOCH₂Ph)₅₁,⁸⁰ [Mn₁₃O₆(OH)₂(OMe)₄L₆]⁴⁺,¹⁴³ and [In₃₅S₄₈O₈(Im)₂]⁹⁻,¹⁵³ partially contain both their two structural factors for cluster stabilization. [Sn₉Pt₂(PPh₃)]²⁻ (ref. 171) can be regarded as a cluster undergoing stabilizing effects by both ligand-protection and Zintl anions. Interestingly, the clusters developed using different methods often exhibit similar structures with reversed atomic arrangements and elemental ratios. Some of the simplest examples are [Co₈S₆(SPh)₈]⁴⁻ (ref. 58) and Co₆Te₈(PR₃)₆,⁷² where the transition metal and chalcogen atoms occupy reversed positions in the same symmetric structure. Moreover, [Sb₃Rh₂₀(CO)₃₆]³⁻ reported as a ligand-protected cluster with a few free post-transition metal atoms¹¹³ and [Sn₉Ni₂(CO)]³⁻ reported as a Zintl cluster with a few ligand-protected transition metal atoms¹⁷¹ have a complementary relationship (Fig. 9A). Additionally, the [Mo₆O₂₂@Ag₅₈S₂(SPhtBu)₃₆(OCOCF₃)₁₀] cluster obtained by the anion-template synthesis of ligand-protected clusters^48,197 and the [Ag₂₇@(Si₂W₁₈O₆₆)₃]³¹⁻ clusters obtained by the expansion of the synthesis method of POMs¹⁴⁰ also have complementary structures. In their skeletons, where the [Mo₆O₂₂]⁸⁻ POM unit was encapsulated in a ligand-protected Ag₅₈ cluster and the [Ag₂₇]¹⁷⁺ unit was encapsulated in three open-Dawson-type POMs [Si₂W₁₈O₆₆]¹⁶⁻, the core and shell structures were completely inverted (Fig. 9B). Ag₆@(MoO₄)₇@Ag₅₆(MoO₄)₂(SiPr)₂₈(p-SO₃PhMe)₁₄ with a nested structure was recently synthesized.¹⁹⁸ This similarity and reversibility of the cluster structures indicate that the area of elements covered by each synthetic method has been extended widely enough to be close to each other in recent investigations. This suggests that a more flexible cluster design can be realized in the future by improving synthetic techniques.

Fig. 9 (A) Crystal structures of [Sb₃Rh₂₀(CO)₃₆]³⁻ (ref. 113) and [Sn₉Ni₂(CO)]³⁻,¹⁷¹ C: gray, O: red, Ni: light gray, Rh: grayish green, Sn: pale purple, and Sb: brown. (B) Crystal structures of Mo₆O₂₂@Ag₅₈S₂(SPhtBu)₃₆(OCOCF₃)₁₀ showing molybdenum oxide polyhedra¹⁹⁷ and [Ag₂₇@(Si₂W₁₈O₆₆)₃]³¹⁻ showing silicon oxide and tungsten oxide polyhedra.¹⁴⁰ C: grayish bone, O: red, Si: pale blue polyhedron, S: yellow, Mo: reddish gray polyhedron, Ag: pale gray, and W: gray polyhedron. Part A reproduced from CCDC 1960490 and 185824. Part B reproduced from CCDC 1050793 and 1949947.

However, there are uninvestigated clusters for which precise synthetic methods that allow mass production, such as multimetallic clusters, have not yet been established. In light of the tendencies mentioned above, blending these individually developed synthetic methods is expected to make a breakthrough in revealing as-yet-unknown clusters. Although such an attempt has already been made, for example, the combination of ligand protection and nanospace-assisted synthesis methods,¹⁹⁹ reports are still rare.

The electronic analogy between the clusters obtained using different methods suggests the possibility of new cluster structures by isomorphic substitution. For example, the ligand-protected [M(SR)₂]_n (M(II) = Ni, Pd, Pt) in section 4.1 might provide as-yet-unknown tiara-type bimetallic clusters, such as [M(SR)₂]_n[M'S₂]_x (M(III) = Mn, Fe, In), by doping based on the concept of chalcogenide clusters. Borane and Zintl clusters often have very similar geometric structures according to the Wade–Mingos rule,^15,16 such as square pyramidal B₅H₉ ²⁰⁰ and [In₅]⁹⁻ (ref. 201) or bicapped-square-antiprismatic [B₁₀H₁₀]²⁻ (ref. 202) and [Pb₁₀]²⁻.¹⁶² As some transition-metal elements doped with ligands have been reported,^171,203 mutual feedback from each chemistry associated with the synthetic methods will become an effective approach for designing new cluster structures. Cation- or anion-templated methods will also contribute to the creation of such hybridized clusters because they are reported in both ligand-protected clusters and ionic compound clusters. Although conventional clusters obtained by ion-templated synthesis are composed of relatively simple anions as core structures, undeveloped ionic species of metals or metal oxides allow expandability in their structures. For example, by tracing these methods, the templated synthesis of clusters adopting uninvestigated ions, such as Ni²⁺, Zn²⁺, VO²⁺, RuO₄⁻, and [Pt(OH)₆]²⁻, may contribute to creating clusters with new combinations of elements. Additionally, the secondary chemical treatment of these clusters, inspired by nanospace-assisted synthesis, is expected to add new lineups, even in Zintl clusters. Unrevealed pure metal clusters typified by such Zintl clusters will be obtained by the reduction of ionic compound clusters with diverse structures typified by POMs as precursors.

In contrast to clusters, synthesis methods for nanoparticles cover a broad range of chemical elements and chemical fields.¹ Therefore, hybridizing conventional synthesis methods for nanoparticles and clusters is expected to contribute significantly and provide new guidelines for cluster synthesis. As described in the sections on ligand-protected clusters, modifying the cluster structures with multidentate ligands is a strong candidate.^123,124 The effectiveness of such an approach following the methods for nanoparticles might ultimately be extended to bulk materials containing clusters as partial structures, such as clathrate compounds, gas hydrates, or minerals^204–208 and cluster units in metallic glasses or quasi-crystals.^209–213

In conclusion, a comprehensive categorization of clusters based on their constituent chemical elements allowed us to understand which method covered which elements and revealed the common points of the structures synthesized by different methods. It is suggested that blending chemical concepts for stabilizing clusters by combining these methods or introducing them into nanoparticles will enable the synthesis of as-yet-unknown clusters not obtained by conventional techniques, affording us many bridgeheads for the next stage of developing cluster fields. Finally, the one-size-fits-all synthetic method constructed using such an approach is a new strategy to promote this cluster chemistry to a more central and larger chemistry field in the future, leading to the creation of next-generation functional materials, such as quantum-sized catalysts.

Author contributions

T. T. composed the entire manuscript.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

The author acknowledges grants from JST PRESTO Grant Number JPMJPR20AA, JSPS KAKENHI Grant Number JP22H01904, the Advanced Technology Institute, the Yoshinori Ohsumi Fund for Fundamental Research, the JGC-Saneyoshi Scholarship Foundation, the Toshiaki Ogasawara Memorial Foundation, the Iwatani Naoji Foundation, the Inamori Foundation, Mizuho Foundation for the Promotion of Sciences, Iketani Science and Technology Foundation, and the Special Fund of Institute of Industrial Science, University of Tokyo. Drawings of the crystal structures of the clusters were reproduced using VESTA²¹⁴ according to the Cambridge Crystallographic Data Centre (CCDC) database.

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