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The founding father of cluster chemistry, Professor Alfred Cotton, defined clusters as “those containing a finite group of metal atoms which are held together entirely, mainly, or at least to a significant extent, by bonds directly between the metal atoms even though some non‐metal atoms may be associated intimately with the cluster” [21]. He continued: “This is essentially the definition suggested earlier [22], but broadened to include compounds in which the metal atoms are held together entirely by metal–metal bonds. It is broad enough also to include compounds containing only two metal atoms, although these are atypic in the same sense as methane is an atypic aliphatic hydrocarbon. It also includes clusters in which not all the metal atoms are identical, although at present scarcely any such clusters, except for binuclear ones, have been identified.” The history of the early developments in the field is nicely covered by Cotton in the review he published later in his career [23].

In addition to cluster cores containing several metal atoms connected by direct bonds established during chemical synthesis, clusters contain ligands (from Latin ligandus, gerund of ligãre, meaning “to bind”): ions or small molecules bonded to the metal atoms via donor atom within the ligand.

Although this field started with clusters containing O and Cl ligands bonded to the metal cluster core, the field soon exploded with advances in cluster chemistry using CO (metal carbonyl clusters) [24–26], phosphines (PR₃) [27] and chalcogen‐based ligands (e.g. ligands containing S, Se, or Te as a donor atom) [28], and, in particular, thiols (‐SR) [29]. Other common organometallic ligands include alkynes [30] and aromatic cyclopentadienyl (C₅R₅⁻) or arene (C₆R₆) ligands, which can bind to the metal cluster core via all five or six carbon atoms, respectively [31, 32]. Transition metals or transition metals with main‐group elements [33] as well as pure main‐group elements [34] and even lanthanides [35] can form clusters.

Chemically made metal clusters can be made in a variety of ways, from “one‐pot” synthesis to multistep sequences of reactions. For example, structurally similar undecagold (Au₁₁(PPh₃)₇Cl₃ or “Au_11–7” and [Au₁₁(PPh₃)₈Cl₂]Cl or “Au_11–8”) clusters stabilized by phosphine ligands can be synthesized using “one‐pot” synthesis approaches by reducing the same mononuclear precursor Au(PPh₃)Cl, with sub‐stoichiometric (0.25 molar equivalents) amounts of NaBH₄ favoring Au_11–8, while excess (5 molar equivalents) yield Au_11–7 [27]. In contrast, the synthesis of [PtRu₅C(CO)₁₅(μ‐SnPh₂)(μ₆‐C)] starting from RuCl₃ involves seven steps, and, although product yields at each individual step are quite high, the overall yield is low, and synthesis process is quite protracted [36]. Each specific subclass of chemically synthesized cluster species has got specific methodologies for building up cluster core, such as thermolysis of metal carbonyl clusters [24] or sequential reduction in gold‐thiolate clusters, as well as various periphery core atom substitution/addition reactions and even “etching” of less stable clusters in the mixture for size “focusing” to the most stable cluster out of the range present in the initial mixture [29]. Despite the maturity of the field, there is no single overarching synthesis methodology that could guarantee access to chemically made clusters of every possible nuclearity (number of metal atoms in the cluster core) and composition (for mixed metal clusters , some, but not necessarily all, combinations of x and y can be made). However, significant progress has been made toward rational total synthesis of thiolate‐protected metal nanoclusters, as highlighted in a recent review [29].

Importantly, the atomically precise nature of chemically synthesized clusters can be confirmed using single‐crystal X‐ray crystallography – a very powerful characterization method that yields the positions of each atom within lattice of the crystal. Chemically made clusters are often charged and, in addition to the metal cluster core and ligands around it, would have charge‐compensating counterions; thus they often can be crystallized as readily as simpler salts. Crystallization is a very important and often undervalued method for purification of chemical compounds because it works on the molecular recognition principle whereby only specific species, typical of the growing crystal, are incorporated into the growing lattice with impurities staying in solution. In some favorable cases, chemical synthesis of metal clusters can be scaled up to tens of grams of the product, which is a lot for the lab‐scale synthesis of such materials and hugely more than UHV techniques discussed earlier could produce [37, 38].

The research team of the author of this chapter has solved a number of crystal structures of gold clusters [39]. Figure 5.4 shows so‐called “space‐filled” and “ball‐and‐stick” representations of some cluster structures and highlights the unique geometries of the metal cluster cores – geometries that are not present in bulk gold or larger gold particles.

Figure 5.4 Structures of Au₈ (left), Au₉ (middle), and Au₁₁ (right) in space‐filled (top) and ball‐and‐stick visualizations with isolated cluster cores shown in the bottom row.

Source: Anderson et al. 2013 [39]. PCCP Owner Societies. CC BY 3.0

. (See online version for color figure).

It is worth highlighting how well the ligands can protect cluster metal cores, which are barely visible in the “space‐filled” (top row, Figure 5.4) structures – remember this for the discussion of catalyst activation later in the chapter.

If a mixture of clusters is obtained during the synthesis, the individual components of the mixture can sometimes be separated using chromatography [40]. If sufficient quantities of each individual cluster can be separated and collected, attempts to crystallize each cluster can be made (in order to resolve their structures using X‐ray crystallography). However, if crystallization fails, high‐resolution mass spectrometry can also be used to confirm the identity of the atomically precise clusters in conjunction with modeling of the expected exact mass of each cluster, as well as the corresponding isotopic and fragmentation patterns [40].

There is a family of materials related to metal clusters called metal colloids [41]. Both clusters and colloids have cores containing metal atoms bonded to each other that are surrounded by a protective layer. In the case of clusters, the layer is formed by ligands, while in the case of colloids the terms “capping agents” and “surfactants” are used more often to describe this layer. Figure 5.5 illustrates key features of both clusters and colloids with respect to metal core size and size distribution.

Figure 5.5 Illustration of the size regimes and particle size distributions of clusters and colloids. (See online version for color figure).

Clusters are atomically precise species (definitely in the light of the original definition by Cotton), while colloids have particle size distributions (i.e. particles with different sizes are present in a mixture). Clusters have metal core sizes ranging from two to hundreds of atoms, with sizes of larger clusters typically sub‐3 nm. A famous example of the large cluster with solved crystallographic structure is Au₁₀₂ [42]. While colloids can have sizes just below 3 nm, most of the time their particle sizes are greater and can be as large as hundreds of nanometers. Ultrasmall colloids with narrow particle size distribution are often called clusters in the literature [43]. The reason to bring up this similarity is that two prominent examples of colloids were assigned cluster‐like formulas – Au₅₅ and Au₁₀₁ [44, 45] – whereas direct imaging by high‐resolution transmission electron microscopy (TEM) confirmed the existence of a particle size distribution [46]. Such species proved impossible to crystallize or to confirm their identity by high‐resolution mass spectrometry, but, although they are not truly atomically precise, they constitute an important complementary example of cluster‐like colloids.

The stability of classical organometallic complexes with one central atom is often explained based on the 18‐electron rule (think octet rule based on 2 + 6 electrons to fill s‐ and p‐orbitals, plus 10 electrons to fill d‐orbitals of the transition metal central atom). Similar electron‐counting rules such as effective atomic number rule (e.g. average of 18 electrons per metal atom in clusters) or Wade's rules (a better fit for delocalized bonding model) were successfully applied to relatively small metal carbonyl clusters [24]. The “magic‐number” concept was popular for rationalization of the high stability of some larger clusters. The idea behind such “magic numbers” is that closed‐shell, highly symmetric structures have a low free energy per atom. For example, Mackay icosahedra are uniquely defined by the number of closed shells around the initial central atom, with the total number of atoms per cluster with increase in number of shells being N = 13, 55, 147, 309, 561, 923, 1415, 2057, 2869, 3871, etc. The abovementioned assignment of the formula Au₅₅ to a synthetically made gold cluster was inspired by this concept [44]. A very recent study demonstrated that, for larger (100+ atoms) cluster sizes, oscillation occurs with respect to the most stable structure between icosahedra, decahedra, and face‐centered cubic (typical for bulk gold) structures [47]. An important recent development was recently proposed – a unified view of ligand‐protected gold clusters as superatom complexes [48]. In this approach, exceptional stability is assigned to systems with electron counts corresponding to filling of shells (n = 2, 8, 18, 34, 58, 92, 138, etc.) and takes into account interactions of the cluster core and ligands. It was successfully applied to explain the stability of a wide range of clusters, including that of Au₁₀₂ mentioned above [42, 48].