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In chemistry, a cluster is an ensemble of bound atoms intermediate in size between a molecule and a bulk solid. Clusters exist of diverse stoichiometries and nuclearities. For example, carbon and boron atoms form fullerene and borane clusters, respectively. Transition metals and main group elements form especially robust clusters.

The phrase cluster was coined by F.A. Cotton in the early 1960s to refer to compounds containing metal–metal bonds. In another definition a cluster compound contains a group of two or more metal atoms where direct and substantial metal metal bonding is present.

The main cluster types are "naked" clusters (without stabilizing ligands) and those with ligands. Typical ligands that stabilize clusters include carbon monoxide, halides, isocyanides, alkenes, and hydrides.

Applications of clusters in catalysis
Synthetic metal carbonyl cluster compounds have been evaluated as catalysts for a wide range of industrial reactions, especially related to carbon monoxide utilization, but no industrial applications exist. The clusters Ru3(CO)12 and Ir4(CO)12 catalyse the Water gas shift reaction, also catalyzed by iron oxide, and Rh6(CO)16 catalyzes the conversion of carbon monoxide into hydrocarbons, reminiscent of the Fischer-Tropsch process, although again iron-oxide based heterogeneous catalysts are used industrially.

Although discrete clusters have no well-defined role in industrial catalysis, they are widespread in Nature. Most prevalent are the iron-sulfur proteins, which are involved with electron-transfer but also catalyse certain transformations. Nitrogen is reduced to ammonia at an Fe-Mo-S cluster at the heart of the enzyme nitrogenase. CO is oxidized to CO2 by the Fe-Ni-S cluster carbon monoxide dehydrogenase. Hydrogenases rely on Fe2 and NiFe clusters.

The term cluster should be pertinent to assembly of more than two metal atoms bound together in a planar or polyhedron arrangements such as Re3Cl9 and Mo6Cl8 units. Metal-Metal cluster could be classified as cages compounds or not when it is planar.

Electronic structure
Metal clusters are frequently composed of refractory metal atoms. In general metal centers with large d-orbitals form stable clusters because of favorable overlap of valence orbitals. Thus, metals with a low oxidation state for the later metals and mid-oxidation states for the early metals tend to form stable clusters. Polynuclear metal carbonyls are generally found in late transition metals with low formal oxidation states.

The polyhedral skeletal electron pair theory or Wade's electron counting rules predict trends in the stability and structures of many metal clusters.

History and classification
The development of cluster chemistry occurred contemporaneously along several independent lines, which are roughly classified in the following sections. The first synthetic metal cluster was probably calomel, which was known in India already in the 12th century. The existence of a mercury to mercury bond in this compound was established in beginning of the 20th century.

Transition metal carbonyl clusters
The development of metal carbonyl compounds such as Ni(CO)4 and Fe(CO)5 led quickly to the isolation of Fe2(CO)9 and Fe3(CO)12. Rundle and Dahl discovered that Mn2(CO)10 featured an “unsupported” Mn-Mn bond, thereby verifying the ability of metals to bond to one another in molecules. In the 1970's, Paolo Chini demonstrated that very large clusters could be prepared from the platinum metals, one example being [Rh13(CO)24H3]2-.

Transition metal halide clusters
Linus Pauling showed that "MoCl2" consisted of Mo6 octahedra. F. Albert Cotton established that "ReCl3" in fact features subunits of the cluster Re3Cl9, which could be converted to a host of adducts without breaking the Re-Re bonds. Because this compound is diamagnetic and not paramagnetic the rhenium bonds are double bonds and not single bonds. In the solid state further bridging occurs between neighbours and when this compound is dissolved in hydrochloric acid a Re3Cl123- complex forms. An example of a tetranuclear complex is hexadecamethoxytetratungsten W4(OCH3)12 with tungsten single bonds and molybdenum chloride (Mo6Cl8)Cl4 is a hexanuclear molybdenum compound and an example of an octahedral cluster. A related group of clusters with the general formula MxMo6X8 such as PbundefinedMo6S8 form a Chevrel phase, which exhibit superconductivity at low temperatures. The eclipsed structure of potassium octachlorodirhenate(III), K2Re2Cl8 was explained by invoking Quadruple bonding. This discovery led to a broad range of derivatives including di-tungsten tetra(hpp), the current (2007) record holder low ionization energy.

Boron hydrides
Contemporaneously with the development of metal cluster compounds, numerous boron hydrides were discovered by Alfred Stock and his successors who popularized the use of vacuum-lines for the manipulation of these often volatile, air-sensitive materials. Clusters of boron are boranes such as pentaborane and decaborane. Composite clusters containing CH and BH vertices are carboranes.

Fe-S clusters in biology
In the 1970s, ferredoxin was demonstrated to contain Fe4S4 clusters and later nitrogenase was shown to contain a distinctive MoFe7S9 active site. With the development of bioinorganic chemistry, a variety of synthetic analogues of these clusters have been described.

Zintl clusters
Zintl compounds feature naked anionic clusters that are generated by reduction of heavy main group p elements, mostly metals or semimetals, with alkali metals, often as a solution in anhydrous liquid ammonia or ethylenediamine. Examples of Zintl anions are [Bi3]3−, [Sn9]4−, [Pb7]4−, and [Sb7]3−. Although these species are called "naked clusters," they are usually strongly associated with alkali metal cations. Some examples have been isolated using cryptate complexes of the alkali metal cation, e.g., [Pb10]2− anion, which features a capped square antiprismatic shape. According to Wade's rules (2n+2) the number of cluster electrons is 22 and therefore a closo cluster. The compound is prepared from oxidation of K4Pb9 by Au+ in PPh3AuCl (by reaction of tetrachloroauric acid and triphenylphosphine) in ethylene diamine with 2.2.2-crypt. This type of cluster was already known as is the endohedral Ni@Pb102− (the cage contains one nickel atom). The icosahedral tin cluster Sn122− or stannaspherene anion is another closed shell structure observed (but not isolated) with photoelectron spectroscopy. With an internal diameter of 6.1 Angstrom it is of comparable size to fullerene and should be capable of containing small atoms as in endohedral fullerenes.

Gas-phase clusters and fullerenes
Unstable clusters can also be observed in the gas-phase by means of mass spectrometry even though they may be thermodynamically unstable and aggregate easily upon condensation. Such naked clusters, i.e. those that are not stabilized by ligands, are often produced by laser induced evaporation - or ablation - of a bulk metal or metal-containing compound. Typically, this approach produces a broad distribution of size distributions. Their electronic structures can be interrogated by techniques such as photoelectron spectroscopy, while infrared multiphoton dissociation spectroscopy is more probing the clusters geometry. Their properties (Reactivity, Ionization potential, HOMO-LUMO-gap) often show a pronounced size dependence. Examples of such clusters are certain aluminium clusters as superatoms and certain gold clusters. Certain metal clusters are considered to exhibit metal aromaticity. In some cases, the results of laser ablation experiments are translated to isolated compounds, and the premier cases are the clusters of carbon called the fullerenes, notably clusters with the formula C60, C70, and C84. The fullerene sphere can be filled with small molecules in Endohedral fullerenes.

Extended metal atom chains
Extended metal atom chain complexes (EMAC) are a novel topic in academic research. They are comprised of linear chains of metal atoms stabilized with ligands. EMACS are known based on nickel (with 9 atoms), chromium and cobalt (7 atoms) and ruthenium (5 atoms). In theory it should be possible to obtain infinite one-dimensional molecules and research is oriented towards this goal. In one study an EMAC was obtained that consisted of 9 chromium atoms in a linear array with 4 ligands (based on an oligo pyridine) wrapped around it. In it the chromium chain contains 4 quadruple bonds.