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Applications of clusters in catalysis
Metal cluster compounds, especially those having numbers of carbonyl ligands, 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 catalyze 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. More examples are shown in the table below.

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.

Metal clusters here refer to polyatomic assemblies having at least two metal-metal bonds, such as LINK TO FE-NI WIKIPEDIA ARTICLE Cluster catalysis can be separated into three types, including (1) homogeneous, relatively low-nuclearity clusters that are soluble in solvents, (2) heterogeneous, insoluble cluster networks or colloids that can be suspended in a solvent, and (3) heterogeneous, relatively high-nuclearity nanoparticles that can be either clean surface or surface-ligated, supported or free.

Cluster catalysis as a unique type of catalysis can be defined with various degrees of rigor. The strictest definition requires that at least two active sites on two different metal atoms be involved in the reaction cycle. Some define cluster catalysis to include clusters that have only one active site on one metal atom. The definition can be further relaxed to include clusters that are completely intact during at least one reaction step, and can be fragmented in all others.

Whether or not cluster catalysis is occurring can be evaluated using the following set of criteria given by Rosenberg et al., which if observed, suggest the occurrence of cluster catalysis:

• Turnover frequency increases with increasing cluster concentration

• Product selectivities are different when using a polynuclear cluster than when using a mononuclear cluster

• Combination of 2 or more metals in a cluster significantly enhances the reaction rate, changes the product selectivity, or allows a reaction to proceed that was not catalyzed when using a homonuclear cluster (this further indicates mixed metal catalysis)

• Modification of a cluster or the reaction conditions in a way that promotes metal-metal bond formation results in an increased reaction rate

• Catalytic asymmetric induction occurs with a chiral metal cluster in which the asymmetry is an inherent property of the cluster

It is important to note that depending on the source, the prefixed terms “nuclear” and “metallic” are used and imply different meanings. For example, polynuclear refers to a cluster with more than one metal atom, regardless of the elemental identities. Heteronuclear refers to a cluster with at least two different metal elements.



Metals clusters have several properties that render them as particularly effective catalysts. The absence of large bulk phases leads to a high surface-to-volume ratio, which is advantageous in any catalyst application as this maximizes the reaction rate per unit amount of catalyst material, which also minimizes cost. Catalysts are characterized by active adsorption and reaction sites that lower an activation barrier to a particular chemical transformation. Metal clusters contain these sites as a rule, as surface metal atoms are inherently undercoordinated, leading to a low adsorption energy barrier. In general, as the number of atoms in a metal particle decrease, their coordination number decreases, and significantly so in particles having less than 100 atoms. This is illustrated by the figure at right, which shows dispersion (ratio of undercoordinated surface atoms to total atoms) versus number of metal atoms per particle for ideal isocahedral metal clusters.

Metal clusters are also characterized by a high degree of fluxionality of surface ligands and adsorbates, or a low energy barrier to rearrangement of these species on the surface. This is analogous to the mechanism of surface diffusion on solid metal surfaces. Interconversion of terminal, double-, or triple-bridging bonding is likewise facile. It has further been found that metal atoms themselves can easily migrate in or break their bonds with the cluster structure. This structural flexibility of metal clusters allows them to catalyze a wide variety of chemical reactions. Some examples are given in the table below.

Species that are typical ligands for a metal cluster represent obvious reactant-catalyst combinations. For example, hydrogenation of CO (Fischer-Tropsch synthesis) can be catalyzed using several metal clusters, as shown in the table above. It has been proposed that coordination of CO to multiple metal sites weakens the triple-bond enough to allow hydrogenation. In principle, due to the great variety of metal clusters, it is possible to conceive of a cluster for any chemical transformation.

In many cases, metal cluster catalysis can lead to not just one product, but a distribution of products. Fischer-Tropsch synthesis, for instance, yields alkanes, alkenes, and various oxygenates, where the selectivity is heavily influenced by the particular cluster used. For example, Ir4(CO)12 produces methanol, whereas Ru2Rh(CO)12 produces ethylene glycol. Selectivity is determined by several factors, including steric and electronic effects. Steric effects are the most important consideration in many cases, however electronic effects dominate in hydrogenation reactions where one adsorbate (hydrogen) is relatively small. Where steric effects are dominating, selectivity can be different depending on the arrangement or types of ligands.



The cyclooligomerization of thiotene provides an example of the influence of steric effects on selectivity. The reaction is shown at right.

The selectivity ratio S3(CH2)9/S6(CH2)18 is 6.0 for Os4(CO)12 and 1.5 for W(CO)6, rationalized by greater steric effects in the Os cluster, leading to a preference for the smaller ring product.

In some cases, a metal cluster must be “activated” for catalysis by substitution of one or more ligands with a better leaving group, such as acetonitrile. For example, Os3(CO)12 will have one active site after thermolysis and the dissociation of a single carbonyl group. Os3(CO)10(CH3CN)2 will have two active sites.

Electronic effects can be illustrated by bimetallic catalysts Fe-Pt and Fe-Rh, where Pt and Rh each contribute a different electronic character to the cluster. Rh atoms can coordinate to the carbon atom of a carbonyl group and an alkyl group simultaneously, whereas Pt coordinates to the carbonyl and a hydrogen atom. The result is that Fe-Pt produces methanol and Fe-Rh produces alkanols. These reactions are illustrated below:





Methods of study
Metal clusters have been studied by both experimental and computational methods. Single-crystal x-ray crystallography has been used for many years to determine the solid state structure of transition metal clusters prepared experimentally. Reactivity studies are also useful, especially in determining the catalytic properties of clusters.

Computational studies have progressed from sum-of-energies calculations (incorporating Huckel theory-type approximations) to Density Functional Theory (DFT). An example of the former is empirical packing energy calculations, where only interactions between adjacent atoms are considered. The packing potential energy can be expressed as follows:

$$E=\Sigma_i\Sigma_j(Ae^{-Br_{ij}}-Cr_{ij}-\frac{q_iq_j}{r_{ij}^{-1}})$$

where index i refers to all atoms of a reference molecule in the cluster lattice and index j refers to atoms in surrounding molecules according to crystal symmetry, and A, B, and C are parameters. The advantage of such methods is ease of computation, however accuracy is dependant on the particular assumptions made.

DFT has been used more recently to study a wide variety of properties of metal clusters. Its advantages are being a first-principles approach without need of parameters and the ability to study clusters without ligands of a definitive size. However the fundamental form of the energy functional is only approximately known, and unlike other methods there is no hierarchy of approximations which allow a systematic optimization of results.

Tight bonding molecular dynamics has been used to study bond lengths, bond energies, and magnetic properties of metal clusters, however this method is less effective for clusters with less than 10-20 metal atoms due to a larger influence of approximation errors for small clusters. There are limitations on the other extreme as well that exist with any computation method, that the approach to bulk-like properties is difficult to capture because at these cluster sizes the cluster model becomes increasingly complex.

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.