# Cluster chemistry

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Cluster chemistry

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.[1]

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.[2] 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.

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

Metal cluster compounds, especially those having numbers of carbonyl ligands, have been evaluated as catalysts for a wide range of reactions, especially related to carbon monoxide utilization,[3] 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, also catalyzed by iron compounds.

Although having no role in industrial catalysis, clusters are common catalysts 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.[4]

Metal clusters here refer to polyatomic assemblies having at least one metal-metal bond, such as Fe-Ni Clusters. 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.

### Definition of cluster catalysis

Although synthetic clusters have few practical applications in catalysis, the promise of their applications has led to extensive academic research. 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.[5]

The participation of clusters in a catalytic reaction can be evaluated using the following set of criteria:[5]

• Turnover frequency increases with increasing cluster concentration
• Product selectivities are different when using a polynuclear cluster than when using a mononuclear complex
• 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

Metal clusters have several properties that suggest that they may prove as useful 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.[6] 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.[5] 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.[7] 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 sometimes characterized by a high degree of fluxionality of surface ligands and adsorbates associated with a low energy barrier to rearrangement of these species on the surface.[8][9] The rearrangement of ligands on a cluster exterior is related to the diffusion of adsorbates on solid metal surfaces. Interconversion ligands between terminal, double-, and triply bridging sites is often facile. It has further been found that metal atoms themselves can easily migrate in or break their bonds with the cluster structure.[10][7]

### Examples of reactions catalysed by metal carbonyl clusters

Although metal carbonyl clusters are rarely used, they have been subjected to many studies aimed at demonstrating their reactivity. Some of these examples include the following

Reaction Core Metals Catalyst Reference
Alkene hydroformylation Mo-Rh Mo2RhCp3(CO)5 [11]
Alkene hydroformylation Rh Rh4(CO)10+x(PPh3)2-x (x=0,2) [12]
CO hydrogenation Ru-Os H2RuOs3(CO)13 [11]
CO hydrogenation Ru-Co RuCo2(CO)11 [11]
CO hydrogenation Ir Ir4(CO)12 [10][12][13]
CO hydrogenation Fe Fe3(CO)12 [14]
Alkene hydrogenation Os-Ni H3Os3NiCp(CO)9 [11]
Alkene hydrogenation Ni Ni2+xCp2+x(CO)2 (x=0,1) [12]
Alkyne hydrogenation Os-Ni Os3Ni3Cp3(CO)9 [11]
Hydrogenation of aromatics Ni Ni2+xCp2+x(CO)2 (x=0,1) [12]
Acetaldehyde hydrogenation Ni Ni4(Me3CNC)7 [12]
Alkene isomerization V-Cr VCrCp3(CO)3 [11]
Hydrocarbon isomerization Fe-Pt Fe2Pt(CO)6(NO)2(Me3CNC)2 [11]
Butane hydrogenolysis Rh-Ir Rh3+xIr3-x(CO)16 (x=0,1,2) [11]
Methanol hydrocarbonylation Ru-Co Ru2Co2(CO)13 [11]
Hydrodesulfurization Mo-Fe Mo2Fe2S2Cp2(CO)8 [11]
CO and CO2 methanation Ru-Co HRuCo3(CO)12 [11]
Ammonia synthesis Ru-Ni H3Ru3NiCp(CO)9 [11]

### Fischer-Tropsch catalysis

Species that are typical ligands for a metal cluster represent obvious reactant-catalyst combinations.[5][8] 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.[10] As in the industrially significant heterogeneous process, Fischer-Tropsch synthesis by clusters yields alkanes, alkenes, and various oxygenates. The selectivity is heavily influenced by the particular cluster used. For example, Ir4(CO)12 produces methanol, whereas Ru2Rh(CO)12 produces ethylene glycol.[10] 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.[5] Where steric effects are dominating, selectivity can be different depending on the arrangement or types of ligands.

### Clusters in the synthesis of thiacrown ethers

The cyclooligomerization of thiotanes illustrates the influence of steric effects on selectivity.[5] 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, such as acetonitrile.[15] 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.[5]

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.[11] 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 using 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.[16][17] Reactivity studies are also useful, especially in determining the catalytic properties of clusters.

### Computational studies

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.[9] 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.[18][19][20] 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.[20]

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.[21] 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 extended 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 1970s, 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 PbMo6S8 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.[22] 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.[23] 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 [24] 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.[25][26] With an internal diameter of 6.1 Angstrom it is of comparable size to fullerene and should be capable of containing small atoms in the same manner as 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.[27] 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. An EMAC is composed 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 [28] 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.

## References

1. ^ Inorganic Chemistry Huheey, JE , 3rd ed. Harper and Row, New York
2. ^ Introduction to cluster chemistry by D. M. P. Mingos, David J Wales 1990 ISBN 0-13-479049-9
3. ^ Cluster Chemistry: Introduction to the Chemistry of Transition Metal and Main Group Element Molecular Clusters Guillermo Gonzalez-Moraga 1993 ISBN 0-387-56470-5
4. ^ Bioorganometallics: Biomolecules, Labeling, Medicine; Jaouen, G., Ed. Wiley-VCH: Weinheim, 2006.3-527-30990-X.
5. ^ a b c d e f g Rosenberg, E; Laine, R (1998). Concepts and models for characterizing homogeneous reactions catalyzed by transition metal cluster complexes. New York: Wiley-VCH. pp. 1–38. ISBN 0-471-23930-5.
6. ^ Jos de Jongh, L (1999). Physical properties of metal cluster compounds. Model systems for nanosized metal particles. New York: Wiley-VCH. pp. 1434–1453. ISBN 3-527-29549-6.
7. ^ a b Martino, G (1979). "clusters: Models and precursors for metallic catalysts". Growth and Properties of Metal Clusters. Amsterdam: Elsevier Scientific Publishing Company. pp. 399–413. ISBN 0-444-41877-6.
8. ^ a b Suss-Fink, G; Jahncke, M (1998). Synthesis of organic compounds catalyzed by transition metal clusters. New York: Wiley-VCH. pp. 167–248. ISBN 0-471-23930-5.
9. ^ a b Calhorda, M; Braga, D; Grepioni, F (1999). Metal clusters - The relationship between molecular and crystal structure. New York: Wiley-VCH. pp. 1491–1508. ISBN 3-527-29549-6.
10. ^ a b c d <Douglas, Bodie; Darl McDaniel, John Alexander (1994). Concepts and Models of Inorganic Chemistry (third ed.). New York: John Wiley & Sons, Inc.. pp. 816–887. ISBN 0-471-62978-2.
11. ^ a b c d e f g h i j k l m Braunstein, P; Rose, J (1998). Heterometallic clusters for heterogeneous catalysis. New York: Wiley-VCH. pp. 443–508. ISBN 0-471-23930-5.
12. ^ a b c d e Smith, A; Basset, J (3 February 1977). "Transition metal cluster complexes as catalysts. A review". Journal of Molecular Catalysis 2 (4): 229–241. doi:10.1016/0304-5102(77)85011-6.
13. ^ Ichikawa, M; Rao, L; Kimura, T; Fukuoka, A (17 January 1990). "Transition Heterogenized bimetallic clusters: their structures and bifunctional catalysis". Journal of Molecular Catalysis 62 (1): 15–35. doi:10.1016/0304-5102(90)85236-B.
14. ^ Hugues, F; Bussiere, P; Basset, J; Commereuc, D; Chauvin, Y; Bonneviot, L; Olivier, D (1981). "Catalysis by supported clusters: Chemisorption, decomposition and catalytic properties in Fischer-Tropsch synthesis of Fe3(CO)12, [HFe3(CO)11]- (and Fe(CO)5) supported on highly divided oxides". Studies in Surface Science and Catalysis 7 (1): 418–431. doi:10.1016/S0167-2991(09)60288-3.
15. ^ Lavigne, G; de Bonneval, B (1998). Activation of ruthenium clusters for use in catalysis: Approaches and problems. New York: Wiley-VCH. pp. 39–94. ISBN 0-471-23930-5.
16. ^ Bruce, M; Rodgers, J; Snow, M; Wong, F (25 June 1982). "Synthesis and reactions of some iron-nickel clusters: Crystal and molecular structure of [Ni(PMe3)2-(eta-C5H5)][Fe2Ni(mu3-C2Ph2)(CO)6(eta-C5H5)]". Journal of Organometallic Chemistry 240 (3): 299–309. doi:10.1016/S0022-328X(00)86796-0.
17. ^ Braunstein, P; Sappa, E; Camellini, A; Camellini, M (29 May 1980). "Synthesis and X-ray structure of (eta-C5H5)2Ni2Fe(CO)3S, the first iron-nickel cluster with a sulphur atom nearly symmetrically bridging three metal atoms". Inorganica Chimica Acta 45 (2): L191–L193. doi:10.1016/S0020-1693(00)80141-3.
18. ^ Nakazawa, T; Igarashi, T; Tsuru, T; Kaji, Y (12 March 2009). "Ab initio calculations of Fe–Ni clusters". Computational Materials Science 46 (2): 367–375. doi:10.1016/j.commatsci.2009.03.012.
19. ^ Ma, Q; Xie, Z; Wang, J; Liu, Y; Li, Y (4 January 2007). "Structures, binding energies and magnetic moments of small iron clusters: A study based on all-electron DFT". Solid State Communications 142 (1-2): 114–119. doi:10.1016/j.ssc.2006.12.023.
20. ^ a b Pacchioni, G; Kruger, S; Rosch, N (1999). Electronic structure of naked, ligated, and supported transition metal clusters from 'first principles' density functional theory. New York: Wiley-VCH. pp. 1392–1433. ISBN 3-527-29549-6.
21. ^ Andriotis, A; Lathiotakis, N; Menon, M (4 June 1996). "Magnetic properties of Ni and Fe clusters". Chemical Physical Letters 260 (1-2): 15–20. doi:10.1016/0009-2614(96)00850-0.
22. ^ "Metal Clusters in Chemistry" P. Braunstein, L. A. Oro, P. R. Raithby, eds Wiley-VCH, Weinheim, 1999. ISBN 3-527-29549-6.
23. ^ A. Spiekermann, S. D. Hoffmann, T. F. Fässler (2006). "The Zintl Ion [Pb10]2−: A Rare Example of a Homoatomic closo Cluster". Angewandte Chemie International Edition 45 (21): 3459–3462. doi:10.1002/anie.200503916. PMID 16622888.
24. ^ itself made by heating elemental potassium and lead at 350°C
25. ^ Tin particles are generated as K+Sn122− by laser evaporation from solid tin containing 15% potassium and isolated by mass spectrometer before analysis
26. ^ Li-Feng Cui, Xin Huang, Lei-Ming Wang, Dmitry Yu. Zubarev, Alexander I. Boldyrev, Jun Li, and Lai-Sheng Wang (2006). "Sn122−: Stannaspherene" (Communication). J. Am. Chem. Soc. 128 (26): 8390–8391. doi:10.1021/ja062052f. PMID 16802791.
27. ^ Fielicke A, Kirilyuk A, Ratsch A, Behler J, Scheffler M, von Helden G, Meijer G (2004). "Structure determination of isolated metal clusters via far-infrared spectroscopy". Phys. Rev. Lett. 93 (2): 023401. Bibcode 2004PhRvL..93b3401F. doi:10.1103/PhysRevLett.93.023401. PMID 15323913.
28. ^ Rayyat H. Ismayilov, Wen-Zhen Wang, Rui-Ren Wang, Chen-Yu Yeh, Gene-Hsiang Lee and Shie-Ming Peng (2007). "Four quadruple metal–metal bonds lined up: linear nonachromium(II) metal string complexes". Chem. Commun. (11): 1121–1123. doi:10.1039/b614597c. PMID 17347712.

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