Bare clusters

Clusters are intennediates bridging the properties of the atoms and the bulk. They can be viewed as novel molecules, but different from ordinary molecules, in that they can have various compositions and multiple shapes. Bare clusters are usually quite reactive and unstable against aggregation and have to be studied in vacuum or inert matrices. Interest in clusters comes from a wide range of fields. Clusters are used as models to investigate surface and bulk properties [2]. Since most catalysts are dispersed metal particles [3], isolated clusters provide ideal systems to understand catalytic mechanisms. The versatility of their shapes and compositions make clusters novel molecular systems to extend our concept of chemical bonding, stmcture and dynamics. Stable clusters or passivated clusters can be used as building blocks for new materials or new electronic devices [4] and this aspect has now led to a whole new direction of research into nanoparticles and quantum dots (see chapter C2.17). As the size of electronic devices approaches ever smaller dimensions [5], the new chemical and physical properties of clusters will be relevant to the future of the electronics industry. 

The Bei3 value is taken from reference (6). Note that the expansion entries in this table supercede those in Ref. 60 where an incorrect value was used for the bare cluster. 

Figure 9. Plots of the rate constants (X) of iron, vanadium and niobium clusters reacting with di hydrogen/di denteri urn, and their respective bare cluster ionization potentials (solid lines) scaled as described in the text.

DF calculations were carried out on CO complexes of small neutral, cationic, and anionic gold clusters Au with n= 1-6. The -coordination mode (terminal C-coordination) was found to be the most favorable one irrespective of the charge of the cluster, and cluster planarity is more stable for the bare clusters and their carbonyls. As expected, adsorption energies are greatest for the cationic clusters, and decrease with size. Instead, the adsorption energies of... 

Apparently Hypoelectronic Deltahedra in Bare Clusters of Indium and Thallium Polyhedra with Flattened Vertices... 

Information on the numbers of skeletal electrons contributed by each cluster vertex is necessary to apply the Wade-Mingos rules [13-16] to bare clusters of the posttransition elements. The mles discussed above for polyhedral boranes can be adapted to bare post-transition metal vertices as follows ... 

The next magic number for jellium clusters is 40. This is a particularly important magic number in cluster chemistry, since numerous 40 valence electron bare clusters with 9 to 11 vertices of the post-transition elements in Groups 13 to 15 are known as isolable species in intermetallics or salts with suitable counterions. Examples of such species include lun, Geg", and Big, all of which have been isolated in intermetallics (for Inn ) or as stable salts with suitable counterions (Geg" and Big ) and characterized by X-ray crystallography. 

The above-mentioned three clusters, B6, Bi2-co, and Bi2-ico in Figure 8.1, have a hollow at the center of the cluster cages, which can be occupied by another atom. Fujimori and Kimura [5] reported that the Bi2-ico cluster with an additional B atom in its hollow site showed metallic bonding, instead of covalent bonding like the original Bi2-ico. In addition, recently the electronic structure of A B12-ico (A=H-He) clusters was studied by Hayami [6]. Boron clusters have been studied extensively as components of new materials. However, these studies have all focused on bare clusters, i.e., there is no reports on the electronic structure of boron clusters in c-Si with another element inside its hollows. 

Compared to the situation described in earlier reviews, the scope of applications has noticeably widened. In particular, more mixed clusters are now being studied (albeit only binary ones). Also, a few papers have appeared that treat clusters other than bare clusters in a vacuum hydrogen-passivated silicon clusters and ligand-coated gold clusters have been investigated, as well as clusters on supporting surfaces. Studies of molecular clusters, however, which were attempted at the very beginning of the development described earlier, are still quite rare, and are limited to comparatively small cluster sizes. This bears testimony to the additional difficulty of this task, and perhaps also to the lack of reliable intermolecular potentials. 

Dangling bonds at the surface make bare clusters highly reactive and hence experimentally difficult to generate and to study. Clusters with surfaces passivated by other elements are more natural and easier to handle. They are, however, more difficult to treat theoretically. As with mixed clusters, various different compositions have to be generated and checked, and suitable interparticle potentials for the different species have to be available. Here, accuracy requirements for these potentials may even be greater, since presence and structure of the outer passivation layer may subtly influence the structure preferences of the whole cluster. Therefore, only a few studies on such systems have appeared so far. 

Wilson and Johnston [100] have studied another common case of passivated clusters, namely gold clusters ( =38,44,55) protected by an outer layer of thiol ligands. Much larger clusters of this type can be produced routinely in solution, with various types of ligands [101-104]. Wilson and Johnston treated the ligand layer only implicitly, but they could show that for the case of Au55 the bare cluster preference of an icosahedral over a cuboctahedral shape is reversed in the presence of a ligand layer. Experimental inference [102] may point in the same direction. 

Besides bare clusters in a vacuum (cluster beam) and clusters with passivation layers, another important experimental environment for clusters is a (solid) support. Nevertheless, this setup has been addressed in very few EA applications. Zhuang et al. [105] have used the EA method to study surface adatom cluster structures on a metal (111) surface. Miyazaki and Inoue [106] have found that n=13 clusters which are icosahedral in vacuo either form islands or form layered structures upon surface deposition, depending on the substrate-cluster interaction potential. 

The story begins in this chapter with the clusters of simplest geometric and electronic structure. These are clusters of p-block elements with defined stoichiometry and structure in which the cluster surface-atom valences are terminated with ligands. The large number known provide the factual base from which clever people have derived models that connect atomic composition with structure. In turn, these p-block models provide a foundation on which to build an understanding of more complex clusters such as condensed clusters, bare clusters and transition-metal clusters. A more comprehensive account of the structural chemistry will be found in older books and reviews, a selection of which will be found in the reading list at the end of each chapter. 

Let us look at bare clusters from a different point of view. What would a naked [Be]2- octahedral cluster be tike It has 20 eve, 6 short of the requirement. This number of electrons is sufficient to serve as the required seven sep and provide three external lone pairs however, three of the out-pointing external cluster orbitals would be empty and a structural rearrangement would be required to create a significant gap between MO 10 and the tiu set 11-13 (left side of Figure 2.21). Hence, in the same way that BH3 is only found as base adducts, so too octahedral [B6]2- would be expected to be found coordinated to bases. 

A spectacular example of the unusual shapes possible for bare clusters is the recent development of naked B wheels and other planar shapes generated by calcula-tional chemistry and supported by quantitative fits to experimental photoelectron spectroscopic data. Two examples, [Bg]2- and [Bg]-, are shown in Figure 2.28... 

The naked C60 cluster (a fullerene) was briefly mentioned at the end of Chapter 2 as an example of a three-connect bare cluster with a delocalized system containing the external cluster electrons. Here we will discuss some properties of fullerene-derived solids (there is C60, but also C70, Cg4, etc.). At room temperature, solid C60 adopts an fee structure with weak van der Waals interactions between the C60 molecules. Look more closely at the structure of C60 itself. It has the highest symmetry possible for a molecule, Ih point group, and consists of a polyhedron with 20 hexagonal... 

A crucial feature of the metal/oxide interface is that it combines the extended nature of the support with the limited size of the supported metal particles - a feature that is common to the study of defects in solids. Such systems pose special problems for realistic modelling. The requirements of defining computationally tractable, as well as accurate models are of particular importance. Three different approaches are common, namely bare clusters, embedded clusters and periodic slab models. All three are associated with approximations, and the best choice must be defined by the correct compromise between cost and accuracy. 

Much of our effort involves studies of the chemical behavior of dusters not only as a function of size, but also as a function of metal type, charge state (neutral, cationic or anionic), and reagent molecule. There are two different operating conditions for which we probe the chemisorption of molecules onto clusters as a function of duster size. The first is such that the rate of reaction is kinetically controlled. Here we obtain information about the rate at which the first reagent molecule chemisorbs onto the otherwise bare cluster. In the second case, chemisorption studies are carried out under near steady-state conditions. In this instance we attempt to determine how many molecules a particular size cluster can bind, i.e. the degree of saturation. 

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