Classification of clusters

For the benefit of clarity, this Chapter has been restricted fundamentally to the discussion of the chemistry of molecular transition metal clusters no dinuclear compounds, which were analyzed to some extent in Chapter 1, nor microcrystalline metal particles are considered. For the same reason the main emphasis is given to homonuclear metal compounds. However, heteronuclear species with different transition metals or containing main group atoms are taken into account whenever they are useful for a better understanding of cluster chemistry. 

The chemistry of cluster containing main group elements is discussed in Chapters 3 and 4. Moreover, selected aspects of the chemistry of some iron-sulfur clusters of great biological interest are analyzed in Chapter 5. 

There are two large classes of molecular clusters in which the ligands are all of the same nature The halide cluster class and the carbonyl or, in general, organometallic cluster class. According to the formal oxidation numbers acquired by metal atoms in these two classes of clusters, they are often classified as high and low-valence clusters respectively. 

In the high-valence cluster species, metal atoms forming the metal network appear to have positive intermediate oxidation states. However, metal oxidation states in cluster are always lower than those characteristic for the same metals in classical mononuclear complexes. The ligands associated to this class of cluster are normally good cr-donors that according to the classification of Pearson would have intermediate hardness. Among these compounds the most frequent are the halides, specially chlorides and bromides. An example of this cluster class is the molybdenum species [Mo6Xs] shown in Fig. 2.1c. 

Low-valence clusters are species in which the metal atoms have an oxidation state zero or negative. They are always associated with ligands able to behave as 7i-acceptors. Some examples of cluster belonging this class are shown in Fig. 2.2. Carbon monoxide is by far the most representative of these ligands but there are also many examples of compounds containing other typical soft ligands such as phosphine, olefines, acetylenes, cyclopentadiene, etc. 

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A useful classification of clusters is based on the number of metal atoms directly bonded to each other in the cluster. In order to be able to refer readily to this number, the term nuclearity is proposed (222). In Table I a portion of the periodic table is presented with an indication... 

B7.19 Enumeration and structural classification of clusters derived from parent solids metal-chalcogenide clusters composed of edge-sharing tetrahedra... 

Jiang Y, Nishikawa RM, Wolverton DE et al (1996) Malignant and benign clustered microcalcifications automated feature analysis and classification. Radiology 198 671-678 Jiang Y, Nishikawa RM, Papaioannou J et al (2001) Dependence of computer classification of clustered microcalcifications on the correct detection of microcalcifications. Med Phys 28 1949-1957... 

SONNIA can be employed for the classification and clustering of objects, the projection of data from high-dimensional spaces into two-dimensional planes, the perception of similarities, the modeling and prediction of complex relationships, and the subsequent visualization of the underlying data such as chemical structures or reactions which greatly facilitates the investigation of chemical data. 

FI Spath. Cluster-Analysis Algorithms for Data Reduction and Classification of Objects. Chichester Ellis Florwood, 1980. 

An example of an application is shown in Fig. 30.10. This concerns the classification of 42 solvents based on three solvatochromic parameters (parameters that describe the interaction of the solvents with solutes) [13]. Different methods were applied, among which was the average linkage method, the result of which is shown in the figure. According to the method applied, several clusterings can be found. For instance, the first cluster to split off from the majority of solvents consists of solvents 36, 37, 38, 39, 40, 41, 42 (t-butanol, isopropanol, n-butanol. 

Fig. 30.12. Forgy snon-hierarchical classification method. A,. ..,G are objects to be classified 1,..., 4 are successive centroids of clusters.

D. L. Massart, L. Kaufman and K.H. Esbensen, Hierarchical non-hierarchical clustering strategy and application to classification of iron-meteorites according to their trace element patterns. Anal. Chem., 54 (1982) 911-917. 

In this chapter we have only addressed a selected number of topics and for lack of space we have left out many others. Cluster analysis has played a larger role in QSAR than appears from our overview. This technique is an established QSAR tool in recognition or classification of known patterns [38,60] as well as for cognition or detection of novel patterns [61]. 

It should be noted that the above classification system of technetium cluster compounds is not the only possible one. In section 4 another classification is described, which is based on thermal stability and the mechanism of thermal decomposition. Section 2.2 is concerned with the classification based on methods of synthesizing cluster compounds. The classifications based on specific properties of clusters do not at all belittle the advantages of the basic structural classification they broaden the field of application of the latter, because for a better understanding and explanation of any chemical, physico-chemical and physical properties it is necessary to deal directly or indirectly with the molecular and/or electronic structures of the clusters. 

At present this is the most widespread system of classification of bi- and polynuclear clusters. 

Such a classification of technetium cluster compounds, in our opinion, reflects the relationship between the thermal stability and structure of the clusters quite well. Moreover, on the basis of this classification it is easier to follow the mechanism of the main thermochemical transitions of technetium clusters, such as (1) dehydration (2) disproportionation and related processes occurring without changes or with only small changes in mass (3) one-stage processes of thermolysis. We shall now consider these main mechanisms of the thermochemical reactions of technetium clusters in greater detail. 

A structural classification of 8 is difficult due to the fact that an arrangement of metal atoms as in 8 is uncommon in the whole field of molecular metal clusters. For this reason, detailed understanding of the bonding properties in 8 requires quantum chemical calculations. Theoretical analysis seems to be especially applicable to learning more about the bond between the two tetrahedra, which appears at first to be an isolated metal-metal bond between two metal atoms in the formal oxidation state zero. 

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