General property of clusters

Clusters can be formed in a variety of ways,1 but share a common property [658] which sets them apart from other forms of matter. They are held together by forces which never saturate, i.e. it should always be possible to add more atoms to a cluster. 

The essential novel ingredient of cluster science is that the objects under study should retain self-similar properties as their size is increased. This is the concept of stackability [658]. Although clusters are finite in size, they may be made to grow indefinitely by stacking one more atom of the element from which they are composed. This may be taken as the defining property of clusters and distinguishes them from ordinary molecules. 

we suppose that any number of atoms can be glued together to form a cluster, in such a manner that the sites on which the atoms are located remain nearly equivalent to each other. This has the interesting consequence that a cluster can grow to macroscopic size without losing fundamental characteristics established when it was born in the microscopic regime. We say that clusters bridge the gap from microscopic to macroscopic physics. 

The clusters of greatest interest to us are those in which all the atoms are the same (homogeneous clusters). It is also possible to create mixed or heterogeneous clusters, in which two atoms of different types (which may or may not be chemically similar) are combined in indefinitely variable proportions. 

As just noted, at the microscopic end of the range, clusters can be confused with molecules and, indeed, share many of their properties. To 

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However, it turns out that this quantity is a rather poor indicator of the bond ionicity, as the system hardly behaves like a classical dipole consisting of two point charges, which is also illustrated by the fact that Mo depends strongly on cluster size. A much better indicator of the bond polarity is contained in the quantities M/, M2, and Ms. For all systems studied, Mj w -1.4 to -1.6, and Ms and M3 are small, and furthermore the cluster size dependence of these quantities is much less than that of Mq. (This points to a general property of cluster calculations already alluded to in Section 111.1 whereas absolute quantities may depend sensitively on cluster size, trends and slopes of trend curves show a much weaker cluster size dependence.) This linear behavior is consistent with an ionic bond where the slope. Mi, is related to the extent of ionicity. The dipole moment of two point charges +q and -q will be = -qx r and d/j/dr = M/ = -q. Hence for an ideal fully ionic halide bond, the curve is expected to be a straight line with slope M, = -l. 

A general property of these carbonyl clusters is their tendency to behave as electron sinks , and their redox chemistry is extensive. [OsioC(CO)24]" has been characterized in no less than five oxidation states (n = 0-4) though admittedly this is exceptional. 

The already voluminous review literature on clusters will be considered as a basis for this review. The topics treated so far are clusters in general (109, 241) and in connection with metal-metal bonding (30, 338, 380), special types of clusters like those with TT-acceptor ligands (231), hydrides (233), carbonyls (85, 86) or methinyl tricobalt enneacarbonyls (313, 317) properties of clusters like structures (56, 316), fluxionality (110), mass spectra (226), vibrational spectra (365), and redox behavior (292). Clusters have been treated in the context of metal carbonyls (3, 4), metal sulfur complexes (2, 381), and in relation to coordination polyhedra (297). Reviews... 

The chapters of this book ire categorized into three sections. The first two chapters are dedicated to explaining general features of clusters theoretically and experimentally. The next three chapters discuss several contemporary methodologies. The final two chapters examine topics related to condensed materials. The first chapter of the book describes the general properties and theoretical treatments of the cluster noting that the cluster... 

Nanostructured clusters of semiconductors and metals, which differ from the corresponding bulk material due to surface, shape, and quantum size effects, have been designed to possess unique properties due to electron confinement. The unique properties of nanosized metal particles can be utilized in a broad range of fields, from catalysis to optical filters as well as nonlinear optical devices. To understand how nanoclusters can be combined with dendrimers, first let s summarize general properties of dendrimers. 

This general property of 10- and 12-vertex clusters is illustrated in Figure 14.6 with a series of carboxylic acids substituted with a propyl group. The conformations in Figure 14.6 are consistent with experimental molecular structures of mesogenic derivatives and relative stability of the mesophase in isostructural derivatives. 

A central issue of our work is to identify general properties of the Na clusters from the large amount of information that we have obtained from the calculations. Instead of discussing the individual clusters, we shall introduce different quantities that are devised to reduce the available information to some few key nmnbers that allow for more general conclusions. 

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