Clustering generally

The metal nuclei of the so-called full-shell clusters, also referred to as magic number clusters, generally exhibit hexagonal or cubic close packing (ccp). Figure 6 shows the stepwise formation of the first magic-number clusters built by 13, 55, 147, and 309 atoms. 

Supramolecular aggregations are commonly referred to by a variety of terms, including adduct, complex, and van der Waals molecule. In this chapter we shall primarily employ the more neutral term cluster, which may, if desired, be qualified with the type of intermolecular interaction leading to clustering (e.g., H-bonded cluster ). General and specific types of intermolecular forces are discussed in the following sections. 

Although cluster roots form an interesting adaptation, species that do not form clusters generally have the same means of accessing nutrients, albeit not in such a condensed form They use root growth and branching to access nutrient-rich areas, exudation to increase nutrient availability, and absorption for uptake (Skene 2003). 

Zr6ZCli2)Cl6]" (Z=Be, B, C, Mn, Fe) in basic melts, the clusters generally show two reversible reduction steps at potentials that are strongly dependent on the net charge on the cluster (n—) [8]. The electrochemistry of [Ti(j -C5H5)2Cl2] has also been examined in acidic and basic melts [9]. 

Nanophase materials are prepared by compacting the nanosized clusters generally under high vacuum. Synthesis of such nanomaterials has been reported in a few systems. The average grain sizes in these materials range from 5 to 25 nm. 

As described in the previous section, a powerful technique to probe most of the chemical or physical properties of molecular clusters is mass spectrometry after ionization of these clusters. Generally, an excess of energy is given by this ionization process and can lead to various dynamical behaviors from the simplest one—fragmentations of the clusters (evaporation)—to intracluster chemical reactions. This means that the observed distribution of the ionic clusters often does... 

For our problem, due to the lack of specific metal-metal potentials for our clusters, general-purpose potentials were used. Specifically, the Extensible Systematic Forcefield (ESFF) [20,21] and the MM+ forcefield [22,23] were used. For these potentials a number of parameters, (not only non-bonded), are used such as bonded and torsional terms, which are calculated from rule-based algorithms. The resulting parameterisation is not expected to be particularly accurate, but allows choice of specifically bonded candidate structures for which the connectivities can be constrained, based on the precursor skeleton, in the energy minimisations. This method has the advantage of retaining chosen structural units and symmetries of the... 

For metal hydride clusters, much less is known about electronic and geometrical size effects, except for very small clusters that can be relatively easily traced with computational methods. Results on other ionic compounds, such as ZnS clusters, indicate less well defined size effects, and only for small cluster sizes [11]. As the size dependence will be clearly different than for metal clusters, potentially there is a large influence of size on the stability differences between small hydride and the corresponding metal clusters. However, the practical impact of these effects is probably limited, as in the bulk experimental preparation of light metal (hydride) clusters, generally, polydisperse samples are obtained, and hence pronounced effects of... 

While for 02, it can work in both positive and negative direction depending on the sum of the first term (always negative) and the second term (always positive) on the right-hand side of Eq. (63). Finally, for the smallest gyration radii a3, DCF always works in the direction that the absolute value of a3 is diminished since af — a < 0 and a — a < 0 in Eq. (64). Thus the four-atom cluster generally tends to be distorted in such a direction that massive directions should become more massive. The role of the DCF in the dynamics of our M4 cluster is studied in Section V.C. 

All of the clusters of this type (see Table 8 and Fig. 14 for examples) possess a single interstitial atom and are characterised by (12 ns + 18 + x) cluster valence electrons. These clusters generally have 3 extra occupied skeletal MO s (i.e. x = 6), which are exclusively involved in tangential bonding in the external cluster polyhedron. 

The possible occupation of the frontier orbital DTD1 pair results in possible SEP counts of n (4) or (n + 2) (6), but not (n + 1) for the tetrahedral clusters. Generally these clusters are characterised by 6 SEP s (as in, for example, [C4Bu4]161) in keeping with their designation as electron-precise 3-connected clusters and nido-trigonal bipyramids, but examples are also known which possess 4 SEP s (e.g. [B4C14]162)). 

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