Very Large Clusters

The largest one, Pt309Phen36O30, where the metallic core consists of 309 platinum atoms packed in a cuboctahedral monomer, gives two lines at around (i95pt) = 11 200 ppm for the inner atoms and + 1450 ppm for the outer ones [82]. The inner platinum atoms henceforth show a pronounced metallic character, which confirm the fact that the metal atoms inside the cluster behave essentially as a metal in the bulk of a metal crystal, as previously outlined for rhodium clusters (see Section 3.4.9). Larger clusters have been observed by Pt NMR but these species are nanoparticles without ligands. Interested readers are referred to refs 1-6 in ref. [83]. 

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A very large cluster Au55(PPh3) 2Cl6 of as yet unknown structure has been reported. Physical measurements indicate the bonding to be substantially metallic in character [188]. 

A. Muller, F. Peters, M.T. Pope, D. Gatteschini, Polyoxometallates very large clusters - nanoscale magnets. 

With such calculations one can approach Hartree-Fock accuracy for a particular cluster of atoms. These calculations yield total energies, and so atomic positions can be varied and equilibrium positions determined for both ground and excited states. There are, however, drawbacks. First, Hartree-Fock accuracy may be insufficient, as correlation effects beyond Hartree-Fock may be of physical importance. Second, the cluster of atoms used in the calculation may be too small to yield an accurate representation of the defect. And third, the exact evaluation of exchange integrals is so demanding on computer resources that it is not practical to carry out such calculations for very large clusters or to extensively vary the atomic positions from calculation to calculation. Typically the clusters are too small for a supercell approach to be used. 

In addition, aided by profound knowledge of the nature and reactivity of some surface organometallic species, it was possible to identify the various steps and the nature of intermediates involved in the nucleation processes occurring on the surface in the selective growth of very large clusters such as for instance in the case of [Os5C(CO)i4] and [OsioC(CO)24] [52]. As this subject is treated in detail elsewhere in this book it is not covered here. 

Formulas to count electrons only seem to be available for small and medium-sized clusters. It is apparent that we need other bond descriptions when moving from mediumsized to very large clusters with co-ordinatively unsaturated surfaces. 

But it is also important to appreciate the fact that all rules have a limited domain in which they are valid. Compounds that do not follow the rules become objects of interest often because they are associated with properties of value, e.g., the Lewis acidity of six-electron BF3. But, as we will discover, very large clusters cannot follow the existing counting rules as they lie outside the domain of validity. Yet these large clusters, nanoparticles, must have a drummer to which they march. A shadowy outline of this presently unknown drummer appears in the context of the existing rules. That is, counting is a place to start ... 

There are a number of metal carbonyl clusters, many of them anionic in nature. They range in size from dinuclear complexes, such as that shown above, to very large clusters and even charged colloidal particles. 

There have been a number of modeling efforts that employ the concept of clustering in supercritical fluid solutions. Debenedetti (22) has used a fluctuation analysis to estimate what might be described as a cluster size or aggregation number from the solute infinite dilution partial molar volumes. These calculations indicate the possible formation of very large clusters in the region of highest solvent compressibility, which is near the critical point. Recently, Lee and coworkers have calculated pair correlation functions of solutes in supercritical fluid solutions ( ). Their results are also consistent with the cluster theory. 

For z < exp r all clusters are small when the activity z increases and exceeds exp t, even by a very slight amount, very large clusters appear. This phenomenon corresponds to condensation, z — exp t corresponding to the state of saturated vapor. Isothermal compressibility —V 1(dVjdP)T takes a finite value at the condensation point as it should at low temperatures. 

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