Mixed clusters polyhedral

Williams [1] has given an excellent review on Early Carboranes and Their Structural Legacy and he defines carboranes as follows Carboranes are mixed hydrides of carbon and boron in which atoms of both elements feature in the electron-deficient polyhedral molecular skeleton . According to the electron counting rules [2] for closo- (2n + 2 SE), nido- (2n + 4 SE) and arachno-clusters (2n + 6 SE SE = skeletal electrons, n = number of framework atoms) and the An + 2 n electron Hiickel rule, small compounds with skeletal carbon and boron atoms may have an electron count for carboranes and for aromatics (see Chapters 1.1.2 and 1.1.3). 

Many metal carbonyl clusters have interstitial atoms or groups located in the eenter of the polyhedron. Such interstitial atoms may be a light atom sueh as boron, carbon, or nitrogen a post-transition element such as germanium, tin, or antimony or a transition metal. Interstitial atoms most frequently provide all of their valence electrons as skeletal electrons since all of their valence orbitals are neeessarily internal orbitals because of the location of the interstitial atom in the center of the polyhedron. Exceptions to this rule may occur when some of the valence electrons of the interstitial atom occupy orbitals of symmetries which cannot mix with any of the molecular orbitals arising from the polyhedral skeletal bonding. 

For metal clusters, it is now possible, through first principle theoretical (calculational) approaches, to predict and better understand vibrational spectra, optical band gaps, polarizability, quantum confinement, and stmctural predictions. One modern approach is to use pseudopotential density functional methods (PDFM), in particular to predict optical and dielectric properties. Similarly, using molecular dynamics simulations, it is possible to create models for cluster structures. This has been especially valuable for predicting a three-dimensional image for mixed metal clusters. Figure 6 illustrates computed stmctures for Cu-Ru bimetallic clusters. Note that in this case the dynamics simuiation predicted an enrichment of Cu at the edges and corners of the polyhedral structure. Indeed, this prediction was supported by later experimental catalysis data. 

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