Icosahedral clusters icosahedron

Lithium has been alloyed with gaUium and small amounts of valence-electron poorer elements Cu, Ag, Zn and Cd. like the early p-block elements (especially group 13), these elements are icosogen, a term which was coined by King for elements that can form icosahedron-based clusters [24]. In these combinations, the valence electron concentrations are reduced to such a degree that low-coordinated Ga atoms are no longer present, and icosahedral clustering prevails [25]. Periodic 3-D networks are formed from an icosahedron kernel and the icosahedral symmetry is extended within the boundary of a few shells. 

Typical examples are carbon interstitial carbonyl clusters such as the octahedral Co6C(CO) -2, the trigonal prismatic Co6C(CO)i52- and its isoelectronic (mononegative) nitrogen interstitial Co6N(CO)15 or the icosahedral clusterNi12Ge(CO)222 with the interstitial atom (Ge or Sn) in the centre of aNi icosahedron. 

The rich-gold clusters [ (Ph3P)Au 7Co(CO)2](PF6)2 343 [435], [ (Ph3P)Au 7Rh (C0)2](N03)2 344 [454] and [ (Ph3P)Au 6(ClAu)2Rh(dmpi)2](PF6) 345 [454, 458] may be described as derivatives of a metal-centered Au12 icosahedron formed by removing five and seven vertices from the icosahedral cage. 

The /3-R105 boron allotrope has a much more complex structure with 105 B atoms in the unit cell (space group R3m, a = 1014.5 pm, a = 65.28°). A basic building unit in the crystal structure is the B84 cluster illustrated in Fig. 13.2.5(a) it can be considered as a central Bi2a icosahedron linked radially to 12 B6 half-icosahedra (or pentagonal pyramids), each attached like an inverted umbrella to an icosahedral vertex, as shown in Fig. 13.2.5(b). 

From the above discussion, it is evident that mixed cluster ions of the type Ar M exhibit strong magic numbers at values of (n + m) = 13, 19, 55, 71, and 147 in a variety of different studies. These values correspond to the completion of the first, second, and third icosahedral shells occurring at 13, 55, and 147 whereas 19 and 71 correspond to especially stable subshells formed by interpenetrating double icosahedron structures. The size and symmetry of the dopant moiety appear to be the most important factors in observing magic numbers that can be rationalized on the basis of icosahedral-like structures. The inability to observe magic numbers has been attributed to the distortion of the icosahedral structure due to size and steric factors associated with the dopant ion which destroys the delicate balance between the monomer interactions. One of the issues that has been interpreted differently involves the location of the dopant atomic/molecular... 

A simple treatment of the stability requirements of a boron icosahedron in a solid was presented early. An icosahedral boron cluster was shown to require two external electrons. The icosahedron is linked to its neighbors via normal covalent bonds. This description leads to a simple understanding of the stability of the BeO and BeP stractures. 

The structures of the large Au clusters with 8-13 gold atoms may be described to be derived from a centered icosahedral Ann cluster by removal of peripheral gold atoms. The structure of [Au9(Ptol3)8] + can be derived from a centered icosahedron, but it is more simply pictured as a bicapped centered chair as shown in (25). The cluster [Au9(Ptol3)9](N03)3 has been prepared by NaBH4 reduction of [Au(Ptol)3(N03)]. The structure of the related ion,... 

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