Condensed polyhedra

In an investigation of Mn5Si3-derivative phases (Mn5Si3-type hosting structures), Zheng et al. (2002) remarked that extended structures featuring polyhedra or condensed polyhedra are ubiquitous in chemistry. Octahedron-based frameworks of reduced halides are known to be very versatile hosts, as they can accommodate... 

Rh4Pt core (Fig. 26) similar to that found in 118, with a dihedral angle of 70° between the two Rh2Pt triangles. The 78-CVE count is consistent with SEPT adapted for condensed polyhedra. 

When the number of metal atoms in a cluster increases, the geometries of the clusters become more complex, and some are often structurally better described in terms of capped or decapped polyhedra and condensed polyhedra. For example, the first and second clusters listed in Table 19.4.3 are a capped octahedron and a bicapped octahedron, respectively. Consequently, capping or decapping with a transition-metal fragment to a deltapolyhedral cluster leads to an increase or decrease in the cluster valence electron count of 12. When a transition-metal atom caps a triangular face of the cluster, it forms three M-M bonds with the vertex atoms, so according to the 18-electron rule, the cluster needs an additional 18 - 6 = 12 electrons. The parent octahedron of [Os6(CO)is]2- has g = 86, the monocapped octahedron Osy(CO)2i has g = 98, and the bicapped octahedron [Oss(CO)22]2- hasg = 110. 

The Capping Principle has been derived for evaluating the electron count in condensed polyhedra from those of its component polyhedra. Thus, it has been established that the total electron count in a condensed polyhedron is equal to the sum of the electron count for the parent polyhedron minus the electron count characteristic of the atom, pairs of atoms, or face of atoms which are common to both polyhedra. The frontier orbitals of the capping fragment are matched in... 

The total electron count for a condensed polyhedron is the sum of the electron counts of parent polyhedra e.g. fusion of two closo metal deltahedra a) with ... 

Another contribution is represented by an investigation of a cubic thallium cluster phase of the Bergmann type Na13(TlA.Cdi A.)27 (0.24 < x <0.33) (Li and Corbett 2004). For this phase too the body centred cubic structure (space group Im 3, a = 1587-1599 pm) may be described in terms of multiple endo-hedral concentric shells of atoms around the cell positions 0, 0, 0, and 14,14,14. The subsequent shells in every unit are an icosahedron (formed by mixed Cd-Tl atoms), a pentagonal dodecahedron (20 Na atoms), a larger icosahedron (12 Cd atoms) these are surrounded by a truncated icosahedron (60 mixed Cd-Tl atoms) and then by a 24 vertices Na polyhedron. Every atom in the last two shells is shared with those of like shells in adjacent units. A view of the unit cell is shown in Fig. 4.38. According to Li and Corbett (2004), it may be described as an electron-poor Zintl phase. A systematic description of condensed metal clusters was reported by Simon (1981). 

The formation of radiation defects under irradiation of the fullerene films by the bombarding particles leads to the essential modification of electronic subsystem, which determines their optical and electrophysical properties. However, the mechanisms of radiation defect formation with the use of different types of irradiation and dose load, and also the nature of a change in the electronic properties in this case are studied insufficiently. It is necessary to note that in the case of the condensed state of fullerenes not only the radiation damages of the molecular polyhedrons, which by themselves influence the redistribution of... 

Figure 7. The Friauf polyhedron. It consists of 12 smaller atoms at the comers of a truncated tetrahedron, which has four hexagonal faces and four triangular faces, and a larger atom at the center. In condensation, hexagonal faces are shared.

Figure 16-11 Au Ni core of the 236-electron [Au6Ni12(CO)24]2 dianion. This 18-vertex polyhedron of cubic Td (43m) symmetry may be viewed as a face-to-face condensation of four octahedral AujNi3 fragments at alternate faces of a central Au octahedron (A. J. Whoolery and L. F. Dahl, J. Am. Chem. Soc. 1991,113, 6683.)...

Figure 20. The carbonyl distribution around the Mu polyhedron found for the anions of (a) Mu-polyhedron based on face-to-face condensed octahedra sharing a common edge coincident with the 3-fold axis (b)(NMe4)3[Rh i(/r-CO)i2(CO)ii).Me2CO (c) (NMe4)3[Rhu(/<-CO)i3(CO)io].C6H5Me (d)(NEt4)3[Pt2Rh,i(/t-CO)u(CO) ].

Papiemik, R., Hubert-Pfalzgraf, L. G., and Massiani, M. C., Synthesis, characterization and reactivity of lead(II) alkoxides and oxoalkoxides Condensation to oxoalkoxides as a general stmctural feature. Polyhedron, 10, 1657 (1991). 

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