Cluster closed cage, closo

Because of their completely deltahedral pseudospherical shapes, the dianions, the singly charged monocarbaborane anions [CB iH ], and the neutral carboranes of formulae C2B 2H are known as closo (closed cage) clusters. Their skeletal shapes are shown in the left-hand column of Figure 3.1. 

There are a number of other important boron cage compounds as well as structurally similar metal atom cluster molecules that are not closed polyhedra. Generally, these may be regarded as derived from closed polyhedra by removal of one or two vertices. The diagram below illustrates how removal of one or two vertices generates the so-called nido and arachno relatives of a closo octahedral structure. 

Boranes and carboranes have structures in which their skeletal B- or C-atoms form triangular-faced polyhedra. There are basically three structural types, namely the closo- (an euphonious modification of the Greek clovo = cage, i. e., a complete or closed polyhedron), the nido (from Latin nest-like ) and the arachno- (from Greek cob-web ) structure. Each of these three types is adopted by cluster compounds of specific atomic ratios. c/o o-Structures occur in borane dianions B H , in car-borane anions (CB iH ) , and carboranes (C2B 2H ). Each skeletal atom has a single H-atom terminally attached by a bond directed outwards, away from the polyhedron center (see the example of BioHio in Fig. 3-1 below). Wo-Structures are adopted by boranes B H +4 and their related carboranes CB iH +3, C2H 2H +2 etc., and amc/z/2o-structures by boranes B H +6 and related carboranes CB iH +5, C2B 2H +4 etc. In other words, carboranes have the general formula [(CH) (BH) Hc] , where the sum a + c + x) is equal to 2 for a closo-structure, 4 for a /do-structure, and 6 for an amc/z o-structure. 

In closo, complete cage, structures all of the atoms of the cluster that are bonded to each other lie approximately, and often accurately, equidistant from the centre of the molecule. That is, they lie on the surface of a sphere. Electrons which are responsible for cluster bonding will lie between the bonded atoms and, so, approximately, will be largely located close to the surface of the sphere. Now, if the sort of orbital which can lie on the surface of a sphere has any particular characteristics, these characteristics are likely to be reflected in the bonding of the cluster atoms. Indeed, as a first... 

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