Polyhedral elements

Rules 3 and 4 Sharing of polyhedral elements. The presence of shared edges, and particularly of shared faces, in a coordinated structure decreases its stability this effect is larger for cations with large valence and small coordination number, and is especially large in case the radius ratio approaches the lower limit of stability of the polyhedron. 

Pauling s fourth rule further exemplifies the preceding one by stating that in a crystal containing different cations, those with large valences and small coordination number tend not to share polyhedral elements with each other. 

Main Group Element Metallaboranes. A variety of metaHaborane clusters, which incorporate main group metals in vertex positions of polyhedral metaHaborane clusters, have been reported. Examples are (BH BeB H Q (165), MgB2QH22 20(C2H )2 (166), [(CH2)HgB2QH22]A (167),... 

Boranes also form derivatives ia which main group elements occupy a bridging position between two boron atoms, rather than a polyhedral vertex. An extensively studied system is -R MB Hg, where R = H, CH, C2H3, halogen, and M = Si, Ge, Sn, Pb (185). The stmcture of l-Br- J.-[(CH3)3Si]-B3H2... 

For Sm, Eu, and Yb, on the other hand, nanocapsules containing carbides were not found in the cathode deposit by either TEM or XRD. To see where these elements went, the soot particles deposited on the walls of the reaction chamber was investigated for Sm. XRD of the soot produced from Sm203/C composite anodes showed the presence of oxide (Sm203) and a small amount of carbide (SmC2). TEM, on the other hand, revealed that Sm oxides were naked, while Sm carbides were embedded in flocks of amorphous carbon[12J. The size of these compound particles was in a range from 10 to 50 nm. However, no polyhedral nanocapsules encaging Sm carbides were found so far. 

So far, three types of i-QCs appear in the literature Mackay [17], Bergman [18], and Tsai types [19], which have been differentiated on the basis of the polyhedral cluster sequences observed in the respective 1/1 AC structures. These are commonly represented as shown in Fig. 2. An i-QC is concluded to be Mackay-type if its 1/1 AC contains a 54-atom multiply endohedral cluster ordered, from the center out, as a small icosahedron (12 atoms), a larger icosahedron (12), and an icosidodecahe-dron (30). This motif occurs in ACs that consist of transition metals and main-group elements on the right side of the periodic table such as Al-(Pd,Mn)-Si [17,20]. In... 

More often, polyhedral clusters with strong metal-metal (or metalloid-metalloid) bonding are the major structural motifs of classic Zintl phases. These are nominally salts composed of reduced p- (i.e., post-transition) elements that are usually inter-bonded into closed shell polyanions plus active metal cations, originally the alkali... 

The polyhedral boranes and carboranes discussed above may be regarded as boron clusters in which the single external orbital of each vertex atom helps to bind an external hydrogen or other monovalent atom or group. Post-transition main group elements are known to form clusters without external ligands bound to the vertex atoms. Such species are called bare metal clusters for convenience. Anionic bare metal clusters were first observed by Zintl and co-workers in the 1930s [2-5], The first evidence for anionic clusters of post-transition metals such as tin, lead, antimony, and bismuth was obtained by potentiometric titrations with alkali metals in liquid ammonia. Consequently, such anionic post-transition metal clusters are often called Zintl phases. 

Rules for counting the number of skeletal electrons provided by each vertex atom need to be established in order to determine the number of skeletal electrons in polygonal and polyhedral clusters of the post-transition elements. The rules discussed above for polyhedral boranes can be adapted to bare post-transition metal vertices as follows ... 

Bare group 13 metal vertices (e.g., Ga, In, Tl) provide, as noted above, only one skeletal electron each to polyhedral cluster structures. Thus it is not surprising that the bare metal cluster ions Enz (E = group 13 element) found in homonuclear alkali-metal/group 13 intermetallic phases [86-89] (mainly for In and Tl) have charges less negative than the — (n + 2) (i.e., z [Pg.21]

Today the chemistry of diborane and the polyboranes is well understood [2] and much of it is textbook knowledge. Therefore, after a brief survey, emphasis will focus on the development of polyhedral borane chemistry within recent decades, and even restricting discussions to homopolyboranes only certain areas can be dealt with. This incorporates synthetic procedures, the chemistry of some polyboranes and particularly polyborane anions. Other chapters of this book are devoted to heteropolyboranes such as the carbaboranes (see Chapter 3.1), azaboranes and related heteropolyboranes (see Chapter 3.3) of the main group elements. In these areas enormous progress has been achieved within the last two decades. 

A metal atom cluster as defined by Cotton [1] is still a very broad term, because non-metal atoms can also be part of the cluster core. In this chapter mainly two types of metal atom clusters are presented the polyborane analogous polyhedral and the metalloid clusters E Rr of group 13 elements E. The structures and bonding of the polyhedral clusters with n < r are similar to those in the well-known polyboranes. 

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). 

Reaction of 13a with elemental Li in Et20 yields 15a, the first derivative of the simplest polyhedral closo-carborane of the anionic series [CH(BH) ] (n = 4) (Scheme 3.2-9). Polyhedral members with n = 3 are transition states of type 5 as shown in Section 3.2.2.1. 

Of course, having flat faces, these elements cannot represent the curved surface on the sphere exactly. Using an adequately large number of such elements, a sufficiently accurate polyhedral approximation is possible. Inside each tetrahedron the unknown potential is approximated using a polynomial that is first order in the space coordinates (x, y, z)- The polynomial can be so written that the four unknown coefficients are the values of the potential at the four nodes (vertices) of the tetrahedron, cfii, d)2, d>3, and <1)4 ... 

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