Boron fullerenes structure

Carbon nanotubes are cylindrical structures related to carbon fullerene structures. Indeed, carbon nanotube cylinders are often capped at their ends with hemispherical carbon fiillerenes, illustrating the close relation of the two types of structure. Nanotube structures are of great interest because of their mechanical and one-dimensional electrical properties [2]. In our discussion of boron nanotubes [8], the duals of carbon nanotubes, we employ a generalization of Descartes-Euler formula, viz., the Euler-Poincare formula for a cylinder,... 

The Descartes-Euler formula, equation 1, has been used to define the class of molecules called boron fullerenes as the topological duals of carbon fiillerenes. In order to extend the concept of duality to nanotubes, however, the Descartes-Euler formula must be generalized to the Euler-Poincare formula as in Equation 2. One may understand why the right side of Equation 2 is zero by use of Betti numbers [10]. Betti numbers may be calculated as a count of the number of critical points of each type (i.e., minima, saddle points, maxima) associated with the geometrical structure of a molecule. The Euler-Poincare formula [11] may be written in a very general way in terms of Bptti numbers as... 

Heteroatom fullerene-type clusters — The possibility of incorporation of hetero atoms into C clusters has excited the attention of both theoreticians and experimentalists since the earliest days of fullerene chemistry, particularly in view of the known stability and ubiquity of organic heterocycles. The structural relationship between Ceo and /3-rhombohedral boron has already been alluded to (p. 142). 

Since the discovery of buckminsterfullerene (C o) [85NAT(318)162] and other fullerenes (Cig. C70), these molecules have been intensely studied, both experimentally and theoretically. Likewise, several reports on heterofullerenes containing heteroatoms such as nitrogen and boron have appeared (91JPC4948 91JPC10564). The incorporation of heteroatoms is expected to modify the structural and electronic features of these structures, and have thus attracted some interest. 

Another early suggestion was that some of the fullerene carbon atoms could be replaced by another element such as nitrogen or boron.1811 Such heterofullerenes are envisaged to have strongly altered chemical properties in comparison to the all-carbon structures.1811 For example, as the substitution number of an electronegative element such... 

In the next example, a mixed SAM is discussed which aims to utilize photoinduced energy and electron transfer processes to create a photocurrent in an approach which is reminiscent of the natural photosynthetic process. Figure 5.33 illustrates the molecular structures of the components of interest, i.e. the molecular triad ferrocene-porphyrin-fullerene (Fc-P-C6o) and a boron dipyrrin thiol (BoDy) [67]. Mixed monolayers were generated by coadsorption onto vacuum-deposited gold... 

Figure 5.33 Structures of disulfide-terminated (a) pyrene (Pyr) and (b) porphyrin (Por), and thiol-terminated (c) boron-dipyrin (BoDy), (d) porphyrin (ThPor), and (e) the ferrocene-porphyrin-fullerene triad (Fc-P-C60)...

The basal B atoms of adjacent pentagonal pyramids are interconnected to form a B60 icosahedron that resembles fullerene-Cgo - The large B60 icosahedron encloses the Bi2a icosahedron, and the resulting Bg4 cluster can be formulated as B 12a B 12 B6o Additionally, a six-coordinate B atom lies at the center of symmetry between two adjacent Bio condensed units, and the crystal structure is an intricate coordination network resulting from the linkage of B10-B-B10 units and B84 clusters, such that all 105 atoms in the unit cell except one are the vertices of fused icosahedra. Further details and the electronic structure of /1-R105 boron are described in Section 13.4.6. 

There are several ways to combine rings into polycychc and cage structures (e.g. spirocyclic systems and fused rings). These will not be discussed here. Theoretical speculations have been made about the possible existence of purely inorganic (carbon-free) fullerene-like polycychc cages, for example, boron-nitrogen molecules or sihcon analogs. ... 

A third type of solid is represented by elements such as carbon (which exists in the forms graphite, diamond, and the fullerenes), boron, silicon, and all metals. These substances all have atoms at the lattice points that describe the structure of the solid. Therefore, we call solids of this type atomic solids. Examples of these three types of solids are shown in Fig. 10.12. 

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