Boron fullerenes

Imitation of carbon fullerenes In an analogy to carbon fullerenes, Lipscomb and co-workers proposed boron fullerenes as large closo boron hydride based on Descartes-Euler formula P + F=E- -2 P for vertices, Ffor faces. 

From Cgo to Bioo Novel boron fullerene Bioo was recently predicted by Mukhopadhyay et al It should be more stable than Bgo predicted by Yakobson and co-workers,and more stable than Bgg isomers. It was developed from Cgo fullerene, which has 12 pentagons and 30 hexagons. 

Belt states of boron fullerenes The enhanced conducting feature of the BFs is closely related to their geometrical and electronic properties, which are characterized by a series of belt states at the celestial equator. 

Proposed New Materials Boron Fullerenes, Nanotubes, and Nanotori... 

Table II. Stability Factors for the Boron Fullerenes BnHn, based on HF/3-21G calculations [12].

Table IV. Stability Factors for the Multicage Boron Fullerenes B H , based on HF/STO-3G calculations [19].

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... 

We have shown how a simple idea, the Descartes-Euler formula, defines the boron fullerenes as the geometrical duals of the carbon fullerenes. As the carbon fullerenes are actually existing molecules, the Descartes-Euler formula is immediately suggestive of the possible existence of their boron duals. This is confirmed by quantum chemical molecular orbital calculations which indicate considerable stability for boron flillerene cage and multi-cage geometries. Therefore we encourage attempts at the synthesis of these proposed compounds. 

There are many properties of carbon fullerenes that have aroused interest. Because of the similarities inherent in the topological relationship of duals, it is assumed boron fullerenes would be equally interesting. We draw attention to one property in particular, viz., superconductivity. The carbon fullerenes can be induced to display high ten erature superconductivity. The mechanism for superconductivity in these compounds is unknown. If the BCS mechanism happened to be relevant, then [2]... 

Gindulyte, A. Lipscomb, W.N. Massa, L. (1998). Proposed Boron Nanotubes. Inorganic Chemistry, Vol. 37, No. 25, (December 1998), pp. 6544-6545, ISSN 0020-1669 Gindulyte, A. Krishnamachari, N. Lipscomb, W.N. Massa, L. (1998). Quantum Chemical Calculations of Propwsed Multicage Boron Fullerenes. Inorganic Chemistry, Vol. 37, No. 25, (December 1998), pp. 6546-6548, ISSN 0020-1669 Golberg, D. Bando, Y. Sato, T. Grobert, N. Reyes-Reyes, M. Terrones, H. Terrones, M. 

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