Propensity Rules for the Stability of Odd-Numbered Fullerenes: A Semiempirical Proposal

The structures of C 119 and C 129, the two lowest odd-numbered fullerenes, are investigated by semiempirical quantum chemical calculations. In the process, the use of a recently proposed parametrization for a tight-binding Extended-Hückel model is validated to study the relative stability of fullerenes. Three general routes for the generation of the structures of odd-numbered fullerenes are described and used to generate systems that can be loosely characterized as having either a four-membered ring or a patch of adjacent pentagons, or a set of multiple connections between the cages of the pristine fullerenes. The structures of the six isomers of C 119 obtained in this manner are optimized and it is confirmed that the most stable isomer of C 119 has C 2 symmetry and forms three bonds between the C 59 and the C 60 moieties. By analogy with C 119, 56 structures of C 129 are generated and their geometries are optimized. As in the case of C 119, it is found that the most stable isomer of C 129 can be formed both from the reaction of C 59 with C 70 and from the reaction of C 60 with C 69 . On the basis of the calculation, five propensity rules for the stability of odd-numbered carbon clusters are proposed and a source of exception is discussed.