Symmetry of infinite tubular polymers: application to buckytubes

Abstract

The geometric «line» symmetries possible for a long tubular polymer are identified and their irreducible representations developed, in a canonical format. Assumptions built around a subgroup of pure translations are avoided, while at the same time maintaining a «local» development that leads to a systematic presentation of band structure for electronic or vibrational structure computations. As an illustration of these techniques, they are applied to analytically solve the Huckel model for all possible «buckytubes», these being long tubular polymers composed entirely from a hexagonal net of carbon atoms