Classification scheme for toroidal molecules

Abstract

A class of planar periodic tilings, which correspond to toroidal arrangements of trivalent atoms, with pentagonal, hexagonal and heptagonal rings, has been constructed. Each tiling is characterized by a set of four integers and defines a toroidal molecule. The tiling rules are motivated by geometric considerations and the tiling patterns are rich enough to describe a wide class of toroidal carbon molecules, with a broad range of shapes and numbers of atoms. The molecular dimensions are simply related to the integers that determine the tiling. The configurational energy and the delocalisation energy of several molecules obtained in this way were computed for Tersoff and Hückel models. The results indicate that many of these molecules are not strained, and may be expected to be stable. The influence of size on the Hückel spectrum bears both similarities and differences compared with the case of tubules.