New carbon molecules in the form of elbow-connected nanotori

Toroidal caged molecules of carbon have been investigated previously as constructed from elbows formed from armchair (5,5) and zigzag (9,0) nanotubes connected through a pentagonal and heptagonal defect at each bend site. In this paper, we consider these elbows, and we describe two new elbows constructed from (3,3)-(5,0) and (4,4)-(7,0) nanotubes. By assuming the constituent atoms remain in their ideal positions on the nanotube sections, we determine the bend angle and nanotube lengths that characterize each elbow in the unconstrained state and also when the elbow is constrained as when incorporated in a toroidal caged molecule. Using these results, we describe specific examples of new families of carbon caged molecules and the associated geometric parameters of these molecules. In order to properly prescribe the new molecules, we need to introduce a new nomenclature N(n(1), m(1))(p)M(n(2), m(2))(q)..., where (n(1), m(1)) and (n(2), m(2)) designate the component nanotubes, p, q, ... are the number of atoms in each nanotube section, and N, M, ... are the number of each section of nanotube making up the complete molecule. Of the numerous molecules introduced here, only two molecules in the 5(5,5)(p)5(9,0)(q) family have been discussed in previous work, while the remainder are new. The modeling of these toroidal molecules as perfect tori is facilitated by the particular method which we adopt to determine the representative geometric parameters for these molecules. Illustrative values of these parameters for various example molecules are also given.