TILING RULES FOR TOROIDAL MOLECULES

We describe a class of periodic tiling that corresponds to toroidal arrangements of trivalent atoms with pentagonal, hexagonal, and heptagonal rings. The relaxation of model carbon atoms in molecules represented by these tilings is used to yield estimates of the energy per bond, the energy of the least bound atoms, and the highest occupied and lowest unoccupied molecular-orbit energies. The results support the point of view that stable toroidal carbon molecules can exist. © 1995 The American Physical Society.