Structure of carbon nanorings

A new family of carbon nanorings with circular centerlines is predicted. The ring structure is parametrized by the chirality of the precursor graphene sheet that is rolled to produce a nanotube and then bent to form a nanoring, and by the number of repeated units defining the ring diameter. The individual atomic positions over rings with zig-zag, armchair, and intermediate chiralities are found by minimizing the Tersoff-Brenner potential with respect to the Cartesian coordinates of the carbon atoms. Rings with large diameters have nearly circular cross-sectional shapes, whereas rings with small diameters have elliptical, wedding-band, and dog-bone cross-sectional shapes. The inside surface of a chiral (10, 5) ring develops periodic ripples in a range of intermediate diameters. The flattened shapes uncovered are similar to those of inorganic nanorings recently observed in the laboratory.