Published by the American Physical Society through the American Institute of Physics
Physical Review B, Condensed matter and materials physics vol:65 issue:11
An infinite series of (3, 6) cages is defined by trivalent carbon polyhedra composed of hexagonal and four triangular rings. A zone-folding construction is applied to the graphene band structure to yield explicit expressions for the pi-molecular orbitals, energies, and symmetries of the cages that depend only on four indices m, n, p, and q. Leapfrog members of the series (m-n=0 mod 3 and p-q=0 mod 3) have closed shells in a neutral form with two filled nonbonding orbitals; all others have closed shells as dications. Quantum chemical calculations on C-12,C-48, and C-52(2+) confirm this result. Embedding relationships are proved for the spectra of (3, 6) cages related by inflation transformations corresponding to stretching and rotation of the polyhedral net.