Tight-binding description of cyclo[n]carbons and carbynes

Abstract

To investigate the electronic properties of one-dimensional sp-hybridized carbon allotropes, we performed tight-binding calculations on an atomic ring and a finite linear chain as theoretical models to the cumulenic cyclo[n]carbons and carbynes, respectively. Our results show that the energies of an atomic ring match the energies of a finite chain when the number of atoms in a ring is twice the number of atoms in the chain and an extra two more atoms. Also, the atomic ring energies have double degeneracies, with values equal to the finite chain except at E_ring = ±2γ, where γ is the hopping parameter of the nearest-neighbor carbon atoms.