Comparative analysis of absorption resonances between carbynes and cyclo[n]carbons.

Two approaches are presented here to analyze the absorption resonances between carbynes and cyclo[n]carbons, namely the analytical tight-binding model to calculate the optical selection rules of cumulenic atomic rings and chains and thetime-dependent density functional theory for the optical investigation of polyynic carbon ring and chains. The optical absorption spectra of the carbon ring match that of the finite chain when their eigen energies align following theNring=2Nchain+2rule, which states that the number of atoms in an atomic ringNringis twice the number of atoms on a finite chainNchainwith two additional atoms. Two representative atomic chains are chosen for our numerical calculations, specifically carbynes withN=7and8carbon atoms as optical resonance spectra match to a recently synthesized carbon ring called cyclo[18]carbon.

2N+4-rule and an atlas of bulk optical resonances of zigzag graphene nanoribbons.

Development of on-chip integrated carbon-based optoelectronic nanocircuits requires fast and non-invasive structural characterization of their building blocks. Recent advances in synthesis of single wall carbon nanotubes and graphene nanoribbons allow for their use as atomically precise building blocks. However, while cataloged experimental data are available for the structural characterization of carbon nanotubes, such an atlas is absent for graphene nanoribbons.