Electronic and Optical Properties of the Narrowest Armchair Graphene   Nanoribbons Studied by Density Functional Methods
  In the present study, a series of planar poly(p-phenylene) (PPP) oligomers with n phenyl rings (n = 1 - 20), designated as n-PP, are taken as finite-size models of the narrowest armchair graphene nanoribbons with hydrogen passivation. The singlet-triplet energy gap, vertical ionization potential, vertical electron affinity, fundamental gap, optical gap, and exciton binding energy of n-PP are calculated using Kohn-Sham density functional theory and time-dependent density functional theory with various exchange-correlation density functionals. The ground state of n-PP is shown to be singlet for all the chain lengths studied. In contrast to the lowest singlet state (i.e., the ground state), the lowest triplet state and the ground states of the cation and anion of n-PP are found to exhibit some multi-reference character. Overall, the electronic and optical properties of n-PP obtained from the omegaB97 and omegaB97X functionals are in excellent agreement with the available experimental data. 
Chia-Nan Yeh, Pei-Yin Lee, Jeng-Da Chai
physics.chem-ph cond-mat.mes-hall cond-mat.mtrl-sci physics.comp-ph quant-ph