  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.
