Unraveling the Band Gap Trend in the Narrowest Graphene Nanoribbons from the Spin-Adapted Excited-Spectra Reduced Density Matrix Method

Polybenzenes as the narrowest graphene nanoribbons with versatile electronic properties are widely studied both theoretically and technologically. Here, we examine the singlet-triplet band gap as a function of length for two members of the oligobenzene family: the acene and phenacene chains. We observe that the prediction of the band gap is highly sensitive to the accurate treatment of the electron correlation. The excited-spectra two-electron reduced density matrix (2-RDM) method, which computes the excited states from a variationally computed ground-state 2-RDM, yields finite band gaps for all finite chain lengths through 10 rings as well as in the extrapolated infinite ring limits of both acenes and phenacenes. In contrast, we find that weakly correlated methods like configuration interaction singles and time-dependent density functional theory predict a crossing of the singlet- and triplet-state energies of the acene chains at a finite ring size, with the triplet becoming the energetically lowest state at longer chain lengths. Recent experiments through decacene and 9-phenacene agree with the correlated 2-RDM calculations, showing that both acene and phenacene chains in the large polymer limit possess finite band gaps.