Time-Dependent Density-Functional Description of the 1La State in Polycyclic Aromatic Hydrocarbons: Charge-Transfer Character in Disguise?

The electronic spectrum of alternant polycyclic aromatic hydrocarbons (PAHs) includes two singlet excited states that are often denoted L-1(a) and L-1(b). Time-dependent density functional theory (TD-DFT) affords reasonable excitation energies for the L-1(b) state in such molecules, but often severely underestimates L-1(a) excitation energies and fails to reproduce observed trends in the L-1(a) excitation energy as a function of molecular size. Here, we examine the performance of long-range-corrected (LRC) density functionals for the L-1(a) and L-1(b) states of various PAHs. With an appropriate choice for the Coulomb attenuation parameter, we find that LRC functionals avoid the severe underestimation of the L-1(a) excitation energies that afflicts other TD-DFT approaches, while errors in the L-1(b) excitation energies are less sensitive to this parameter. This suggests that the L-1(a) states of certain PAHs exhibit some sort of charge-separated character, consistent with the description of this state within valence-bond theory, but such character proves difficult to identify a priori. We conclude that TD-DFT calculations in medium-size, conjugated organic molecules may involve significant but hard-to-detect errors. Comparison of LRC and non-LRC results is recommended as a qualitative diagnostic.