States S 1 and S 2 are optically dark in one-photon spectroscopy but S 3 is dipole-allowed and doublydegenerate. Calculations at the TD-B3LYP/6-31G* level conform to this simple four-orbital model with > 99% fidelity, and though the TD-DFT results might at first seem complex, in the sense that there is no excited state that is primarily HOMO(2e 1g ) → LUMO(1e 2u ) in nature, given the symmetry of the system there is little else that these states could have been. Symmetry here is a parlor trick that makes the situation seem more complicated than it really is, leading to unresolvable multiconfigurational character. wherein a minimum of four orbitals and two determinants is required to describe the low-lying excited states, even within the single-excitation ansätze of CIS and TD-DFT. A more interesting example, which is not driven by symmetry, is the keto-defect polyfluorene oligomer whose S 0 → S 2 transition was considered in Figs. and and whose S 0 → S 3 transition is depicted in Fig. . There is interest in these molecules for fabrication of organic light-emitting devices, as this is one of the few classes of materials that can span the whole range of visible wavelengths at low operating voltage, and also one of the few classes of materials with good emission properties for blue light. These properties arise from highly delocalized excited states of the π system that may exhibit large polarizabilities and hyperpolarizabilities, giving rise to nonlinear optical properties. In the present example, such states are accessed at higher excitation energies such as ω = 4.5 eV for S 0 → S 3 . The oscillator strength for this delocalized transition (f = 4.5) is about 25 times greater than that of the defect-localized S 0 → S 2 excitation.