The
description of low-lying ππ* states of linear acenes
by standard electronic structure methods is known to be challenging.
Here, we broaden the framework of this problem by considering a set
of fused heteroaromatic rings and demonstrate that standard electronic
structure methods do not provide a balanced description of the two
(typically) lowest singlet state (La and Lb)
excitations. While the Lb state is highly sensitive to
correlation effects, La suffers from the same drawbacks
as charge transfer excitations. We show that the comparison between
CIS/CIS(D) can serve as a diagnostic for detecting the two problematic
excited states. Standard TD-DFT and even its spin-flip variant lead
to inaccurate excitation energies and interstate gaps, with only a
double hybrid functional performing somewhat better. The complication
inherent to a balanced description of these states is so important
that even CC2 and ADC(2) do not necessarily match the ADC(3) reference.