The electronically excited states of methylene (CH2), ethylene (C2H4), butadiene (C4H6), hexatriene (C6H8), and ozone (O-3) have long proven challenging due to their complex mixtures of static and dynamic correlations. The semistochastic heat-bath configuration interaction (SHCI) algorithm, which efficiently and systematically approaches the full configuration interaction (FCI) limit, is used to provide close approximations to the FCI energies in these systems. This article presents the largest FCI-level calculation to date on hexatriene, using a polarized double-zeta basis (ANO-L-pVDZ), which gives rise to a Hilbert space containing more than 10(38) determinants. These calculations give vertical excitation energies of 5.58 and 5.59 eV, respectively, for the 2(1)A(g) and 1(1)B(u) states, showing that they are nearly degenerate. The same excitation energies in butadiene/ANO-L-pVDZ were found to be 6.58 and 6.45 eV. In addition to these benchmarks, our calculations strongly support the presence of a previously hypothesized ring-minimum species of ozone that lies 1.3 eV higher than the open-ring-minimum energy structure and is separated from it by a barrier of 1.11 eV.