  The electronically excited states of methylene (CH$_2$), ethylene
(C$_2$H$_4$), butadiene (C$_4$H$_6$), hexatriene (C$_6$H$_8$), and ozone
(O$_3$) have long proven challenging due to their complex mixtures of static
and dynamic correlations. Semistochastic heat-bath configuration interaction
(SHCI), 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 $2^1{\rm A}_{\rm g}$ and $1^1{\rm B}_{\rm
u}$ 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.
