  In previous work we have shown that the Density Matrix Renormalization Group
(DMRG) enables near-exact calculations in active spaces much larger than are
possible with traditional Complete Active Space algorithms. Here, we implement
orbital optimisation with the Density Matrix Renormalization Group to further
allow the self-consistent improvement of the active orbitals, as is done in the
Complete Active Space Self-Consistent Field (CASSCF) method. We use our
resulting DMRGCASSCF method to study the low-lying excited states of the
all-trans polyenes up to C24H26 as well as \beta-carotene, correlating with
near-exact accuracy the optimised complete \pi-valence space with up to 24
active electrons and orbitals, and analyse our results in the light of the
recent discovery from Resonance Raman experiments of new optically dark states
in the spectrum.
