  The nature and extent of the spin-entanglement in the triplet-triplet
biexciton with total spin zero in correlated-electron $\pi$-conjugated systems
continues to be an enigma. Differences in the ultrafast transient absorption
spectra of free triplets versus the triplet-triplet can give a measure of the
entanglement. This, however, requires theoretical understandings of transient
absorptions from the optical spin-singlet, the lowest spin-triplet exciton as
well as from the triplet-triplet state, whose spectra are often overlapping and
hence difficult to distinguish. We present a many-electron theory of the
electronic structure of the triplet-triplet, and of complete
wavelength-dependent excited state absorptions (ESAs) from all three states in
a heteroacene dimer of interest in the field of intramolecular singlet fission.
The theory allows direct comparisons of ESAs with existing experiments as well
as experimental predictions, and gives physical understandings of transient
absorptions within a pictorial exciton basis that can be carried over to other
experimental systems.
