  Bound and unbound Frenkel-exciton pairs are essential transient precursors
for a variety of photophysical and biochemical processes. In this work, we
identify bound and unbound {Frenkel}-exciton complexes in an electron push-pull
polymer semiconductor using coherent two-dimensional spectroscopy. We find that
the dominant $A_{0-1}$ peak of the absorption vibronic progression is
accompanied by a sub-peak, each dressed by distinct vibrational modes. By
considering the Liouville pathways within a two-exciton model, the imbalanced
cross peaks in one-quantum rephasing and non-rephasing spectra can be accounted
for by the presence of pure biexcitons. The two-quantum non-rephasing spectra,
on the other hand, provide direct evidence for unbound exciton pairs and
biexcitons with dominantly attractive force. In addition, the spectral features
of unbound exciton pairs show mixed absorptive and dispersive character,
implying many-body interactions within the correlated {Frenkel}-exciton pairs.
Our work offers novel perspectives on the rich photophysical processes in
semiconductor polymers with the presence of Frenkel exciton complexes.
