  Frenkel excitons are primary photoexcitations in molecular semiconductors and
are unequivocally responsible for their optical properties. However, the
spectrum of corresponding biexcitons - bound exciton pairs - has not been
resolved thus far in organic materials. We correlate the energy of two-quantum
exciton resonances with that of the single-quantum transition by means of
nonlinear coherent spectroscopy. Using a Frenkel exciton model, we relate the
biexciton binding energy to the magnitude and the sign of the exciton-exciton
interaction energy and the inter-site hopping energy, which are molecular
parameters that can be quantified by quantum chemistry. Unexpectedly, excitons
with interchain vibronic dispersion reveal intrachain biexciton correlations,
and vice-versa. The details of biexciton correlations determine exciton
bimolecular annihilation, which is ubiquitous in organic semiconductors. It is
crucial to quantify these interactions in order to establish a
quantum-mechanical basis for their rate constants. Our work enables new
opportunities for general insights into the many-body electronic structure in
molecular excitonic systems such as organic semiconductor crystals, molecular
aggregates, photosynthetic light-harvesting complexes, and DNA.
