  The solution of the Bethe-Salpeter equation within the framework of many-body
perturbation theory has turned out to be a benchmark for ab-initio calculations
of optical properties of semiconductors and insulators. Commonly, however, the
coupling between the resonant and anti-resonant excitations is neglected which
is referred to as the Tamm-Dancoff approximation (TDA). This is well justified
in cases where the exciton binding energy is much smaller than the band gap.
Here, we report on the optical properties of a representative series of organic
semiconductors where we find the TDA to no longer hold. We observe an increase
of the exciton binding energy of up to 44% thereby improving the agreement with
experiment.
