Optical spectra and exchange-correlation effects in molecular crystals*

We report first-principles GW-Bethe Salpeter Equation and Quantum Monte Carlo calculations of the optical and electronic properties of molecular and crystalline rubrene (C$_{42}$H$_{28}$). We predict the formation of intermolecular, charge-transfer spin-singlet excitons with energies in close agreement with the observed yellow-green photoluminescence in rubrene microcrystals. In contrast, spin-triplet excitons are localized and intramolecular with a predicted phosphorescence at the red end of the optical spectrum. We find that the exchange energy plays a fundamental role in raising the energy of intramolecular spin-singlet excitons above the intermolecular ones. Exciton binding energies are predicted to bearound 0.5~eV (spin singlet) to 1~eV (spin triplet). The calculated electronic gap is 2.8~eV. The theoretical absorption spectrum agrees very well with recent ellipsometry data.