Optical spectra and exchange-correlation effects in molecular crystals

We report the first-principles $GW$-Bethe--Salpeter equation and quantum Monte Carlo calculations of the optical and electronic properties of molecular and crystalline rubrene $({\mathrm{C}}_{42}{\mathrm{H}}_{28})$. Many-body effects dominate the optical spectrum and quasiparticle gap of molecular crystals. We interpret the observed yellow-green photoluminescence in rubrene microcrystals as a result of the formation of intermolecular, charge-transfer, spin-singlet excitons. 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 be around $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ (spin singlet) to $1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ (spin triplet). The calculated electronic gap is $2.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The theoretical absorption spectrum agrees very well with recent ellipsometry data.