Lowest Optical Excitations in Molecular Crystals: Bound Excitons versus Free Electron-Hole Pairs in Anthracene

By solving the Bethe-Salpeter equation for the electron-hole Green function for crystalline anthracene we find the lowest absorption peak generated by strongly bound excitons or by a free electron-hole pair, depending on the polarization direction being parallel to the short or the long molecular axis, respectively. Both excitations are shifted to lower energies by pressure. The physical difference of these excitations is apparent from the electron-hole wave functions. Our findings are a major contribution to solve the long-standing puzzle about the nature of the lowest optical excitations in organic materials.