Electronic and optical properties of doped organic semiconductors are dominated by local interactions between donor and acceptor molecules. However, when such systems are in crystalline form, long-range order competes against short-range couplings. In a first-principles study on three experimentally resolved bulk structures of quaterthiophene doped by (fluorinated) tetracyanoquinodimethane, we demonstrate the crucial role of long-range interactions in donor/acceptor co-crystals. The band structures of the investigated materials exhibit direct band-gaps decreasing in size with increasing amount of F atoms in the acceptors. The valence-band maximum and conduction-band minimum are found at the Brillouin zone boundary and the corresponding wave-functions are segregated on donor and acceptor molecules, respectively. With the aid of a tight-binding model, we rationalize that the mechanisms responsible for these behaviors, which are ubiquitous in donor/acceptor co-crystals, are driven by long-range interactions. The optical response of the analyzed co-crystals is highly anisotropic. The absorption onset is dominated by an intense resonance corresponding to a charge-transfer excitation. Long-range interactions are again responsible for this behavior, which enhances the efficiency of the co-crystals for photo-induced charge separation and transport. In addition to this result, which has important implications in the rational design of organic materials for opto-electronics, our study clarifies that cluster models, accounting only for local interactions, cannot capture the relevant impact of long-range order in donor/acceptor co-crystals.
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