Real Temperature Model of Dynamic Disorder in Molecular Crystals

Charge carrier mobilities in ordered organic semiconductors are limited by inherent vibrational phonons that scatter carriers. To improve a material's intrinsic mobility, restricting particularly detrimental modes with molecular substitutions may be a viable strategy. Here, we develop a probabilistic temperature-dependent displacement model that we couple with the density functional dimer projection protocol to predict effective electronic coupling fluctuations. The phonon-induced deviations from the equilibrium electronic couplings are used to infer the detriment of low-frequency phonons on charge carrier mobilities in a set of organic single crystals. We show that asymmetric sliding motions in pentacene and 2,6-diphenylanthracene induce large electronic coupling fluctuations, whereas seesawlike motions cause large fluctuations in rubrene, 9,10-diphenylanthracene, and, 2,6-diphenylanthracene. Vibrational analyses revealed that the asymmetric sliding phonon in rubrene persists only in the low-mobility direction of the crystal. Therefore, rubrene's intrinsic high mobility is likely due to the absence of this source of disorder in its high-mobility conduction channels. This model can be used to identify particularly harmful or helpful phonons in crystalline materials and may provide design rules for developing materials with intrinsically low disorder.