Efficiently predicting directional carrier mobilities in organic materials with the Boltzmann transport equation

Describing charge carrier anisotropy in crystalline organic semiconductors with ab initio methods is challenging because of the weak intermolecular interactions that lead to both localized and delocalized charge transport mechanisms. Small polaron hopping models (localized) are generally used to describe materials with small charge carrier mobilities, while periodic band models (delocalized) are used to describe materials with high charge carrier mobilities. Here, we prove the advantage of applying the constant relaxation time approximation of the Boltzmann transport equation (BTE) to efficiently predict the anisotropic hole mobilities of several unsubstituted (anthracene, tetracene, pentacene, and hexacene) and substituted (2,6-diphenylanthracene, rubrene, and TIPS-pentacene) high-mobility n-acene single crystals. Several density functionals are used to optimize the crystals, and the composite density functional PBEsol0-3c/sol-def2-mSVP predicts the most experimentally similar geometries, adequate indirect bandgaps, and the theoretically consistent n-acene charge transport mobility trend. Similarities between BTE and Marcus mobilities are presented for each crystal. BTE and Marcus charge carrier mobilities computed at the same geometry result in similar mobility trends, differing mostly in materials with more substitutions or structurally complex substituents. By using a reduced number of calculations, BTE is able to predict anisotropic carrier mobilities efficiently and effectively for a range of high-mobility organic semiconductors.