The charge transport properties of hybrid halide perovskites are investigated with a combination of density functional theory including van der Waals interaction and the Boltzmann theory for diffusive transport in the relaxation time approximation. We find the mobility of electrons to be in the range 5-10 cm<sup>2</sup>V<sup>-1</sup>s<sup>-1</sup> and that for holes within 1-5 cm<sup>2</sup>V<sup>-1</sup>s<sup>-1</sup>, where the variations depend on the crystal structure investigated and the level of doping. Such results, in good agreement with recent experiments, set the relaxation time to about 1 ps, which is the time-scale for the molecular rotation at room temperature. For the room temperature tetragonal phase we explore two possible orientations of the organic cations and find that the mobility has a significant asymmetry depending on the direction of the current with respect to the molecular axis. This is due mostly to the way the PbI3 octahedral symmetry is broken. Interestingly we find that substituting I with Cl has minor effects on the mobilities. Our analysis suggests that the carrier mobility is probably not a key factor in determining the high solar-harvesting efficiency of this class of materials.
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