We present a density functional theory (DFT) study aimed at understanding the injection and recombination processes that occur at the interface between PbS QDs and TiO2 oxide nanoparticles with different morphologies. The calculated injection rates fall in the picosecond timescale in good agreement with the experiments. In addition, our simulations show that the (101) facet of TiO2 more favourably accommodates the QD, resulting in stronger electronic couplings and faster electron injections than the (001) surfaces. Despite this, the (101) slab is also more prone to faster electron recombination with the valence band of the QD, which can lead to overall lower injection efficiencies than the (001) surface.