  Photochemical reactions on semiconductors are anisotropic, since they occur
with different rates on surfaces of different orientation. Understanding the
origin of this anisotropy is crucial to engineering more efficient
photocatalysts. In this work, we use hybrid density functional theory (DFT) to
identify the surfaces associated with the largest number of photo-generated
carriers in different semiconductors. For each material we create a spherical
heat map of the probability of optical transitions at different wave vectors.
These maps allow to identify the directions associated with the majority of the
photo-generated carriers and can thus be used to make predictions about the
most reactive surfaces for photochemical applications. Results indicate that it
is generally possible to correlate the heat maps with the anisotropy of the
bands observed in conventional band-structure plots, as previously suggested.
However, we also demonstrate that conventional bands-structure plots do not
always provide all the informations and that taking into account the
contribution of all possible transitions weighted by their transition dipole
moments is crucial to obtain a complete picture.
