Squaraine dyes are known to photosensitize large band gap semiconductors via a charge-injection process from a singlet excited state. We have modeled this process with the simplest squaraine chromophore and titanium dioxide (TiO2). A TiO2-squaraine excited-state complex has been optimized with an adjacent conical intersection. This suggests that the charge injection from the excited-state squaraine into the conduction band of the semiconductor should be an ultrafast photochemical process in agreement with recent experimental results. In terms of Marcus-Hush electron transfer theory, the charge transfer for the TiO2-squaraine model occurs in the inverted region, which is a strong indication for the equivalence between electron transfer in the inverted region and radiationless decay through a sloped conical intersection.