Overpotential for photocatalytic water-splitting with TiO2
Photon absorption by titania results in an excitation of an electron from the valence band to the conduction band.  The difference in energy of an electron in the valence band and the conduction band is the band gap, which for titanium dioxide is about 3.3 eV.

What matters for electrochemistry, though, is the absolute voltage of (i) the excited electron, and (ii) the absolute voltage of the "hole" left in the valence band, not the just the difference between them (gap).  That is far more difficult.

The effective electrochemical voltages of the excited electron (or hole) can differ from what the desired electrochemical reaction is.  So there could still be an overpotential.  For titania, one paper I found estimates of the absolute energies of the valence band "hole" and the conduction band electron of -7.8 eV and -4.5 eV, respectively (at pH 0).  The thermodynamic potential for water oxidation is -5.8 eV, 2 eV higher than the hole energy.  That energy is lost if the hole is used to power water oxidation.  You could thus view excited titania having an overpotential of 2 eV for the water oxidation reaction.  In contrast, the theoretical potential for proton reduction is -4.5 eV, close to the conduction band electron energy. 

Thus the energetics of bulk titania provide lots of overpotential for the water oxidation reaction but the tradeoff is that a high band gap means only high-energy photons can power the electrochemistry.  Lowering the band gap would make more and longer wavelengths of radiation available to power water photolysis, but the band gap can only be lowered in certain ways.  For titania, it would not be very desirable to lower the energy of the conduction band, because that would mean excited electrons would not be able to reduce protons to hydrogen .  Thus, the only way to lower the band gap is by raising the energy of the valence band, which would both lower the overpotential and and make more types of radiation accessible for powering water photolysis.