  The rutile TiO$_2$ (110) surface reduced by the bridging oxygen vacancy,
bridging hydroxyl group or Ti interstitial atom has been investigated by
calculating their electronic structures using the density functional theory
plus U method. It is found that defect states located in the forbidden band gap
can enhance optical absorption. When the surface is highly reduced, the defect
states approach the valence band. More importantly, defects induce a
substantial up-shift of the conduction band edge, rendering the reduced surface
stronger reducibility. The shifts of both conduction and valence band edges are
due to the dipole moments created by these defects.
