Electronic structure of reduced titanium dioxide

We use the local spin-density approximation in density-functional theory to study the electronic structure of ${\mathrm{TiO}}_{2}$ and its (110) stoichiometric surface, as well as ${\mathrm{Ti}}_{2}{\mathrm{O}}_{3}$ and the reduced (110) surface, which are examples of reduced ${\mathrm{TiO}}_{2},$ in order to address the question of how donated electrons are distributed among the previously unoccupied Ti $3d$ states. We conclude that, whereas a split-off band in ${\mathrm{Ti}}_{2}{\mathrm{O}}_{3}$ probably leads to Mott-Hubbard insulating behavior, a picture of itinerant electrons in approximately one-electron states with Stoner exchange splitting is an appropriate description in the case of the reduced surface. Our calculations will be useful in interpreting photoemission experiments as well as measurements of core-level shifts at surfaces.