First-principles spin-polarized calculations on the reduced and reconstructed<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">TiO</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>(110) surface

We have performed plane-wave pseudopotential density-functional theory calculations on the stoichiometric and reduced ${\mathrm{TiO}}_{2}$ (110) surface, the 2\ifmmode\times\else\texttimes\fi{}1 and 1\ifmmode\times\else\texttimes\fi{}2 reconstructions of the surface formed by the removal of bridging-oxygen atoms, and on the oxygen vacancy in the bulk. The effect of including spin polarization is investigated, and it is found to give a qualitatively different electronic structure compared with a spin-paired description. In the spin-polarized solutions, the excess electrons generated by oxygen reduction occupy localized band-gap states formed from Ti (3d) orbitals, in agreement with experimental findings. In addition, the inclusion of spin polarization substantially lowers the energy of all the systems studied, when compared with spin-paired solutions. However, spin-polarization does not change the relative stability of the two reconstructions, which remain energetically equivalent.