A GGA+U study of electron localization and oxygen vacancy clustering in rutile TiO_2-x

Using the a generalized gradient approximation + Hubbard U (GGA + U) method in the framework of the density functional theory (DFT), we probe the insights into the electron localization and oxygen vacancy (V_O) clustering in rutile TiO_2-x. First, we examine the dependence of the characteristic gap level in the intrinsic rutile TiO₂ on the Hubbard U parameter through investigating a single oxygen vacancy in 3 × 3 × 4 supercell of rutile TiO₂. Results show that the use of a moderate effective U (3–5 eV) accounts well for the Ti 3d electrons to induce a localized state within the band gap, consistently addressing the characteristic gap level observed experimentally. Furthermore, two oxygen vacancies are found to energetically cluster in a V_O-Ti-V_O chain, which induces several states inside the forbidden energy region of TiO₂. The appearance of these gap states leads to the enhancement in photoabsorption through effectively functioning as stepping stones for valence electrons to jump into conduction band, offering an accountable explanation for the experimentally observed promotion in the photocatalytic activities of rutile TiO₂ under high temperature. Detailed thermodynamic and kinetic analyses have been made to present the high favorability for forming such a cluster. The present work provides a new insight for tailoring the photonic and optoelectronic applications of TiO₂-based materials.