Classification of defects on rutile TiO₂ (110) surface: Hybrid versus Hubbard-U DFT

Titanium oxide surfaces are among the most important oxide surfaces with applications as catalytic, anti-bacterial, construction materials, etc. Defects on these surfaces play an important role in their applications. Using two different DFT treatments, hybrid functionals and DFT+U, we have attempted classification of oxygen vacancy, single and double hydrogen defects. In agreement with previous DFT+U modeling we find that electronic signatures of all three defects are very similar. In addition, for each defect we have found dozens of quasi-degenerate minima differing by their position, orbital character, and spin coupling. The estimated migration barriers for some of the minima indicate that they may be thermally populated at finite temperatures. The main result of the study is the coupling between the hybrid DFT solution and the DFT+U maintaining the defect electronic signature. We find that the values of the U so determined are unexpectedly small, around 2.7 eV. We have also addressed the possibility of existence of charged defects. Our calculations indicate that charge defects are not favored.