Bipolaron formation induced by oxygen vacancy at rutile TiO ₂(110) surfaces

The formation of polarons in the presence of oxygen vacancies at the rutile TiO₂ surfaces is a widely studied topic due to its importance in complex surface reactions. In this paper, we have studied polaron formation both near and infinitely far away from the oxygen vacancy on the (110) rutile TiO₂ surface by ab initio density functional theory and screened hybrid functionals. We conclude that a polaron prefers to stay near the oxygen vacancy due to electrostatic attraction between the positively charged oxygen vacancy and polaron. Although two polarons introduced by an oxygen vacancy repel each other, the oxygen vacancy effectively binds two polarons, forming a bipolaron. Moreover, our calculated vacancy formation energies elucidate the conditions under which the polarons are likely to be formed.