Oxygen Vacancy Diffusion in Rutile TiO₂: Insight from Deep Neural Network Potential Simulations

Defects play a crucial role in the surface reactivity and electronic engineering of titanium dioxide (TiO₂). In this work, we have used an active learning method to train deep neural network potentials from the ab initio data of a defective TiO₂ surface. Validations show a good consistency between the deep potentials (DPs) and density functional theory (DFT) results. Therefore, the DPs were further applied on the extended surface and executed for nanoseconds. The results show that the oxygen vacancy at various sites are very stable under 330 K. However, some unstable defect sites will convert to the most favorable ones after tens or hundreds of picoseconds, while the temperature was elevated to 500 K. The DP predicated barriers of oxygen vacancy diffusion were similar to those of DFT. These results show that machine-learning trained DPs could accelerate the molecular dynamics with a DFT-level accuracy and promote people's understanding of the microscopic mechanism of fundamental reactions.