Molecular Dynamics Simulations of SrTiO$_3$ with Oxygen Vacancies using Neural Network Potentials

A precise analysis of point defects in solids requires accurate molecular dynamics (MD) simulations of large-scale systems. However, ab initio MD simulations based on density functional theory (DFT) incur high computational cost, while classical MD simulations lack accuracy. We perform MD simulations using a neural network potential (NNP) model (NNP-MD) to predict the physical quantities of both pristine SrTiO$_3$ and SrTiO$_3$ in the presence of oxygen vacancies (V$_{\text{O}}$). To verify the accuracy of the NNP models trained on different data sets, their NNP-MD predictions are compared with the results obtained from DFT calculations. The predictions of the total energy show good agreement with the DFT results for all these NNP models, and the NNP models can also predict the formation energy once SrTiO$_3$:V$_{\text{O}}$ data are included in the training data sets. Even for larger supercell sizes that are difficult to calculate using first-principles calculations, the formation energies evaluated from the NNP-MD simulations well reproduce the extrapolated DFT values. This study offer important knowledge for constructing accurate NNP models to describe point-defect systems including SrTiO$_3$:V$_{\text{O}}$.