Predicting interface structure using the minima hopping method

We adapt the minima hopping method (MHM) to the problem of interfacial structure prediction and apply it to study a canonical problem, the tilt grain boundaries in ${\mathrm{SrTiO}}_{3}$. Our method employs a hybrid approach by first exploring the potential energy surface (PES) of different grain boundary samplings with an empirical force field, among which the fifteen candidates with lower energies are then refined using ab initio density functional theory (DFT) calculations. During the exploratory stage, we bias the search using a local order parameter to primarily sample various reconstructions in the vicinity of the interface, while preserving the crystallinity of the bulk regions. We further enhance the search by incorporating initial structures with rigid body displacements to account for translational variations between bulk phases, enabling the MHM to effectively generate both stoichiometric and nonstoichiometric ${\mathrm{SrTiO}}_{3} \mathrm{\ensuremath{\Sigma}}3$(111)[110] and $\mathrm{\ensuremath{\Sigma}}3$(112)[110] grain boundaries. From an algorithmic standpoint, MHM outperforms earlier studies based on genetic algorithms (GA) by identifying more stable interfacial structures of several ${\mathrm{SrTiO}}_{3}$ grain boundaries. The performance of the present implementation of the MHM approach is primarily limited by exploring an approximate description of the PES with a rather simple Buckingham potential. This limitation leads to variations in performance when compared to approaches utilizing more advanced surrogate PES models, such as direct DFT-PES sampling or GA with the embedded atom method (EAM). Despite the present limitations, the MHM approach is able to yield interfacial structures with comparable or lower interfacial energies in specific cases, such as $\mathrm{\ensuremath{\Sigma}}3$(111)[110] $\mathrm{\ensuremath{\Gamma}}=1,\ifmmode\pm\else\textpm\fi{}0.5$ and $\mathrm{\ensuremath{\Sigma}}3$(112)[110] $\mathrm{\ensuremath{\Gamma}}=\ifmmode\pm\else\textpm\fi{}1,\ensuremath{-}2$, underscoring the robustness of the MHM approach even with a simple approximation of the DFT PES. The MHM interfacial structure prediction method thus offers an efficient approach to understanding the grain boundaries and heterointerfaces at the atomic scale, providing an important prerequisite for effective materials design.