A posteriori error estimate and adaptivity for QM/MM models of defects

Hybrid quantum mechanics/molecular mechanics (QM/MM) models play a pivotal role in molecular simulations. These models provide a balance between accuracy, surpassing pure MM models, and computational efficiency, offering advantages over pure QM models. Adaptive approaches have been developed to further improve this balance by allowing on -the -fly selection of the QM and MM subsystems as necessary. We propose a novel and robust adaptive QM/MM method for practical material defect simulations. To ensure mathematical consistency with the QM reference model, we employ machine -learning interatomic potentials (MLIPs) as the MM models (Chen et al., 2022 and Grigorev et al., 2023). Our adaptive QM/MM method utilizes a residual -based error estimator that provides both upper and lower bounds for the approximation error, thus indicating its reliability and efficiency. Furthermore, we introduce a novel adaptive algorithm capable of anisotropically updating the QM/MM partitions. This update is based on the proposed residual -based error estimator and involves solving a free interface motion problem, which is efficiently achieved using the fast marching method. We demonstrate the robustness of our approach via numerical tests on a range of crystalline defects comprising edge dislocations, cracks and di-interstitials.