A Posteriori Error Estimate and Adaptivity for QM/MM Models of Crystalline Defects

Abstract

Hybrid quantum/molecular mechanics models (QM/MM methods) are widely used in material and molecular simulations when pure MM models cannot ensure adequate accuracy but pure QM models are computationally prohibitive. Adaptive QM/MM coupling methods feature on-the-fly classification of atoms, allowing the QM and MM subsystems to be updated as needed. The state-of-art "machine-learned interatomic potentials (MLIPs)" can be applied as the MM models for consistent QM/MM methods with rigorously justified accuracy. In this work, we propose a robust adaptive QM/MM method for practical material defect simulation, which is based on a developed residual-based error estimator. The error estimator provides both upper and lower bounds for the approximation error, demonstrating its reliability and efficiency. In particular, we introduce three minor approximations such that the error estimator can be evaluated efficiently without losing much accuracy. To update the QM/MM partitions anisotropically, a novel adaptive algorithm is proposed, where a free interface motion problem based on the proposed error estimator is solved by employing the fast marching method. We implement and validate the robustness of the adaptive algorithm on numerical simulations for various complex crystalline defects