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

TL;DR

This paper introduces a robust adaptive QM/MM method for crystalline defect simulations that employs machine-learning potentials and a residual-based error estimator to efficiently and reliably improve model accuracy.

Contribution

It presents a novel adaptive algorithm with anisotropic updates for QM/MM partitions, ensuring mathematical consistency and efficiency in defect modeling.

Findings

The method provides reliable error bounds for QM/MM approximations.

Numerical tests demonstrate robustness across various crystalline defects.

The approach efficiently updates partitions using free interface motion and fast marching.

Abstract

Hybrid quantum/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. 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 wide range of crystalline defects.