Bridging Ab Initio Accuracy and Semi-Empirical Efficiency with a Physics-Informed Machine Learning Force Field

High-fidelity quantum chemical calculations are prohibitively expensive for large systems and long molecular dynamics simulations. Semi-empirical methods offer efficiency but often sacrifice accuracy and generalizability. Purely data-driven machine learning force fields struggle with out-of-training-data generalization and physical interpretability. We introduce NeuroForceTB, a novel Physics-Informed Machine Learning force field, to overcome these limitations. It combines a Generalized Tight-Binding (GXT-TB) theory framework with a neural network. NeuroForceTB leverages GXT-TB's physical foundation to efficiently extract robust descriptors: eigenvalues and gradient information of the atomic local density matrix, which encode spin, local charge, and atomic environment structures. The neural network then learns high-level quantum mechanical corrections to GXT-TB's predictions, refining accuracy while preserving computational efficiency. Our comprehensive evaluation demonstrates that NeuroForceTB achieves near-ab initio accuracy for energies and forces, outperforming existing methods across diverse chemical challenges. It exhibits superior force prediction on a standard benchmark, enhanced accuracy for diverse long-range non-covalent interactions (including hydrogen-bonded and van der Waals systems), and robust performance for open-shell systems and complex chemical reactions, accurately describing reactant and transition state energies. Crucially, NeuroForceTB maintains high computational efficiency with near-linear scaling, making it ideal for stable, efficient, and high-precision molecular dynamics simulations of complex systems over extended timescales.