PM6-ML: The Synergy of Semiempirical Quantum Chemistry and Machine Learning Transformed into a Practical Computational Method

Machine learning (ML) methods offer a promising route to the construction of universal molecular potentials with high accuracy and low computational cost. It is becoming evident that integrating physical principles into these models, or utilizing them in a ∆-ML scheme, significantly enhances their robustness and transferability. This paper introduces PM6-ML, a ∆-ML method that synergizes the semiempir- ical quantum-mechanical (SQM) method PM6 with a state-of-the-art ML poten- tial applied as a universal correction. The method demonstrates superior perfor- mance over standalone SQM and ML approaches and covers a broader chemical space than its predecessors. It is scalable to systems with thousands of atoms, which makes it applicable to large biomolecular systems. Extensive benchmarking confirms PM6-ML’s accuracy and robustness. Its practical application is facili- tated by a direct interface to MOPAC. The code and parameters are available at https://github.com/Honza-R/mopac-ml.