Supercharging semi-empirical Quantum Chemistry with Machine Learning

Understanding the mechanisms that underpin chemical and biological processes under realistic conditions is crucial for the development of novel pharmaceutical and technological applications. Over the past years, machine learning (ML) has revolutionized our approach to gain such insights promising to bypass the prohibitive costs of ab initio calculations. However, purely data-driven ML models often suffer from limited transferability as well as reduced access to consistent molecular properties and chemical insights. Another computationally-efficient alternative is semi-empirical quantum chemistry (SEQC), which constructs effective, reduced-order Hamiltonians from parametric interaction models. While offering seamless access to electronic properties, SEQC can show poor accuracy outside the domain of its usual fixed, element-wise parametrization. Here, we present an extended SEQC formalism dynamically parametrized via ML. This hybrid approach provides an accurate description of organic molecules outperforming fixed-parameter SEQC as well as standard ML in terms of accuracy, transferability, and data efficiency. The hybrid framework allows us to avoid deep ML architectures without loss of performance, which together with the SEQC structure offers a high degree of interpretability. Combining computational efficiency, transferability, and scalability, hybrid SEQC/ML paves the way to an accurate understanding of chemical processes at practically relevant length and time scales.