Beyond Scalar Electrostatics: Multipole Features for Long-Range Molecular Machine Learning

Simulating long-range interactions remains a significant challenge for molecular machine learning potentials due to the need to accurately capture interactions over large spatial regions. In this work, we integrate the multipole expansion into equivariant ML potentials to model long-range interactions in QM/MM simulations more accurately. By incorporating the multipole expansion, we capture structured environmental effects beyond scalar electrostatic descriptors. Benchmark evaluations on solvated QM/MM systems demonstrate that including higher-order multipole features improves the accuracy of predicted energies and forces compared to scalar Coulomb descriptors and Ewald-based approaches, with low-order terms providing a favorable accuracy-cost trade-off. Furthermore, we show that transfer learning from foundational models trained without explicit environmental information improves data efficiency in QM/MM settings. These results demonstrate the effectiveness of our approach for accurate and scalable simulations of complex molecular systems with long-range interactions.