Incorporating long-range interactions via the multipole expansion into ground and excited-state molecular simulations

Simulating long-range interactions remains a significant challenge for molecular machine learning (ML) 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 present in QM/MM simulations more accurately. By incorporating the multipole expansion, we are able to effectively capture environmental long-range effects in both ground and excited states. Benchmark evaluations demonstrate the superior performance of including higher-order features from atoms in the environment. To showcase the efficacy of our model, we accurately predict properties such as energies and forces for nickel complex systems and simulate the nonadiabatic excited-state dynamics of a ring-opening reaction in solution. Furthermore, we show that transfer learning from foundational models trained without any explicit environment enhances data efficiency, reducing the need to generate large QM/MM datasets before training. These examples demonstrate the versatility of our approach, paving the way for efficient, accurate, and scalable simulations of complex molecular systems and materials across electronic states.