Incorporating Long-Range Interactions via the Multipole Expansion into Ground and Excited-State Molecular Simulations

TL;DR

The paper tackles the challenge of modeling long-range electrostatics in molecular simulations with machine learning. It develops FieldMACE, which integrates a multipole expansion into the MACE framework and couples a QM region to an MM environment via attention-weighted long-range terms, enabling accurate ground- and excited-state predictions with improved efficiency. Key contributions include the attention-weighted multipole expansion, scalable QM/MM interfacing, demonstrated accuracy on solvated molecules, and substantial data-efficiency gains through transfer learning from foundational models. The approach offers a scalable, transferable tool for large-scale, environment-sensitive quantum simulations, with potential impact on photochemistry and biomolecular modeling.

Abstract

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 introduce FieldMACE, an extension of the message-passing atomic cluster expansion (MACE) architecture that integrates the multipole expansion to model long-range interactions more efficiently. By incorporating the multipole expansion, FieldMACE effectively captures environmental and long-range effects in both ground and excited states. Benchmark evaluations demonstrate its superior performance in predictions and computational efficiency compared to previous architectures, as well as its ability to accurately simulate nonadiabatic excited-state dynamics. Furthermore, transfer learning from foundational models enhances data efficiency, making FieldMACE a scalable, robust, and transferable framework for large-scale molecular simulations.

Figures (4)

• Figure 1: Architecture of the message-passing neural network integrated with the multipole expansion a) The short-range blocks operate through a message-passing scheme aggregating information in the atoms local neighborhood, whereas the long-range blocks collect information on molecular mechanics (MM) nodes through the multipole expansion. b) The long-range block uses pairwise attention weightings that are computed between the quantum mechanics (QM) region and MM atoms. These are combined with MM node features and the QM node features in the multipole expansion described in Section \ref{['sec:MPE']}.
• Figure 2: a) Power spectrum produced from the dynamics of benzene in a water box. Population curves resulting from photodynamics simulations using b) FieldMACE and c) quantum chemistry, showing the ring-opening reaction of furan after being excited to the second excited state ($S_2$). Transitions to $S_1$ and $S_0$ are present in both approaches.
• Figure 3: Comparison of transfer learning from MACE-OFF foundational model (red curves) against randomly initialized FieldMACE models (blue curves). Evaluation of transfer and ordinary learning models with respect to energies (top row) and forces (bottom row) of molecules solvated in water: a) and d) benzene , b) and e) uracil and c) and f) retinoic acid .
• Figure 4: Population curves of furan starting in the third excited singlet state for transfer learning models using a) 600, b) 150, and c) 30 data points and non-transfer learning models using d) 600, e) 150, and f) 30 data points.