Integrating Graph Neural Networks and Many-Body Expansion Theory for Potential Energy Surfaces

Rational design of next-generation functional materials relies on quantitative predictions of their electronic structures beyond single building blocks. First-principles quantum mechanical (QM) modeling becomes infeasible as the size of a material grows beyond hundreds of atoms. In this study, we developed a new computational tool, FBGNN-MBE, which integrates fragment-based graph neural networks (FBGNN) into the fragment-based many-body expansion (MBE) theory, and demonstrated its ability to reproduce full-dimensional potential energy surfaces (FD-PES) for hierarchic chemical systems with manageable accuracy, complexity, and interpretability. In particular, we divided the entire system into basic building blocks (fragments), evaluated their single-fragment energies using a first-principles QM model, and addressed many-fragment interactions using structure–property relationships trained by FBGNNs. In our preliminary investigations, we evaluated the performance of FBGNN-MBE models in predicting two-body (2B) and three-body (3B) energies for three benchmark systems - water, phenol, and water-phenol mixture clusters. Both models demonstrated excellent accuracy, which are significantly outperformed conventional GNN models, with R2 values
above 0.92 for 2B energies and greater than 0.84 for 3B energies, while maintaining low mean absolute errors (MAEs) (< 1.0 kcal/mol). Our development of FBGNN-MBE showcased a promising new framework that integrates deep learning models into fragment-based QM methods, with future applications focused on replacing QM methods for efficient potential energy surface evaluations in complex multi-fragment systems, marking a significant step toward the computational design of large functional materials.