CPGN: A Coordination Polyhedron Graph Network for Multi-Scale Crystal Property Prediction Using Dual-Level Atomic and Geometric Representations

Accurate prediction of crystal properties remains a fundamental challenge in computational materials science. Although graph neural networks (GNNs) such as CGCNN, MEGNet, ALIGNN, and SchNet have achieved consistent performance, they represent crystals solely at the atomic level, relying on message passing to implicitly capture local environments. However, many material properties are governed by coordination polyhedra rather than individual atoms. To address this limitation, we propose the Coordination Polyhedron Graph Network (CPGN), a multi-scale GNN that jointly learns from atom-, bond-, and coordination-polyhedron-level representations. CPGN integrates an atom graph, a line graph for angular interactions, and a coordination polyhedron graph connected through shared polyhedral relationships. Polyhedra are described using physically meaningful geometric descriptors, while an interleaved message-passing framework with bidirectional cross-attention enables effective information exchange across structural scales. CPGN is evaluated on three benchmark datasets: Materials Project (69,239 structures), JARVIS-DFT (75,993 structures), and QM9 (130,831 molecules) using standardized splits for fair comparison. On Materials Project, CPGN achieves a formation energy MAE of 0.054 eV/atom and the band-gap MAE of 0.251 eV, outperforming CGCNN, SchNet, MEGNet, and ALIGNN. On JARVIS-DFT, CPGN provides accurate multi-task predictions, achieving MAEs of 0.0925 eV/atom for formation energy, 0.227 eV for optical band gap, 14.01 GPa for bulk modulus, 11.28 GPa for shear modulus, and 0.088 eV/atom for stability. On QM9, CPGN achieves a HOMO MAE of 0.030 eV and competitive performance for LUMO (0.023 eV) and HOMO–LUMO gap (0.038 eV), demonstrating its effectiveness across both crystalline and molecular systems.