Description of Metavalent Bonding in Chalcogenide System—A Comparative Study of Machine Learning Potential Models

Metavalent bonding (MVB) is a unique and important bonding mechanism that differs from traditional ionic, covalent, and metallic bonds. Materials with MVB found in certain chalcogenides exhibit distinctive properties such as high electrical conductivity, low thermal conductivity, and enhanced electronic polarizability. These attributes make MVB materials suitable for various applications like thermoelectrics, phase-change memory, and topological insulators. Understanding MVB would be essential for designing and optimizing next-generation functional materials.<br/>Previous studies using density functional theory (DFT) have analyzed the structural and electronic properties of MVB at the atomic level. However, the size limitations of DFT pose challenges in accurately representing the competition between electron delocalization found in metallic bonding and electron localization seen in covalent or ionic bonding. The localized states in MVB materials, which are critical for functional electronic devices, can be larger than the tight periodic boundary conditions used in DFT calculations, potentially misrepresenting them as delocalized states. Additionally, the high computational cost of DFT makes it difficult to observe the dynamic properties of MVB, such as the crystallization behavior in phase-change memory devices. These challenges highlight the need for alternative approaches to study MVB properties.<br/>Recently, there has been increasing interest in using machine learning potentials (MLPs) as an alternative to DFT. MLPs can compute energy and atomic forces much faster than DFT while maintaining similar accuracy. However, replicating the distinct structural characteristics resulting from the complex nature of MVB remains a challenge for MLPs. This study investigates the feasibility of describing MVB in the chalcogenide GeSe system using different MLP models: Behler-Parrinello type neural network (BPNN) with atom-centered symmetry functions via the SIMPLE-NN package,¹ the moment tensor potential (MTP) using the MLIP package,² and the equivariant graph neural network (GNN) with the SevenNet package.³ We compared the amorphous structures produced by these MLP models to the amorphous structures generated by DFT. The amorphous structures generated with MLPs exhibit subtle differences in local structures, such as radial distribution functions (RDFs) and angular distribution functions (ADFs). The MTP and GNN models showed higher accuracy in describing ring-topology compared to the BPNN model by considering higher-order many-body interactions. Interestingly, only the GNN model succeeds in describing fine details in Peierls-like structural distortions that characterize MVB in amorphous chalcogenides. We confirmed that GNN models can overcome the limitations of atom-centered descriptor models and effectively reproduce the characteristics of MVB by transferring the neighboring environment through message-passing. Additionally, the electronic structures of the amorphous structures were calculated using DFT single-point calculations, revealing that only the structures generated with the GNN potential accurately reproduced the energy gap and density of states (DOS) characteristics, while the other models exhibited the gap closing. To understand how GNN models can capture MVB characteristics, we also test various hyperparameters, including the maximum degree of spherical harmonics for graph nodes and edges, the number of interaction layers, and the maximal correlation order of tensor products.<br/><br/>1. Lee, Kyuhyun, et al. "SIMPLE-NN: An efficient package for training and executing neural-network interatomic potentials." <i>Comput. Phys. Commun.</i> 242 (2019).<br/>2. Novikov, Ivan S., et al. "The MLIP package: moment tensor potentials with MPI and active learning." <i>Mach. Learn.: Sci. Technol.</i> 2.2 (2020).<br/>3. Park, Yutack, et al. "Scalable Parallel Algorithm for Graph Neural Network Interatomic Potentials in Molecular Dynamics Simulations." <i>J. Chem. Theory Comput.</i> (2024).