Atomic Charge Schemes Comparison for Fe Single Atom in Graphitic Carbon: Insights from Quantum Simulations and Machine Learning

Single-atom catalysts (SACs), where a transition-metal atom is embedded in graphitic carbon materials, have shown great potential as effective catalysts. The metal atom plays a major role in determining the catalytic reactivity, and substrate–metal interaction can tailor the intrinsic properties of metal, for example, the atomic partial charge. However, in quantum simulations, various charge schemes are used to assign charges for molecules and materials. It remains unclear whether the atomic partial charge of the metal in SACs is correlated across different charge schemes and if they exhibit different behaviors in response to variations in metal–substrate interactions. In this study, we investigated the behavior of Bader, Mulliken, Hirshfeld, Charge Model 5 (CM5), and Density Derived Electrostatic and Chemical 6 (DDEC6) charge schemes for Fe-centered SACs using quantum simulations and machine learning models. By tuning the structural and chemical parameters in the systems, we examined 166 Fe-centered graphene flakes and compared different charge schemes on the Fe atom. We observed that the DDEC6, Mulliken, and Hirshfeld charges exhibit more noticeable correlations than Bader and CM5 charges. Our findings also indicate that the local chemical environment plays a crucial role in determining the atomic charge of Fe in SACs and that different charge schemes present varied responses to changes in metal–substrate interactions. Additionally, we utilized machine learning (ML) models to predict all five charge schemes by gathering features from geometric, atomic, and electronic properties. Our machine learning models successfully predicted the CM5 scheme, which is primarily determined by electronic properties. However, for DDEC6, Bader, Mulliken, and Hirshfeld schemes, geometric features played a significant role, resulting in lower prediction accuracy than CM5. We expect that the insights gained from this study will contribute to a better understanding of the selection of appropriate charge schemes for SACs design.