Machine Learning Prediction of Two-Dimensional Polymerization of Nitrogen in FeN x

Nitrogen-rich iron nitrides (FeN x ), a representative class of transition metal nitrides, have attracted a considerable amount of interest due to their polymeric nitrogen motifs and outstanding mechanical and energetic properties. However, accurately modeling such transition metal compounds within DFT+ U frameworks requires careful U value selection. Moreover, no polymerized nitrogen structures beyond one-dimensional have been reported within the FeN x system. Here, we develop a machine learning-integrated DFT+ U (DFT+ U ML ) approach to capture the Hubbard effects and systematically explore the FeN x ( x = 1, 2, 4, 6, 8, or 10) system. By applying this approach, we report for the first time a novel two-dimensional nitrogen-polymerized phase P 2 1 / c -FeN 4 and resolve the existing controversy regarding the ambient-pressure ground state of FeN. Remaining stable at 0 GPa, the P 2 1 / c -FeN 4 phase outperforms conventional chain-like FeN x materials in both energetic and mechanic properties and exhibits potential for application. This study offers new strategies for designing nitrogen-rich energetic materials and guiding high-pressure synthesis.