Machine Learning Prediction of Two-Dimensional Polymerization of Nitrogen in FeN _<i>x</i>

Nitrogen-rich iron nitrides (FeN_<i>x</i>), 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+<i>U</i> frameworks requires careful <i>U</i> value selection. Moreover, no polymerized nitrogen structures beyond one-dimensional have been reported within the FeN_<i>x</i> system. Here, we develop a machine learning-integrated DFT+<i>U</i> (DFT+<i>U</i>_ML) approach to capture the Hubbard effects and systematically explore the FeN_<i>x</i> (<i>x</i> = 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 <i>P</i>2₁/<i>c</i>-FeN₄ and resolve the existing controversy regarding the ambient-pressure ground state of FeN. Remaining stable at 0 GPa, the <i>P</i>2₁/<i>c</i>-FeN₄ phase outperforms conventional chain-like FeN<i>_x</i> 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.