Unveiling Universal Reactivity Descriptors of Metal Clusters toward Dinitrogen Activation: A Machine Learning Protocol with Three-Level Feature Extraction

The activation of dinitrogen (N₂) by metal clusters is a fundamental challenge in chemistry and has been extensively studied. However, previous studies have primarily focused on case-by-case interpretations of experimental reactivity, resulting in a lack of universal reactivity descriptors and predictive models that can quantitatively estimate reaction rates and elucidate structure–activity relationships. In this study, we develop predictive, interpretable, and transferable machine learning models for metal cluster reactivity toward N₂, employing a systematic and hierarchical feature extraction strategy that generates electronic and intrinsic features from three structural levels. Crucial features influencing cluster reactivity were identified, and the mechanisms by which these features govern reactivity were elucidated. To enhance model robustness and transferability, pairwise learning (data augmentation) and feature interaction (feature augmentation) strategies were employed, leading to a deep neural network model that correlates feature differences with reaction rate differences. Trained on 159 homonuclear metal clusters, the model demonstrates satisfactory transferability to 57 heteronuclear metal clusters, enabling reaction rate predictions based on their feature differences. This work presents an expert-guided machine learning protocol for developing generalizable models to predict and understand metal cluster reactivity.