Same but different: how permutation degeneracy enhances machine learning in single-atom catalyst discovery

Abstract

Accurately predicting the catalytic performance of single-atom catalysts (SACs) remains a significant challenge due to the structural diversity of metal coordination environments. In this work, we demonstrate that explicitly incorporating permutation degeneracy, i.e. the positional variation of chemically identical ligands, into machine learning descriptors leads to substantial improvements in predictive accuracy and model transferability. Based on DFT-calculated adsorption free energies (ΔG_*OH, ΔG_*O, and ΔG_*OOH) for 175 TM-N_xS_y motifs, we trained six regression models on three levels of structural representation: (i) stoichiometry only, (ii) stoichiometry with coordination environment, and (iii) stoichiometry with coordination environment and permutation degeneracy. Across all ML algorithms, the inclusion of permutation degeneracy consistently reduced prediction errors and improved R² values. These improvements enabled reliable identification of high-performance SACs, including previously reported active configurations. Our findings highlight permutation degeneracy as a transferable and essential component for accurately encoding local coordination in ML models, offering a generalizable strategy for accelerating data-driven catalyst discovery.