General Model for d-Center Prediction in Multi-Principal-Element Alloys

The center of the d-band or d-orbital of a transition metal site serves as a key electronic structure descriptor in electrocatalysis, yet its prediction across diverse material systems remains challenging, particularly for disordered multi-principal-element alloys (MPEAs). In this study, we present a general, physically interpretable model for predicting d-center values across a wide range of surfaces and compositions, including 10,680 density functional theory (DFT)-relaxed slabs and over 1.2 million d-center values. Inspired by cluster expansion theory, the model captures local coordination environments to accurately estimate d-centers, achieving a mean absolute error (MAE) of ∼0.09 eV, even when considering only the first nearest-neighbor interactions. We further demonstrate the influence of structural orientation of surface and featurization schemes for surface slabs, as well as regression methods, revealing potential for further improvements with a trade-off between model generalizability and complexity with accuracy. The resulting model offers rapid and reliable d-center estimation, enabling high-throughput screening and mechanistic interpretation in catalysis design. Additionally, the model coefficients provide a direct and accessible tool for both experimentalists and theorists to gain valuable insights into the MPEA surface electronic behavior.