Unifying theory of electronic descriptors of metal surfaces upon perturbation

We present a unifying theory for predicting electronic descriptors (e.g., the $d$-band center ${\ensuremath{\epsilon}}_{d}$) of transition and noble metal surfaces by interpretable deep learning. Distinct from black-box machine learning models, fundamental insights into underlying physical processes can be obtained without sacrificing prediction accuracy. In addition to the charge transfer, strain, and ligand effects in the conventional wisdom, we identified orbital resonance in $d$-electron hopping as a crucial factor that modulates the shape of the $d$-state distribution, thereby shifting ${\ensuremath{\epsilon}}_{d}$ of a $d$-metal site upon perturbation. Our findings reveal the promise of machine learning in advancing domain knowledge, paving the way toward theory-guided, data-driven design of materials beyond brute-force screening.