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Abstract The electrochemical nitrate reduction reaction (NO₃RR) to ammonia is an essential step toward restoring the globally disrupted nitrogen cycle. In search of highly efficient electrocatalysts, tailoring catalytic sites with ligand and strain effects in random alloys is a common approach but remains limited due to the ubiquitous energy-scaling relations. With interpretable machine learning, we unravel a mechanism of breaking adsorption-energy scaling relations through the site-specific Pauli repulsion interactions of the metald-states with adsorbate frontier orbitals. The non-scaling behavior can be realized on (100)-type sites of ordered B2 intermetallics, in which the orbital overlap between the hollow *N and subsurface metal atoms is significant while the bridge-bidentate *NO₃is not directly affected. Among those intermetallics predicted, we synthesize monodisperse ordered B2 CuPd nanocubes that demonstrate high performance for NO₃RR to ammonia with a Faradaic efficiency of 92.5% at −0.5 V_RHEand a yield rate of 6.25 mol h⁻¹g⁻¹at −0.6 V_RHE. This study provides machine-learned design rules besides thed-band center metrics, paving the path toward data-driven discovery of catalytic materials beyond linear scaling limitations. 

Small nanoparticles, a.k.a. nanoclusters, of transition metals have been studied extensively for a wide range of applications due to their highly tunable properties dependent on size, structure, and composition. For these small particles, there has been considerable effort towards theoretically predicting what is the most energetically favorable arrangement of atoms when forming a nanocluster. In this work, we develop a computational framework that couples density-functional theory calculations with mathematical optimization modeling to identify highly stable, mono-metallic transition metal nanoclusters of various sizes. This is accomplished by devising and solving a rigorous mathematical optimization model that maximizes a general cohesive energy function to obtain nanocluster structures of provably maximal cohesiveness. We then utilize density-functional theory calculations and error term regression to identify model corrections that are necessary to account with better accuracy for different transition metals. This allows us to encode metal-specific, analytical functions for cohesive energy into a mathematical optimization-based framework that can accurately predict which nanocluster geometries will be most cohesive according to density-functional theory calculations. We employ our framework in the context of Ag, Au, Cu, Pd and Pt, and we present sequences of highly cohesive nanoclusters for sizes up to 100 atoms, yielding insights into structures that might be experimentally accessible and/or structures that could be used as model nanoclusters for further study.