Atomic-level design principles for the hydrogen evolution reaction on high-entropy MXene catalysts

High-entropy materials, with their rich compositional diversity, offer an exceptional platform for tailoring catalytic performance through synergistic interactions among multiple metal elements. This inherent heterogeneity gives rise to a wide distribution of local atomic environments, resulting in a broad spectrum of binding energies for catalytic intermediates. In this work, we investigate the hydrogen evolution reaction (HER) on high-entropy MXenes (HE-MXenes) by combining high-throughput density functional theory (DFT) calculations with machine learning, aiming to uncover atomic-scale design principles that govern catalytic activity. Specifically, we systematically probe hydrogen adsorption across a statistically diverse set of local environments on TiVNbMoC₃O₂ surfaces. While Mo-based MXenes are widely regarded as highly active HER catalysts in pristine or low-component systems, our results demonstrate that, in HE-MXenes, catalytic behavior is governed primarily by the local atomic coordination rather than by the identity of any single metal species. In particular, our findings reveal that the identity of the first-nearest neighbor shell to the surface oxygen termination plays a dominant role in determining HER activity, with the activity following the trend V < Mo < Ti < Nb within the first shell. Notably, configurations such as Nb₃, Ti₁Nb₂ and Nb₂Mo₁ exhibit particularly outstanding performance. To elucidate the underlying factors, we employ machine learning and identify the average covalent radius of neighboring metal atoms as a key descriptor governing adsorption behavior. This insight enables rapid, descriptor-based screening of high-performance HER catalysts without the need for exhaustive DFT calculations. Overall, our work highlights the pivotal role of local atomic environments in catalytic activity and establishes an efficient, data-driven platform to accelerate the discovery of HE-MXenes for next-generation electrocatalysis.