Breaking the Brønsted–Evans–Polanyi relationship in N2 adsorption driven by potential-dependent repositioning of frontier orbitals: a sweet marriage of machine learning-assisted screening and the electric double-layer effect

Abstract

The discovery of metal–N₄ as a promising catalytic center has sparked great interest in single-atom catalysts for nitrogen reduction (NRR), but their poor activity and low selectivity remain far below industrial requirements. By integrating density functional theory and machine learning, we conducted an upgrade prediction for targeted NRR electrocatalysts on g-C₁₆N₅ featuring the local coordination of TM–N₄, with Mo@g-C₁₆N₅ standing out. The introduction of H⁺ ligand facilitates a synergistic intermediate (*NH₂ + *H), resultant interactions further lower the free energy barrier, as clarified by density of states and crystal orbital analysis. Using the constant-potential method combined with an implicit solvent model, we find that the electric double-layer capacitance is instrumental in modulating the kinetic barrier. The intricate modulation of frontier orbitals under varying electrochemical potentials provided direct support for the shifts in the Fermi level and refined reconfigurations of d-occupation, thereby highlighting the elegant synergy between the discretized atomic d-orbitals and the continuous electronic bands of g-C₁₆N₅. The influence of these shifts on N₂ adsorption energies uncovers a captivating inversion under negative electrochemical potentials, driven by the pivotal role of the d_xy and d_x²−y² orbitals in stabilizing the N₂-π* orbitals.