Density Functional Theory and Machine Learning Study of Zirconium-Based Single-Atom Catalysts on Graphene and Graphene Nanoribbons for Oxygen Reduction and Evolution

This work establishes a design principle for zirconium-based single-atom catalysts by linking their ORR/OER activity to specific atomic-scale descriptors. Singly boron-doped O–Zr–N 4 -graphene is identified as the optimal bifunctional catalyst (η ORR = 0.23 V, η OER = 0.24 V), and the origin of its activity is further decoded through machine learning. The key finding is that the adsorption strengths of the critical *OOH and *OH intermediates are dictated by different Zr d-orbitals (4d zx for *OOH and d x 2 – y 2 /d zy for *OH), an insight validated by electronic structure analysis. This orbital-specific understanding explains why substrate geometry (e.g., flat graphene vs edged nanoribbons) tunes activity by altering these orbital interactions. Therefore, beyond reporting a high-performance catalyst, this study provides a strategic blueprint for catalyst optimization by targeting specific electronic structures for the desired intermediate binding.