Heteromultimetallic Conductive Metal–Organic Framework as Bifunctional Electrocatalyst for Water Splitting: A Combined DFT and Machine Learning Study

Abstract

Conductive metal–organic frameworks (c-MOFs) represent a promising platform for designing bifunctional electrocatalysts toward the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER). However, identifying optimal compositions through conventional “trial-and-error” approaches remains formidable due to their vast compositional complexity. Here, we present a theoretical investigation that integrates high-throughput density functional theory calculations with machine learning to explore entropy-driven design strategies in 2,3,6,7,10,11-hexaimino-triphenylene (HITP)-based c-MOFs. Systems incorporating Fe, Co, Ni, Cu, and Zn metal centers were found to be thermodynamically and electrochemically stable. Screening 75 potential active sites across 35 M3(HITP)2 frameworks identified CoCoZn(HITP)2 as the most efficient bifunctional catalyst with a total overpotential of 0.39 V. Counterintuitively, bimetallic configurations systematically outperformed their higher-entropy trimetallic analogues, revealing that optimal electronic synergy supersedes configurational entropy in governing catalytic efficiency. Electronic structure analysis revealed that the near-ideal orbital energy alignment between Fe d-states and H s-states renders Fe sites intrinsically favorable for HER. Concurrently, the Co d-band center in CoCoZn(HITP)2 suffer an downshift and enhanced electron transfer to *OH intermediates, thus strengthening OER activity. Finally, the stacking ensemble machine learning framework provides a reliable model for bifunctional activity prediction (R2 = 0.907), identifying the combination of electron affinity and valence electron count as the most critical activity descriptor.