First-Principles Study of Hydrogen Evolution on M–N ₄ Sites in Porphyrin–Zigzag Graphene Nanoribbons

The hydrogen evolution reaction (HER) is a key half-reaction in water electrolysis, motivating the development of efficient non-noble-metal electrocatalysts with well-defined active sites. Here, we employed recently synthesized metalloporphyrin-graphene nanoribbons (MPor-3ZGNRs) as a structurally precise model system to systematically investigate the intrinsic HER activity of atomically dispersed M–N 4 sites (M = Sc–Zn). In MPor-3ZGNRs, metalloporphyrin units are periodically embedded into zigzag graphene nanoribbons via peri-fusion, enabling strong π– d electronic coupling and continuous charge-transport pathways while preserving molecularly defined coordination environments. First-principles calculations show that the hydrogen adsorption free energy ( ΔG *H ) can be tuned over a wide range (0.12–2.26 eV) by metal selection, with V–N 4 and Co–N 4 sites exhibiting nearly thermoneutral hydrogen adsorption. Electronic structure analyses reveal that optimal HER activity arises from a balance between local M–H bonding and adsorption-induced electronic reorganization. Comparative studies with other porphyrin-based architectures further highlight the important roles of coupling mode and metal identity in governing HER thermodynamics.