Intrinsic Electronic Structure and OER Thermodynamics of the Co-N4 Motif: A Molecular DFT Study of a Single-Atom Catalyst

Abstract

Understanding the electronic structure, spin states, and interactions of single-atom catalysts (SACs) is crucial for the rational design of efficient electrocatalysts for water splitting. Herein, density functional theory (DFT) calculations were performed for Co–N₄ SAC at the B3LYP-D3BJ/def2-TZVP level, with comprehensive spin-resolved investigations of OER intermediates and explicit consideration of water coordination. Mulliken spin analysis indicates that the unpaired electron (+1.138 μB) is predominantly localized on Co, confirming a doublet ground state (S = 1/2, ⟨S²⟩ = 0.803). The first and second axial water molecules exhibit binding energies of −1.32 and −0.68 eV, respectively, supporting the formation of a thermodynamically favorable pseudo-octahedral Co–N₄–(H₂O)₂ complex and a possible proton-solvation relay. The calculated HOMO–LUMO gap of 1.95 eV (635 nm) suggests visible-light activity, while TD-DFT identifies a strong absorption band at 476 nm (f = 0.0438) associated with metal-to-ligand charge-transfer transitions. Spin-state analysis reveals ground-to-quartet energy differences of 9.2–6.5 kcal/mol, with quartet OOH stabilized by 2.2 kcal/mol, supporting spin crossover during O–O bond formation. The *O → *OOH step is potential-determining (ΔG = 1.62 eV), yielding an overpotential of 0.39 V. These results establish Co–N₄ as a promising dual electro/photo catalyst for sustainable hydrogen and oxygen production.