Fig. 3: Theoretical investigation of the dynamic OER mechanism.

a Relative free energy diagram of OER over Ni-Fe₂ triple-atom sites in alkaline media at the equilibrium potential of 1.23 V. Insets show the corresponding atomic structures. b Evolution of ^Fe*O−H, ^Ni*O−H, and Ni−O bond lengths during the AIMD simulation on ^Ni*OH−^Fe*OH model. The insets are the side and top views of the initial state with full explicit solvation shells in the AIMD trajectories. c PDOS analysis of Fe 3d, O 2p, and OH orbitals (σ* and π_2p, pink area) for OH transfer in the ^Ni*OH−^Fe*O and ^Ni*(bare)−^Fe*O models. Insets show the corresponding atomic structures. d Calculated electron density distribution of the LUMOs of ^Ni*OH−^Fe*O and ^Ni*(bare)−^Fe*O. Red and green regions represent positive and negative signs of the wave function, respectively. Silver, gold, brown, red, and white balls represent Ni, Fe, C, O, and H atoms, respectively.