6.

Concerted mode diffusion pathways between the most stable occupation positions for A⁺ ions. (a) The potential energy profiles and (b–d) their diffusion pathways of (b) Li⁺, (c) Na⁺, and (d) K⁺ ions (the pink, green, and purple spheres correspond to the FC, the off-FC, and the BC positions, respectively). (e) Minimum distance between the A⁺ ion and the N atoms (min­(d _A⁺–N)). In (b–d) panels, the red spheres correspond to barrier geometries (corresponding energies represented as the red points in panel (a)). (f) The first and second closest N atoms and the first closest Fe_N ion from A⁺ ions on the xy-plane (θ_{N–Fe–N, in xy} ). In (g–i), the local framework distortions of the occupied FC positions by the A⁺ ion (corresponding geometries are marked with an empty cycle with ″FC _A ″ labels). Note that in parts (b–d), we visualize the blue, gray, yellow, and orange lines indicate N atoms, C atoms, the Fe ions coordinating with the N atom, and the Fe ions coordinating with the C atom to clearly display the pathways. We designated the label “Norm. react. coord.” meaning normalized reaction coordinate.