Schematic energy profiles for M³⁺ displacement with H₂O (the “broken” solid curve) or without H₂O (the full dashed curve) from Site-A to Site-A′ along the vertical Ĉ₅ axis of the Preyssler cluster. The “broken” solid line includes green and blue parts, where green represents the movement from A to the center of the cavity while blue represents from A′ to the center. The green and blue curves cannot be connected because of the different orientation of the water molecule. Color code: Preyssler framework (red), M³⁺ cation (green), and H₂O (Λ-shaped black sticks).