path. An extended discussion as to why the Hubbard U -correction was dropped for the NEB calculations can be found in the SI in the section "Supplementary Discussion: The failure of GGA+U". To allow for migration in Prussian White, one charge carrier atom was removed from the fully sodiated cell. The reported structure was determined to be sufficiently large to ensure a negligible interaction between the periodic images of the migrating sodium ions. All structures were fully relaxed until the forces on the atoms were converged within 10 -2 eV/ Å.