Fig. 4. Results from DFT simulations of hydrated cryptomelane. (a) K_0.80Mn₈O₁₆·(0.40)H₂O: four K⁺ and two H₂O in five unit cells of α-Mn₈O₁₆ in a single tunnel, shown along the a-axis. The two outer K⁺ ions occupy ‘2b’ sites; the two inner K⁺ ions are displaced by H₂O molecules to ‘2a’ sites. One H₂O solvates two K⁺ ions – one above and one below. (b) Mean charge density plot for K_0.80Mn₈O₁₆·(0.40)H₂O from the [100] axis, showing the displacement of K⁺ ions from ‘2b’ to ‘2a’ sites by H₂O molecules inside the tunnel. The tunnel-centered sites corresponding to red-colored charge densities are ‘2b’ sites, while those corresponding to yellow densities are ‘2a’ sites. (c) Binding energy of K⁺ at varying concentrations of H₂O for K_xMn₈O₁₆·yH₂O. The blue, orange and green curves indicate low-K⁺ concentrations; red, purple and brown indicate high-K⁺ concentrations in the tunnel. Experimentally realized concentrations are closest to the brown curve.