The optimal U-values we find are smaller than those used by the Materials Project and those reported in other works. These previously reported U-values are typically derived from smaller sets of binary Mn oxides, which exclude Mn (oxy)hydroxides. Therefore, the optimal Uvalue we report likely yields better overall accuracy in predicting bulk electrochemical redox behavior, particularly in aqueous environments. Notably, we find that PBE+U systematically displays lower errors in predicted formation energies than SCAN+U regardless of U-value. At their respective minima, PBE+U displays almost half the error of SCAN+U (Fig. ). However, the difference in error between the two functionals is small compared to the absolute error incurred by both functionals with no Hubbard-U corrections. The PBE(+U) functional is less computationally expensive than SCAN(+U), which is important for investigating large electrochemical phase spaces, and is known to perform well in surface calculations. For these reasons, we chose to perform all subsequent calculations using PBE+U with U eff = 2.75 eV. There are tradeoffs to using PBE+U over SCAN+U, however. For example, SCAN+U displays lower error in computed lattice parameters (Table ), although the difference is less than 1% of the experimental values. SCAN(+U) also correctly predicts β-MnO 2 to be the ground state polymorph, whereas PBE(+U) does not. Caution should therefore be exercised when analyzing small differences in energy between MnO x structures with identical stoichiometry. However, these errors have minimal effect on the topotactic electrochemical properties of a given MnO x polymorph. 2 . Applying the DFT correction scheme detailed above, we compute the energies of H + , Li + , Na + , K + , Mg 2+ , Ca 2+ , Zn 2+ and Al 3+ ions inserting into 𝛼, β, R, 𝛿 & λ-MnO 2 (Fig. ). These ions were chosen for their relevance to advanced energy storage and conversion technologies. While the ion insertion behavior of 𝛾-MnO 2 (i.e. electrolytic MnO 2 , "EMD", the common intergrowth polymorph used in alkaline batteries) was not computed directly, it is expected to be similar to that of its constituent polymorphs, β and R-MnO 2 . A full list of computed structures and their energies is given in Table and is available online. To distinguish solid-solution from two-phase intercalation behavior, we conducted a convex hull analysis for each structure-ion pair (Fig. ). From the resulting set of equilibrium structures, ion insertion voltages were calculated according to the following equation: To enable a direct comparison between ions, all voltages were referenced to the standard hydrogen electrode (SHE). Figure displays these ion insertion voltages and their corresponding Mn oxidation states calculated at 1 M concentration for all ions except H + . Proton concentration was set to 10 -14 M, corresponding to a pH of 14 in aqueous conditions. For easier comparison of the voltages and capacities that could be achieved in non-aqueous batteries with metal anodes, Fig. plots the ion-insertion voltages vs. A/A n+ . In both figures, higher voltages signify more favorable insertion events. On the left, MnO 2 crystal structures are shown with representative ions occupying their lowest-energy crystallographic sites.