Origin of the High Specific Capacity in Sodium Manganese Hexacyanomanganate

Sodium manganese hexacyanomanganate, Na_xMn­[Mn­(CN)₆], is an electrochemically active Prussian blue analogue (PBA) that has been studied experimentally as an electrode material in rechargeable sodium-ion batteries. It has a reversible specific capacity of 209 mA h g^–1, which is substantially higher than the theoretical specific capacity of 172 mA h g^–1 expected for two reduction events conventional in PBAs. It has been suggested that the high specific capacity originates from this compound’s unique ability to insert a third sodium ion per formula unit. However, the plausibility of this mechanism has remained ambiguous. Here, we use density functional theory (DFT) with a hybrid functional to calculate the formation energies of various oxidation states and magnetic phases of the Na_xMn­[Mn­(CN)₆] system. We confirm that the compound Na₃Mn^II[Mn^I(CN)₆] is, indeed, thermodynamically stable. It contains manganese­(I), and the sodium ions occupy the interfacial position of the lattice subcubes. We also provide strong evidence that the phase of the fully oxidized Mn­[Mn­(CN)₆] compound is charge-disproportionated, containing manganese­(II) and manganese­(IV). We proceed to show that the presence of crystalline water increases the reduction potential of the system and that the hydrated compounds have theoretical crystal geometries and reduction potentials that closely match the experiment. This work clarifies the charge-storage mechanism in a well-known but less-understood PBA.