Structural Stability and Electronic Properties of Na$_2$C$_6$O$_6$ for a Rechargeable Sodium-ion Battery*

Sodium-ion batteries have been explored as a promising alternative to lithium-ion batteries owing to a significant advantage of a natural abundance of sodium. Recently, it has been reported that disodium rhodizonate, Na$_2$C$_6$O$_6$, exhibit good electrochemical properties and cycle performance as a minor-metal free organic cathode for sodium-ion batteries. However, its crystal structures during discharge/charge cycle still remain unclear. In this work, we theoretically propose feasible crystal structures of Na$_{2+x}$C$_6$O$_6$ using first principles calculations. A structural phase transition has been found: Na$_4$C$_6$O$_6$ has a different C$_6$O$_6$ packing arrangement from Na$_2$C$_6$O$_6$. Electronic structures of Na$_{2+x}$C$_6$O$_6$ during discharge/charge cycle are also discussed. Our predictions could be the key to understanding the discharge/charge process of Na$_2$C$_6$O$_6$.