Theoretical investigation of intermediate phases between Li$_2$NH and LiNH$_2$

The cycling between Li imide (Li$_2$NH) and Li amide (LiNH$_2$) represents the key reactions in the Li-N-H hydrogen storage system. It is important to know whether there exist intermediate phases between these two stable compounds in order to fully understand the mechanism of these reactions. We investigate from first principles possible intermediate compounds Li$_{2-x}$NH$_{1+x}$ and Li$_{1+x}$NH$_{2-x}$ with $x$ equal to 1/8 and 1/4. Li$_{2-x}$NH$_{1+x}$ is created by replacing a certain amount of NH$^{2-}$ with NH$_2^-$ in pure Li imide and removing a proper amount of Li$^+$ to satisfy charge neutrality. Similarly, Li$_{1+x}$NH$_{2-x}$ is created by replacing a certain amount of NH$_2^-$ with NH$^{2-}$ in Li amide and adding a suitable amount of Li$^+$. At $T=0$ K, Li$_{2-x}$NH$_{1+x}$ is energetically favorable with respect to phase separation into pure Li$_2$NH and LiNH$_2$. On the amide side, Li$_{1+x}$NH$_{2-x}$ is only slightly less stable than the phase-separated mixture of amide and imide. These findings suggest that the intermediate phases may appear during the cycling reactions at finite temperatures. Electronic signatures for the intermediate phases resulting from the coexistence of NH$_2^-$ and NH$^{2-}$ anions will also be discussed.