Theoretical prediction of intermediates in the decomposition of Mg(BH$_4$)$_2$

We have studied the decomposition pathway of Mg-borohydride using density-functional theory (DFT) calculations of the free energy (including vibrational contributions) in conjunction with a Monte Carlo-based crystal structure prediction method, the prototype electrostatic ground state (PEGS) method. We find that a recently proposed Mg(B$_3$H$_8$)$_2$ intermediate [Chong, etc, {\it Chem. Commun.} {\bf 47}, 1330, (2011)] is energetically highly unfavorable with respect to decomposition into MgB$_{12}$H$_{12}$. We systematically search for low-energy structures of Mg-triboranes [Mg(B$_3$H$_8$)$_2$, MgB$_3$H$_7$, and Mg$_3$(B$_3$H$_6$)$_2$], closo-borane MgB$_{\rm n}$H$_{\rm n}$ (n=6,7,8,9,10,11), and Mg(B$_{11}$H$_{14}$)$_2$ compounds using PEGS+DFT simulations. We find that only the reaction enthalpy to Mg$_3$(B$_3$H$_6$)$_2$ is close to the stable MgB$_{12}$H$_{12}$ pathway, and falls within the thermodynamic conditions for reversibility [e.g., $\Delta$ H = 20$\sim$50 kJ/(mol H$_2$)]. Careful control over experimental conditions might allow for Mg$_3$(B$_3$H$_6$)$_2$ as a possible intermediate in the decomposition of Mg(BH$_4$)$_2$, and might allow Mg$_3$(B$_3$H$_6$)$_2$ to be rehydrided back to Mg(BH$_4$)$_2$ under modest H$_2$($T,p$) conditions.