First-Principles Study of Experimental and Hypothetical Mg(BH₄)₂ Crystal Structures

We have used first-principles density functional theory to relax the experimentally reported crystal structures for the low- and high-temperature phases of Mg(BH 4 ) 2, which contain 330 and 704 atoms per unit cell, respectively. The relaxed low-temperature structure was found to belong to the P 6 1 22 space group, whereas the original experimental structure has P 6 1 symmetry. The higher symmetry identified in our calculations may be the T = 0 ground-state structure or may be the actual room-temperature structure because it is difficult to distinguish between P 6 1 and P 6 1 22 with the available powder diffraction data. We have identified several hypothetical structures for Mg(BH 4 ) 2 that have calculated total energies that are close to the low-temperature ground-state structure, including two structures that lie within 0.2 eV per formula unit of the ground-state structure. These alternate structures are all much simpler than the experimentally observed structure. We have used Bader charge analysis to compute the charge distribution in the P 6 1 22 Mg(BH 4 ) 2 structure and have compared this with charges in the much simpler Mg(AlH 4 ) 2 structure. We find that the B−H bonds are significantly more covalent than the Al−H bonds; this difference in bond character may contribute to the very different crystal structures for these two materials. Our calculated vibrational frequencies for the P 6 1 22 structure are in good agreement with experimental Raman spectra for the low-temperature Mg(BH 4 ) 2 structure. The calculated total energy of the high-temperature structure is only about 0.1 eV per formula unit higher in energy than the low-temperature structure.