For the high pressure region, the tetragonal and trigonal phases are found to be the most stable ones in structure searches at 25 GPa and 1020 GPa, respectively. Interestingly, within the whole pressure range (up to 20 GPa), we did not find the structure proposed by Filinchuk et al. for the phase ^{126}, but instead found the phase with four formula units (44 atoms) per cell and phase with 2 formula units per cell at pressures below 5 GPa (see Fig. 4.2). Given that the structure is dynamically unstable at ambient pressure, and based on our enthalpy calculations, we hypothesized that the and structures might correspond to the experimentally observed and phases. Further investigation confirmed this suggestion, as we will show below.
Lattice constants of the most interesting candidate structures are listed in Table I. The calculated zeropressure lattice constant ( = = = 15.79 ) of the phase is in excellent agreement with the experimental value (15.76 ) ^{126}, which gives a benchmark of the typical accuracy to expect of DFT simulations for this system. For the structure, the Mg atom occupies the crystallographic site at (0.5, 0, 0), the B atom occupies the site at (0.533, 0.25, 0.375), and the H atoms are at the sites with coordinates (0.439, 0.247, 0.295) and (0.627, 0.123, 0.369). For the structure, the Mg atoms occupies the site at (0, 0, 0) and site at (0.5, 0.5, 0.5), the B atom occupies at the site at (0.25, 0.25, 0.25), and the H atoms are at the sites with coordinates (0.459, 0.282, 0.210), (0.139, 0.327, 0.089), (0.223, 0.038, 0.286), and (0.174, 0.354, 0.416). From Table I, one can see that relaxing the experimental structure, one gets unexpectedly large changes in the lattice constants – so large that, in fact, the relaxed lattice constants of the structure are the closest match to the experimental ones ^{126}. One has to keep in mind that what is called the “experimental" cell parameters in many cases is a nonunique result of indexing powder XRD spectra, and this is the case here.
Symmetry 





(Theory) 
(Expt) 

() 
7.69 
8.32 
5.58 
5.79 
5.44 
() 
7.69 
8.32 
5.58 
5.79 
5.44 
() 
12.30 
10.52 
5.99 
5.73 
6.15 
(g/cm) 
0.986 
0.984 
0.963 
0.933 
0.987 
B (GPa) 
24.0 
31.0 
31.7 
28.5 
28.5 

4.3 
3.6 
3.6 
3.6 
5.8 
(kJ/mol) 
17.0 
15.5 
13.6 
0 

(kJ/mol) 
21.2 
19.3 
15.4 
0 
Mg(BH) becomes more stable than the phase at pressures above 0.7 GPa (Fig. 4.3). In the roomtemperature experiment, a pressureinduced structural transformation is observed for the porous phase, and occurs in two steps: The phase turns into a diffractionamorphous phase at 0.40.9 GPa, and then at approximately 2.1 GPa into the phase ^{126}. The calculated phase transition pressure from the phase to the proposed phase with symmetry is 1.2 GPa (the corresponding phase transition pressure for phase is 0.8 GPa), which are in good agreement with the experimental values (0.40.9 GPa). We note a tiny enthalpy difference between and structures at pressures around 1 GPa. As pressure increases to 9.8 GPa, the structure becomes the most stable one, in agreement with earlier predictions ^{128; 136}. Bil et al. ^{131} indicated that it is important to treat longrange dispersion interactions to get the ground state structures of magnesium borohydrides correctly. We have examined the energetic stability of the considered structures through a semiempirical Grimme correction to DFT energies, stresses and forces ^{67} (see the inset of Fig. 4.3). When this correction is included, the and structures once again come out as more stable than the structure, by 21.2 kJ/mol and 15.4 kJ/mol, respectively. Energetic stability seems to correlate with the degree of disparity of bond lengths and atomic Bader charges. The structure has two inequivalent MgH distances, 2.26 and 2.07 , compared to 2.11 and 2.07 in the structure, and 2.12 and 2.06 in the structure. As we can see, the more homogeneous bond lengths, the greater stability. Bader charges show the same picture: for H atoms, we find them to be 0.63 and 0.59 in the structure, 0.63 and 0.62 in the structure, and 0.63 and 0.61 in the structure ^{137}. More homogeneous Bader charges and bond lengths in the and structures correlate with their greater thermodynamic stability at ambient pressure, in agreement with proposed correlations between local bonding configurations and energetic stability ^{135}.
Our calculations suggest that the structure, proposed by experiment for the phase, is unstable. This implies that either density functional theory calculations are inaccurate for this system, or experimental structure determination was incorrect. To assess these possibilities, we simulated the XRD patterns of the and structures, and compared them with the experimental XRD pattern of the phase at ambient pressure (see Fig. 4.4a). One observes excellent agreement, both for the positions and the intensities of the peaks (including both strong and weak peaks), of the structure with experiment ^{126}. The situation is very peculiar: two structures, and , have nearly identical XRD patterns, both compatible with the experiment – but one, , is the true thermodynamic ground state (global minimum of the enthalpy), whereas the other, , is not even a local minimum of the enthalpy (dynamically unstable structure, incapable of sustaining its own phonons). In this situation, the true structure is clearly . This example gives a clear reallife example of the fact that very different structures can have very similar powder XRD patterns, making structure determination from powder data dangerous, and in such cases input from theory is invaluable. The structure also has a rather similar XRD pattern, but the peak positions are slightly shifted. Comparison with an independent experimental XRD pattern collected at 10 GPa (Fig. 4.4b) shows that the peak positions and intensities of the structure are once again in excellent agreement with the experimental data ^{128}, while the strong peaks of the structure at , , and obviously deviate from the observed ones. This reinforces our conclusion that the structure is the best candidate for the high pressure phase. At pressures below 10 GPa a mixture of and phases is possible, as the XRD peaks of these two structures are quite similar. We remind that in the experiment, the and phases are nearly indistinguishable ^{126}.
Filinchuk et al. demonstrated the bulk modulus of the phase (28.5 GPa) is almost three times higher than that (10.2 GPa) reported by George et al. by fitting the Murnaghan equation of state ^{126; 128}. Our thirdorder BirchMurnaghan ^{138} fits of the equation of state yielded bulk moduli of the and structures equal to 24 GPa and 31.7 GPa, respectively, consistent with the measured value (28.5 GPa) ^{126}. The observed large density difference with respect to the phase at ambient conditions (44%) is equally consistent with 45% (43%) for () structures ^{126}. Therefore, it is difficult to discriminate between the and structures by their compression behavior, density or bulk modulus. Our calculations show that the structure does not only match all experimental observations for the phase and has the lowest enthalpy among all sampled structures at the relevant pressure range, but is also dynamically stable – phonons were computed at 0, 5 and 10 GPa. The phonon densities of states (PDOS) of and phases at ambient pressure are shown in Fig. 4.5, and once again we see a great degree of similarity. The similarity of all characteristics of these two phases parallels the observed similarity of characteristics of the and phases and invites one to propose that while the I41/acd structure corresponds to the phase, the phase may have the structure.