Hexagonal structure of phase III of solid hydrogen

A hexagonal structure of solid molecular hydrogen with $P{6}_{1}22$ symmetry is calculated to be more stable below about 200 GPa than the monoclinic $C2/c$ structure identified previously as the best candidate for phase III. We find that the effects of nuclear quantum and thermal vibrations play a central role in the stabilization of $P{6}_{1}22$. The $P{6}_{1}22$ and $C2/c$ structures are very similar and their Raman and infrared data are in good agreement with experiment. However, our calculations show that the hexagonal $P{6}_{1}22$ structure provides better agreement with the available x-ray diffraction data than the $C2/c$ structure at pressures below about 200 GPa. We suggest that two phase-III-like structures may be formed at high pressures: hexagonal $P{6}_{1}22$ below about 200 GPa and monoclinic $C2/c$ at higher pressures.

Figure 1

Relative stability of $P{6}_{1}22$ (blue), $C2/c$-12 (green), $P{2}_1/c$ (orange), and $P{6}_3/m$ (violet) with respect to $C2/c$-24 (red) at the static lattice level, $T=0\mathrm{K}$, and $T=300\mathrm{K}$.

Figure 2

The $P{6}_{1}22$ and $C2/c$-24 layered molecular structures.

Figure 3

(a) Band structure along a high-symmetry path (left) and electronic density of states (right) of $P{6}_{1}22$ at 200 GPa. The dashed black line represents the Fermi level. (b) Phonon dispersion along a high-symmetry path (left) and vibrational density of states (right) of $P{6}_{1}22$ at 200 GPa.

Figure 4

Raman and IR spectra of $C2/c$-24 and $P{6}_{1}22$ at $P=200$ GPa.

Figure 5

Experimental x-ray diffraction data for phase III [11], and simulated x-ray diffraction data for the $C2/c$-24 and $P{6}_{1}22$ structures at $P=174$ GPa and wavelength $\lambda =0.4122$ Å. The black arrows in the experimental data indicate the ${\mathrm{H}}_2$ peaks, while the other peaks correspond to the rhenium metal gasket. The two arrows in the calculated spectrum of $C2/c$-24 indicate the double peak at around $15.5^{\circ }$ caused by the monoclinic distortion, and the arrow in the $P{6}_{1}22$ spectrum shows that in this hexagonal structure there is a single peak around $15.5^{\circ }$.