Density functional theory study of phase IV of solid hydrogen

We have studied solid hydrogen up to pressures of 300 GPa and temperatures of 350 K using density functional theory methods and have found “mixed structures” that are more stable than those predicted earlier. Mixed structures consist of alternate layers of strongly bonded molecules and weakly bonded graphene-like sheets. Quasiharmonic vibrational calculations show that mixed structures are the most stable at room temperature over the pressure range 250–295 GPa. These structures are stabilized with respect to strongly bonded molecular phases at room temperature by the presence of lower frequency vibrational modes arising from the graphene-like sheets. Our results for the mixed structures are consistent with the experimental Raman data [M. I. Eremets and I. A. Troyan, Nat. Mater. 10, 927 (2011) and R. T. Howie et al., Phys. Rev. Lett. 108, 125501 (2012)]. We find that mixed phases are reasonable structural models for phase IV of hydrogen.

Figure 1

Side and top views of the $Pc$ structure at 250 GPa. The side view shows the four-layer repeat with a weakly bonded graphene-like layer on top (shaded atoms). The red lines show the next-nearest contacts within the layer.

Figure 2

Evolution of the bond lengths of $C2/c$, $Cmca$-12, and $Pc$ with pressure. The molecular bond lengths of $C2/c$ and $Cmca$-12 slowly expand with increasing pressure, while the short bonds in the strong layers of $Pc$ undergo a slight contraction. The most notable feature is the behavior of the bonds in the weak layers. The short bonds in the weak layers expand with pressure rather more rapidly than those of $C2/c$ and $Cmca$-12, while the long bonds in the weak layers contract rapidly with pressure.

Figure 3

Phonon dispersion relations of (a) $Pc$, (b) $Pc$-96, (c) $Pbcn$, (d) $C2/c$, (e) $Cmca$-12, and (f) $Cmca$-4 at 250 GPa. The right-hand panels show the vibrational densities of states. The modes shown with negative frequencies indicate dynamical instabilities. The modes below 2500 cm${}^{-1}$ are lattice modes and those at higher frequencies are vibronic modes. The densities of states of the $Pc$, $Pc$-96, and $Pbcn$ mixed phases are very similar and each has three distinct bands of vibrons. $Pc$ has some unstable modes near Z while the unstable modes of $Pbcn$ cover a substantial fraction of the zone. The $Pc$-96, $C2/c$, $Cmca$-12, and $Cmca$-4 structures are dynamically stable.

Figure 4

Enthalpies/free energies of the $Cmca$-12, $Pc$, and $Cmca$-4 structures relative to $C2/c$ for (a) the static lattice structures, (b) with proton ZP motion, and (c) with full vibrational motion at 300 K. The static-lattice enthalpy of $Cmca$-4 is too high for it to appear in (a).

Figure 5

Computed phase diagram of hydrogen at high pressures.

Figure 6

Raman spectra of $C2/c$, $Cmca$-12, and $Pc$ at (a) 200 GPa and (b) 250 GPa.

Figure 7

Pressure dependence of the Raman vibron frequencies of $C2/c$ (blue solid line), $Cmca$-12 (red solid line), and $Pc$ (black solid line). The experimental data for phase III at 100 K (dashed orange line) are from Ref. 16 and the room temperature data for phases III and IV are from Ref. 15 (dashed green line).

Figure 8

Infrared spectra of $C2/c$, $Cmca$-12, and $Pc$ at (a) 200, (b) 250, and (c) 300 GPa.

Figure 9

Electronic band structures of $C2/c$ (a), $Cmca$-12 (b), and $Pc$ (c) at 250 GPa. The states below the blue horizontal line are occupied and those above are unoccupied. Note that the DFT calculations predict that $Cmca$-12 is slightly metallic at this pressure.

Figure 10

Band gaps of $C2/c$, $Cmca$-12, and $Pc$ as a function of pressure. The solid symbols show the thermal (minimum) band gaps while the striped symbols represent the minimum optical (direct in $k$ space) gaps.