Bonding, structures, and band gap closure of hydrogen at high pressures

We have studied dense hydrogen and deuterium experimentally up to 320 GPa and using ab initio molecular dynamic (MD) simulations up to 370 GPa between 250 and 300 K. Raman and optical absorption spectra show significant anharmonic and quantum effects in mixed atomic and molecular dense phase-IV of hydrogen. In agreement with these observations, ab initio MD simulations near 300 K show extremely large atomic motions, which include molecular rotations, hopping, and even pair fluctuations, suggesting that phase IV may not have a well-defined crystalline structure. The structurally diverse layers (molecular and graphenelike) are strongly coupled, thus opening an indirect band gap; moreover, at 300 GPa, we find fast synchronized intralayer structural fluctuations. At 370 GPa, the mixed structure collapses to form a metallic molecular Cmca-4 phase, which exhibits a new interstitial valence charge bonding scheme.

Figure 1

Vibrational properties of H${}_2$ and D${}_2$ at 300 K up to 320 GPa. (a) Intensity normalized Raman spectra with pressure; the hatched area corresponds to Raman signal of stressed diamonds; (b) experimental Raman frequencies of the soft vibron modes in H${}_2$ and D${}_2$ with pressure; the frequencies of D${}_2$ are multiplied by$\sqrt{2}$; discontinuities of the vibron frequencies at 230 GPa are due to the III-IV transition; there is a 10–15 GPa pressure range of phase coexistence; (c) vibrational spectra deduced from MD simulations. The vertical red lines show the behavior of two major Raman vibrons.

Figure 2

The results of the Raman modes analysis performed using a coupled oscillator model (Ref. 20). Panel (a) shows the positions of the experimentally measured Raman bands as a function of pressure determined by applying this model to the intensity corrected Raman spectra. The positions of the bare frequencies are given in two cases: (i) the 300, 800, and 1050 cm${}^{-1}$ modes are coupled to the soft mode and the intensities of these modes are fully due to the coupling (green circles); (ii) there is no coupling (red circles), the positions of the bands and their intensities correspond to the measured ones. These cases correspond to two extremes; we expect that the reality is somewhere in-between. Panel (b) shows the relative intensities of the four most intense low-frequency Raman bands with respect to that of the soft vibron mode. This illustrates the diverse behavior of the modes with respect to the vibrational coupling, which is expected to increase with pressure as the soft vibron mode and other modes become closer in frequencies.

Figure 3

The atomic motions for the most prominent Raman modes of Pbcn hydrogen as the result of the DFT calculations: (a) low-frequency libron mode; (b) soft vibron mode of the graphenelike layer; (c) vibron mode of the Br${}_2$- like layer.

Figure 4

(a) The Raman isotope effect on the vibron frequency determined as $\alpha =\log {}_{10}(\sqrt{2}{\nu }_{{\mathrm{D}}_2}/{\nu }_{{\mathrm{H}}_2})/\log {}_{10}\left(2\right)$; the dashed lines correspond to linear extrapolations of the D${}_2$ data to higher pressures; (b) vibron linewidths of H${}_2$ as a function of pressure. Data for phases I and III are from Refs. 22 and 23 (gray triangles and cyan triangle, respectively).

Figure 5

Raman frequencies of the lattice and librational modes of H${}_2$ and D${}_2$ with pressure; the Raman frequencies of D${}_2$ are multiplied by $\sqrt{2}$. Inset: the Raman isotope effect on the lowest-frequency libron frequency determined as $\alpha =\log {}_{10}(\sqrt{2}{\nu }_{{\mathrm{D}}_2}/{\nu }_{{\mathrm{H}}_2})/\log {}_{10}\left(2\right)$; the dashed lines correspond to linear extrapolations of the D${}_2$ data to higher pressures.

Figure 6

Effective intramolecular potential for dense hydrogen at 320 GPa determined from the Raman data for the soft vibron mode of H${}_2$ and D${}_2$ [Fig. 1b] (Ref. 21). The data for D${}_2$ are extrapolated using the best second-order polynomial fit shown in Fig. 1b. The potential is approximated by the Morse function and is plotted as a function of a dimensionless linear coordinate (Ref. 21). Horizontal lines represent the vibrational levels. Only two lowest-energy vibrational levels correspond to the bound states at 320 GPa (solid lines).

Figure 7

Molecular dynamics trajectories of three runs. The top row corresponds to the Br${}_2$-like layer, while the bottom row to the $G$ layer. Different colors correspond to different atoms.

Figure 8

The vibrational spectra deduced from MD simulations (the lines are guides to the eye showing the evolution of the H${}_2$ vibrons with increasing pressure).

Figure 9

Band gap of phase IV of H${}_2$. (a) Experimental optical absorption spectra at 318 GPa. The inset shows that the square root of absorbance is linear with energy near the absorption edge, which is characteristic of indirect gap absorption. (b) Experimental and theoretical band gaps for phases III and IV of H${}_2$ and D${}_2$. The data presented correspond to the following references: Howie et al. (Ref. 5) reanalyzed here assuming that the band gap is indirect, resulting in lower values than in the original paper, Azadi & Kuhne (Ref. 25), Loubeyre et al. (Ref. 23), and Zha et al. (Ref. 26).

Figure 10

Electronic band structure of Pbcn H${}_2$ at 300 GPa. Black and red lines are the results for GGA and $GW$ methods, respectively.

Figure 11

Full and partial density of electronic states of Pbcn hydrogen at 300 GPa.

Figure 12

Electron topology of high-pressure phases of H${}_2$. (a) Total electron density difference for Pbcn from the constituent hydrogen ($\Delta \rho =-0.176$ e/Å${}^3$). (b), (c) Electron density isosurfaces for the values of 1.0 e/Å${}^3$ and 0.5 e/Å${}^3$, respectively, for the Cmca-4 structure.

Figure 13

The Bader analysis (Ref. 28) of the $G$ layers of Pbcn hydrogen at 250 GPa. The $ab$ plane is shown. The (3, −1) bond critical points are at 0.236, 0.079, 0.250; 0.730, 0.757, 0.251; 0.500, 0.343; 0.250; 0.000, 0.486, 0.250; 0.243, 0.414, 0.249; 0.00, 0.172, 0.250. The electrons in the graphene layer are not delocalized. The bond critical points between a pair of H atoms can be clearly defined. The H${}_2$ remain molecular in nature.