Dual quantum locking: Dynamic coupling of hydrogen and water sublattices in hydrogen filled ice

Abstract

Hydrogen hydrates (HH) are a unique class of materials composed of hydrogen molecules confined within crystalline water frameworks. Among their multiple phases, the filled ice structures, particularly the cubic C2 phase, exhibit exceptionally strong host-guest interactions due to ultra-short H2-H2O distances and a 1:1 stoichiometry leading to two interpenetrated identical diamond-like sublattices, one comprised of water molecules, the other of hydrogen molecules. At high pressures, nuclear quantum effects involving both hydrogen molecules and the water lattice become dominant, giving rise to a dual-lattice quantum system. In this work, we explore the sequence of pressure- and temperature-driven phase transitions in HH, focusing on the interplay between molecular rotation, orientational ordering, lattice symmetry breaking and hydrogen bond symmetrization. Using a combination of computational modeling based on classical and path-integral molecular dynamics, quantum embedding, and high pressure experiments, including Raman spectroscopy and synchrotron X-ray diffraction at low temperatures and high pressures, we identify signatures of quantum-induced ordering and structural transformations in the C2 phase. Our findings reveal that orientational ordering in HH occurs at much lower pressures than in solid hydrogen, by inducing structural changes in the water network and enhancing the coupling of water and hydrogen dynamics. This work provides new insights into the quantum behavior of hydrogen under extreme mechanochemical confinement and establishes hydrogen-filled ices as a promising platform for the design of hydrogen-rich quantum materials.

Figures (12)

• Figure A1: Pressure-Temperature phase diagram of the C2 hydrogen hydrate as derived by our quantum embedded calculations and experimental data. Some experimental pattern are indicated in Figure : XRD data are shown as circles, colored red or black depending on whether they belong to the temperature- or pressure-ramp series; raman measurements are indicated by squares. The summary of experimental thermodynamic path is reported in Table \ref{['tab:experimental_conditions']}. Symbols are filled in the cubic phase and open in the tetragonal phase, while half-filled symbols indicate the transition between them. The background color represents S, the orientation factor (defined in Methods) of H$_2$ computed in the quantum embedded framework. The white triangles with their associated error bars are derived from our molecular dynamics simulations, utilizing the orientation factor as detailed in the Methods section. The dashed lines serve as a guide to the eye to locate the cubic to tetragonal transition. The three insets display the optimized geometries obtained via DFT (0 K) for the quantum plastic phase (upper left), herringbone phase (lower left), and nematic phase (right) of H$_2$ orientational states.
• Figure A2: Raman spectra as a function of temperature at P= 14.7(1) GPa (a) and as a function of pressure at T=300 K (b). Represnetative X-ray diffraction data as a function of temperature at P=2.45(3) GPa (left panel,c-e) and as a function of pressure at T=300 K (right panel, f-h). The extracted evolution of the lattice parameters(in the tetragonal setting) and the degree of asymmetrization upon cooling (i,j) and compression (k,l), are plotted in the bottom panels, respectively.
• Figure A3: Isosurfaces of the density $\rho(\vec{r})$ and angular potential $P_{r_{eq}}(\theta, \phi)$ evaluated at the equilibrium H$_2$ bond length, shown as a function of temperature at $P = 3$ GPa (a), and as a function of pressure at $T = 300$ K (b). The density is projected onto the three planes ($xy$, $yz$, and $xz$) and normalized with respect to the maximum density at 0 K, 3 GPa for panel (a), and at 300 K, 50 GPa for panel (b). Pressure dependence of the first nine eigenvalues at $T = 0$ K. Ortho and para levels are shown as circles and squares, respectively (c). Boltzmann weights vs. temperature at P = 50 GPa for the first five eigenvalues (d). Isosurfaces of the wavefunctions squared modulus for the ground state (para, $l = 0$) and the first three excited states (ortho, $l = 1$) of the H$_2$ molecule at P = 50 GPa (e).
• Figure A4: (a) Comparison of the experimental Raman points and all simulated S$_0$(0) and S$_0$(1) rotons. The blue and orange lines are theoretical whilst the red and green point indicate the S$_0$(0) and S$_0$(1) rotons respectively. The rotons were modelled with three components each, as indicated by the square, crosses and diamonds (b) Pressure dependence of the S$_0$(1) frequency ratio $\omega_{H_2}/\omega_{D_2}$ derived from the experimental Raman data. The rigid rotor ratio is indicated by the dotted line at $\omega_{H_2}/\omega_{D_2} = 2$, whilst the quantum harmonic oscillator ratio is indicated by the dashed line at $\omega_{H_2}/\omega_{D_2} = \sqrt{2}$. HH crosses into the harmonic oscillator regime at around 27 GPa, the same pressure a structural change is previously reported Andriambariarijaona2025 (c) Experimental Raman frequencies derived from the fitting procedure described in Methods (squares) and computed Raman frequencies obtained via DFPT (circles) for the hydrogen vibron upon compression of the hydrogen hydrate. The change in slope, highlighted by the shadow area, corresponds to the pressure where the hydrogen molecules order.
• Figure A5: (a) Crystal structure of C2 hydrogen hydrate at low pressures ($P \lesssim 30$ GPa), showing the two interpenetrating cubic sublattices of $H_2O$ and $H_2$. The water–proton network is disordered, while the $H_2$ molecules are orientationally disordered at high temperature and adopt a herringbone-like arrangement at low temperature. (b) Pressure dependence of the first (solid lines) and second (dotted lines) peak positions in the radial distribution functions $g(r)$ for the $H_w–O$ and $O–O$ pairs, from PIMD simulations at $T = 300$ K. The background color gradient represents the orientation factor $S_{\text{PIMD}}$ extracted from those simulations. (c) Crystal structure of C2 hydrogen hydrate in the symmetrized (water–proton) state at high pressures ($P \gtrsim 30$ GPa). At the highest pressures, $H_2$ molecules become nematic along the $c$-axis, coinciding with the tetragonal distortion direction.