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Pressure-induced metallization of dense (H2S)2H2 with high-Tc superconductivity

The high pressure structures, metallization, and superconductivity of recently synthesized H2-containing compounds (H2S)2H2 are elucidated by ab initio calculations. The ordered crystal structure with P1 symmetry is determined, supported by the good agreement between theoretical and experimental X-ray diffraction data, equation of states, and Raman spectra. The Cccm structure is favorable with partial hydrogen bond symmetrization above 37 GPa. Upon further compression, H2 molecules disappear and two intriguing metallic structures with R3m and Im-3m symmetries are reconstructive above 111 and 180 GPa, respectively. The predicted metallization pressure is 111 GPa, which is approximately one-third of the currently suggested metallization pressure of bulk molecular hydrogen. Application of the Allen-Dynes-modified McMillan equation for the Im-3m structure yields high Tc values of 191 K to 204 K at 200 GPa, which is among the highest values reported for H2-rich van der Waals compounds and MH3 type hydride thus far.

Recently, Strobel et al. reported that mixing hydrogen sulfide (H 2 S) and hydrogen (H 2 ) can form a stoichiometric compound (H 2 S) 2 H 2 near 3.5 GPa, which is characteristic of a rotationally disordered structure 2 . X-ray diffraction (XRD) results have indicated that this structure belongs to the tetragonal space group I4/mcm. The experimental Raman data indicated that an ordering process occurred with structural transformation above 17 GPa. A candidate structure with space group I222 was proposed by ab initio density functional theory (DFT) calculations through structural optimizations. However, obtaining the most stable structure only by structural relaxation is difficult because of potential energy barrier. Another unexpected structure can possibly become stable instead.
We have taken a new route in this study using the recently fast-developed evolutionary algorithm Universal Structure Predictor: Evolutionary Xtallography (USPEX) [30][31][32] to explore the high-pressure ordered crystal structures of (H 2 S) 2 H 2 . We found that a triclinic (P1) structure is energetically favorable. Motivated by the metallization and potential high-temperature superconductivity in (H 2 S) 2 H 2 , higher pressure structures have been extensively explored. Our calculations reveal a metallization pressure of 111 GPa and a high T c of 200 K at 200 GPa. The lower metallization pressure is within the reach of current diamond-anvil techniques, which will inevitably stimulate extensive experiments.

Results
Variable-cell structure prediction simulations with 1 to 4, 6, and 8 H 3 S formula units per cell (f.u./cell) at pressures between 20 and 300 GPa were performed. A group of new structures was uncovered under high pressure-triclinic P1 (8 f.u./cell), orthorhombic Cccm (16 f.u./cell), trigonal R3m (3 f.u./cell), and cubic Im-3m (2 f.u./cell) as shown in Fig. 1. The lattice parameters of these structures at different pressures are also listed in Table S1 of the supplementary information.
Enthalpy difference curves (relative to the Cccm structure) for different structures are presented in Fig. 2. P1 is the most stable structure below 37 GPa, which has lower energy than that of the proposed experimental I222 structure 2 . This P1 structure consists of an ordered H-bonded H 2 S network and two anti-parallel hydrogen molecules occupying the interstitial sites. One molecule lies at z 5 0, whereas the other lies at the z 5 1/2 plane (Figs. 1a and 1b). The Cccm structure is energetically stable between 37 and 111 GPa. Unlike the P1 structure, partial hydrogen bond symmetrization is formed in the Cccm structure. This structure consists of 3D H 2 S networks that trap two different types of hydrogen molecules in channels: one type is arranged such that the head-tail hydrogen molecule (H2-H2) alignment follows the c-axis, whereas the other type is characterized by parallel hydrogen molecule (H1-H1) configuration pointing to the b-axis (Figs. 1c and 1d). The absence of any imaginary frequency also confirms the dynamic stability of the P1 and Cccm phases (see supplementary Fig. S1).
The lattice angles a 5 90.12u, b 5 89.85u, and c 5 90.15u is approximately equal to 90u for the P1 structure at 20 GPa (see supplementary Table S1), which can thus be viewed as a slightly distorted orthorhombic lattice. This condition can explain the experimental suggestion of an orthorhombic structure. We compared the XRD patterns of the P1 structure with that of the experimental pattern in Fig. 3a. A theoretical pattern was obtained with the same X-ray wavelength of 0.39796 Å as the experimental one. The simulated XRD patterns for the P1 structures agree well with those for the experiment data 2 . The calculated equation of states (EOS) for the P1 structure was also compared with experimental one in Fig. 3b. Good agreement between the theoretical and experimental results provides another support for the validity of the P1 structure. Given that hydrogen atoms are undetectable by XRD patterns, the Raman spectrum of P1 is presented for comparison with the experimental results (see supplementary Fig. S2). Two H 2 vibron-peaks are well reproduced, and the two low-frequency features agree qualitatively between theory and experiment. This Raman result, together with the XRD and EOS evidence, support our predicted P1 structure in (H 2 S) 2 H 2 .  Calculated enthalpy curves for various structures relative to our predicted Cccm structure as a function of pressure. The decomposition enthalpies into S13/2H 2 and H 2 S11/2H 2 are also plotted. The Cccm structure transforms to a denser R3m structure above 111 GPa with a volume collapse of 9.2% on further compression (Fig. 3b). The R3m structure shows a disappearing H 2 molecule and forms a pyramidal H 3 S molecular unit as depicted in Fig. 1e. A high-symmetry Im-3m structure becomes favorable above 180 GPa. This structure is characterized by two S atoms located at a simple body centered cubic lattice and H atom located symmetrically between the S atoms (Fig. 1f). The hydrogen bond symmetrization completed in the R3mRIm-3m transition is observed. The coordination number of the S atom increased from three to six with the formation of hydrogen-shared SH 6 .
The decomposition enthalpies into S 1 H 2 and H 2 S 1 H 2 are examined to check the phase stability of (H 2 S) 2 H 2 under pressure (Fig. 2). The structures of P6 3 m, C2/c, and Cmca for H 2 33 , I4 1 /acd 34 , and b-Po 35 for S, P2/c, Pc, Pmc2 1 , P-1, and Cmca for H 2 S 36 in their corresponding stable pressures are adopted. The most stable phases of (H 2 S) 2 H 2 have lower enthalpy than S 1 H 2 and H 2 S 1 H 2 over the pressure range of 20 GPa to 300 GPa. Thus, the (H 2 S) 2 H 2 crystal remains stable against decomposition in our studied pressure range. The calculated pressure-volume data of (H 2 S) 2 H 2 is also shown in Fig. 3b. The volume collapses with 1.5% for P1 to Cccm transition and 9.2% for Cccm to R3m transition, suggesting a first-order phase transition character, whereas the volume change is continuous for R3m to Im-3m transition, supporting a second-order nature.
The pressure dependence of the nearest intramolecular and intermolecular bond distances are plotted in Fig. 3c to understand the molecular interactions observed in (H 2 S) 2 H 2 . Four types of intramolecular H-H bond lengths are nearly equal with distances of approximately 0.75 Å and slightly longer than that 0.74 Å in solid H 2 at 20 GPa, indicating a weak interaction between H 2 S and H 2 . The two H-H bond lengths increased, whereas the other two decreased with increasing pressure, consistent with the observed redshift and blueshift of H-H Raman vibrons 2 , respectively. The hydrogen bond (H2???S2) is also relatively weak with distance of 2.01 Å at 20 GPa. The strength of the hydrogen bond gradually increases with increasing pressure and significantly elongates one of the H2-S1 covalent bonds for a single molecule. The length of the H3-S1 bond (symmetrization hydrogen bond) is 1.59 Å , the H4-S1 covalent bond is 1.39 Å , and the H4???S2 bond is 1.84 Å in the Cccm structure at 40 GPa, indicating a strong hydrogen bond. The length of the strong hydrogen bond decreases, whereas the length of the H4-S1 bond slightly increases with increasing pressure. Notably, the length of the H1-H1 bond decreases to 0.744 Å , whereas the length of the H2-H2 bond increases to 0.757 Å at 110 GPa (Fig. 3d), indicating a slightly increased interaction between S and H2 under pressure. The R3m structure is reconstructive with the disappearing H 2 molecule and forms new H-S bonds at 111 GPa. Thus, a large kinetic barrier is formed for the transformation from Cccm to R3m. The length of the H1-S1 bond increases with increasing pressure, whereas the length of the hydrogen bond (H1???S2) decreases. Thus, the hydrogen bond symmetrized completely accompanied by the R3mRIm-3m phase transition at a pressure of 180 GPa. The nearest H-H distance at 110 GPa in the R3m structures is 1.599 Å , much longer than the H-H bond length of ,1.2 Å in CaH 6 which is characteristic of a weak covalent bond 27 . The H-H distance decreases slowly and becomes 1.433 Å at 300 GPa with increasing pressure, indicating that H and H atoms do not present any bond.
The electronic band structure and projected density of states (DOS) for all (H 2 S) 2 H 2 structures were also explored. The P1 structure is an insulator with an indirect band gap of 3.34 eV at 20 GPa (see supplementary Fig. S3). The bands are flat, indicating that the P1 structure is a typical molecular crystal. The band gap for the Cccm structure decreases with increasing pressure and closes at approximately 110 GPa. Given the deficiency of DFT associated with generalized gradient approximation (GGA), the calculated band gaps are likely to be underestimated. Therefore, the Cccm structure should be an insulator in its stable pressure range. Notably, both the R3m and Im-3m structures are good metals with a large DOS at the Fermi level, as shown in Fig. 4. The projected DOS clearly indicates strong hybridizations of S and H orbitals. Energy band structures near the Fermi level for both R3m and Im-3m are characterized as ''flat band-steep band'', indicating that they may be good superconductors 37 . The predicted metallization pressure of 111 GPa is significantly lower than the currently suggested pressure for the metallization of bulk molecular hydrogen 38 .
The calculated phonon dispersion curves and projected phonon DOS for R3m and Im-3m structures are presented in Fig. 5. The absence of any imaginary frequency indicates their dynamical stability. The low-frequency bands come mainly from the vibrations of the S atom, whereas higher-frequency modes are mostly related to the H atoms. The electron phonon coupling (EPC) l, logarithmic average phonon frequency v log , and the Eliashberg phonon spectral function a 2 F(v) 39 are investigated to explore the possible superconductivity of (H 2 S) 2 H 2 . The resulting l of R3m is 2.07 at 130 GPa, indicating a fairly strong EPC; the v log calculated from the phonon spectrum is 1125.1 K. The calculated l of Im-3m is 2.19 at 200 GPa, whereas the v log is 1334.6 K. Using the calculated v log and commonly accepted values of the Coulomb pseudopotential m* (0.1-

Discussion
Motivated by the metallization and potential high-temperature superconductivity in hydrogen-rich materials of (H 2 S) 2 H 2 or H 3 S, high-pressure structures at a wide pressure range of 20 GPa to 300 GPa were extensively explored. Four order structures under high pressure have been predicted: P1 (stable below 37 GPa), Cccm (stable at 37 GPa-111 GPa), R3m (stable at 111 GPa-180 GPa), and Im-3m (stable above 180 GPa). The R3m and Im-3m structures are good metals above 111 GPa. The estimated T c of the Im-3m phase at 200 GPa is 191 K-204 K, which are among the highest values reported for H 2 -rich van der Waals compounds 28,29 and MH 3 (M 5 Ga, Ge, Si)-type hydride [17][18][19] thus far. In a survey of literature, many similarities in structures, metallization, and superconductivity for the MH 3 [17][18][19] are observed. They all have a high-symmetry cubic structure under high pressure, with high superconducting transition temperature. The lowest T c value is 86 K for GaH 3 . They are also good metals at an experimentally accessible pressure, with the highest metallization pressure at 190 GPa for Si 2 H 6 . Although the crystal structure-predicting methods implemented by USPEX code are efficient for global structural convergence, it is limited by the sizes of the simulation cell employed. Given that the number of energy minima on the potential-energy surface grows exponentially with increasing cell size, making an extensive structural search is impossible. Thus, we cannot rule out the possibility that the actual high-pressure phase of (H 2 S) 2 H 2 with larger unit cells may exist.
Notably, no H 2 molecules were observed in the R3m and Im-3m structures. However, H 2 molecules still exist up to 300 GPa for other H 2 -containing compounds 28,29,42 , such as SiH 4 (H 2 ) 2 , GeH 4 (H 2 ) 2 , and Ar(H 2 ) 2 , although the intramolecular H-H bond was stretched under high pressure. We calculated the electron localization function (ELF) to understand the bonding nature in the R3m and Im-3m structure (Fig. 6). The ELF value for the S-H bonds is close to 1.0, which suggests a strong polar covalent bond. The ELF value between the nearest H-H is very low, indicating the absence of covalent bond characteristics between hydrogen atoms. This scenario is different from MH 3 (M 5 Ga, Ge, Si) [17][18][19] , where the charge transfer from M to H atoms forms a strong ionic character. We propose a possible formation process of covalent bond in the R3m structure as follows: the H 2 molecules dissociated to hydrogen atoms under high pressure, and the hydrogen atoms then cooperated with sulfur atoms to form a strong polar covalent bond. This strong bond makes the H and S atoms tightly bound to form a dense H 3 S structure, yielding the reduction of its volume.
The predicted high T c for (H 2 S) 2 H 2 or H 3 S in the order of ,200 K is very encouraging, which prompted us to study the underlying superconducting mechanism. The corresponding Eliashberg spectral function a 2 F(v) and integrated l as a function of the frequency for the R3m at 130 GPa and Im-3m at 200 GPa are presented in Fig. 5. S vibrations in the frequency region below 15 THz contribute approximately 33.1% in total l for the R3m structure, whereas H vibrations above 18 THz contribute 66.9% of l. The low-frequency S vibrations (, 18 THz) and high-frequency H vibrational mode (. 20 THz) contribute 18.4% and 82.6% to the EPC, respectively, for the Im-3m structure. This result highlights that the H atoms play a significant role in superconductivity, although the S vibrations at low frequencies are also contributors. This physical mechanism is similar to GaH 3 18 and GeH 4 (H 2 ) 2 29 , but different from SiH 4 (H 2 ) 2 28 where the strong interactions between H 2 and SiH 4 molecules vibrations dominate the superconductivity. Notably, the calculated metallization pressure of (H 2 S) 2 H 2 (111 GPa) is within the diamond anvil cell capability. The DFT calculation is well known to underestimate the band gap because of its systematic defects for treating the excited states. Thus, the actual metallization pressure for (H 2 S) 2 H 2 is likely higher than the DFT estimated values in this study. Nevertheless, the calculated metallization pressure for (H 2 S) 2 H 2 is approximately one-third of the suggested pressure for the metallization of solid hydrogen 38 . The estimated maximal T c of 200 K in (H 2 S) 2 H 2 is higher than those predicted for most hydrogencontaining compounds, such as SnH 4 (H 2 ) 2 28 , GeH 4 (H 2 ) 2 29 , and MH 3 (M 5 Ga, Ge, Si) [17][18][19] . Our findings represent a significant step toward the understanding of the high pressure behavior of metallic hydrogen and hydrogen-rich hydrides, which can stimulate future high-pressure experiments on structural and conductivity measurements.

Methods
The high-pressure crystal structure of (H 2 S) 2 H 2 were explored by merging the evolutionary algorithm and ab initio total-energy calculations, as implemented in the USPEX code [30][31][32] . Structures (population size: 10-60 structures, increasing with system size) were produced randomly in the first generation. The subsequent generation is created from 60% of the lowest-enthalpy structures of the preceding generation. New structures are created by heredity (60%), permutation (10%), and lattice mutation (30%) operations. The best structure of each generation is also carried over to the next generation. The calculation stops when the best structure does not change for more than 20 generations.  The underlying structure relaxations are performed using density functional theory within the Perdew-Burke-Ernzerhof parameterization of the GGA 43 , as implemented in the Vienna ab initio simulation package VASP code 44 . The all-electron projector augmented wave method 45 is adopted with the core radii of 0.8 a.u. for H (1s 2 ) and 1.5 a.u. for S (3s 2 3p 4 ). Brillouin zone (BZ) sampling using a grid of spacing of 2p 3 0.05 Å 21 and a plane-wave basis set cutoff of 500 eV are sufficient for the initial search over structures. However, we recalculated the enthalpy curves with higher accuracy using the energy cutoff 800 eV and k-point mesh of 2p 3 0.03 Å 21 . These values were selected to ensure that the total energy are well converged to be better than 1 meV/atom. Lattice dynamics and superconducting properties were calculated using density functional perturbation theory 46 and the plane-wave pseudopotential method with Vanderbilt-type ultrasoft potentials 47 , as implemented in the QUANTUM-ESPRESSO code 48 . Convergence tests provide a suitable value of 80 Ry kinetic energy cutoff. The q-point mesh in the first BZ of 3 3 3 3 5 for R3m and 8 3 8 3 8 for Im-3m structures are used in the interpolation of the force constants for the phonon dispersion curve calculations. A denser k-point mesh 16 3 16 3 24 for R3m and 32 3 32 3 32 for Im-3m structures are adopted to ensure k-point sampling convergence with a Gaussians width of 0.03 Ry, which approximates the zero width limits in the calculation of EPC parameter l.