Computational Design of Novel Hydrogen-Rich YS-H Compounds.

The recent successful findings of H3S and LaH10 compressed above 150 GPa with a record high T c (above 200 K) have shifted the focus on hydrogen-rich materials for high superconductivity at high pressure. Moreover, some studies also report that transition-metal ternary hydrides could be synthesized at a relatively low pressure (∼10 GPa). Therefore, it is highly desirable to investigate the crystal structures of ternary hydrides compounds at high pressure since they have been long considered as promising superconductors and hydrogen-storage materials with a high T c, and can be possibly synthesized at low pressure as well. In this work, combining state-of-the-art crystal structure prediction and first-principles calculations, we have performed extensive simulations on the crystal structures of YSH n (n = 1-10) compounds from ambient pressure to 200 GPa. We uncovered three thermodynamically stable compounds with stoichiometries of YSH, YSH2, and YSH5, which became energetically stable at ambient pressure, 143, and 87 GPa, respectively. Remarkably, it is found that YSH contains monoatomic H atoms, while YSH2 and YSH5 contain a mixture of atomlike and molecular hydrogen units. Upon compression, YSH, YSH2, and YSH5 undergo a transition from a semiconductor to a metallic phase at pressures of 168, 143, and 232 GPa, respectively. Unfortunately, electron-phonon coupling calculations reveal that these compounds possess a weak superconductivity with a relatively low T c (below 1 K), which mainly stem from the low value of density of states occupation at the Fermi level (E F). These results highlight that the crystal structures play a critical role in determining the high-temperature superconductivity.

Introduction

Much efforts have been devoted into the investigation of hydrogen-containing systems at extreme conditions, such as in the field of superconductivity (e.g., compressed hydrogen sulfides,[1−3] lanthanum hydrides[4−7]) and hydrogen-storage materials (e.g., RhH2,[8][8] lithium borohydrides,[9] lithium beryllium hydrides[10,11]), where high pressure[12] is a useful tool for helping design and synthesize the compounds that are not accessible at ambient conditions. H3S, being one of most successful examples, was observed with Tc of 203 K at 150 GPa;[3] such a record high value of Tc at that time led to a subsequent surge in theoretical and experimental studies.[1,13−23] Further studies reveal that the Tc of 203 K arises mainly from the dissociation product of H2S at high pressure, H3S;[2,15,17] also, in this cubic symmetry structure (Im3̅m phase), one S atom is linked to 6 H atoms to form strong H–S covalent bonds, which may play a key role in producing high Tc value in the H3S system.[23−26] Several H–S compounds (e.g., H2S, HS2, H4S3, H5S2, and H5S8)[1,13,17,19] have subsequently been identified under high pressure as well. Beside the above-mentioned H–S compounds, abroad range of hydrogen-containing materials have also attracted considerable attention under high pressure, e.g., iron hydrides,[27,28] LaH10, YH10,[4,5] etc. Remarkably, unique sodalite-like hydrogen cages are interpreted to play a key role in improving the superconductivity of YH6 (H24 cages) and YH10 (H32 cages), as estimated with Tc of 250–320 K at high pressure, which have much higher Tc than fcc-YH3 (∼40 K) is found at lower pressure.[4,5,29]

YS, one of the monochalcogenides of yttrium, has recently received great attention as a result of the finding of superconducting nature (∼2 K) at ambient conditions with a NaCl-type structure.[30,31] Upon compression, the NaCl-type phase was found to transform into the CsCl-type structure at around 50 GPa.[31,32] However, the superconducting nature of this material was suppressed with increasing pressure, where Tc decreases monotonically with pressure and no superconductivity was observed in the CsCl-type phase at high pressure.[33]

Recently, ternary hydrides are considered as promising candidates for high-temperature superconductors, since a high Tc is predicted in compressed ternary hydrides. Moreover, some transition-metal hydrides are also synthesized at a relatively low pressure (below 10 GPa),[34] indicating it may be feasible to search for high Tc materials in ternary hydrides at low pressure. Since superconducting YS compound is found to be stable at ambient pressure, a natural question is what if YS and hydrogen (YS–H compounds) are mixed together at high pressure. In view of a possibly novel structure and superconductivity of the YS–H system and so to better understand novel physicochemical properties at high pressure, we have performed extensive simulations on YS–H compounds up to 200 GPa. Three stable compounds, YSH, YSH2, and YSH5, are obtained, with monoatomic H atoms in the YSH structures, while YSH2 and YSH5 were found to contain a mixture of atomic H and molecular H2. All the predicted compounds became metallic phases with weak superconductivity, which demonstrates that the crystal structure plays an essential role in determining a high superconductivity.

Results and Discussion

Figure shows the thermodynamic stability of YSH by calculating the formation enthalpy dissociation into YS and solid H2, where YS is a reference decomposition product of YSH since YS compound has been experimentally reported at ambient pressure. It is clearly seen that three thermodynamically stable compounds with stoichiometries of YSH, YSH2, and YSH5 are predicted at high pressure, as shown in Figure . The optimized structural parameters of the predicted structures are summarized in Table S1.

Figure 1

Formation enthalpies (ΔH) of various YSH compounds for decomposition into YS and H2 (P63/m and C2/c) from 0 to 200 GPa. Data points on the convex hull (solid lines) represent species stable toward any type of decomposition. The structures of YS and H2 are from the refs (31) and (35), respectively.

YSH is found to be energetically stable from ambient pressure to 200 GPa (Figures and 2a), which is the highest pressure studied in the current work. It is not unreasonable that the YSH compound adopted a lower-energy electronic configuration, satisfying the octet rule that two of the three extra valence electrons of the Y atom are assigned to the S atom and the rest belong to the H atom.

Figure 2

Thermodynamic stability of YSH under high pressure relative to the most possible decomposition path in the corresponding pressure. Static enthalpy curves of (a) YSH (relative to YS + H2) and (b) relative enthalpies of the YSH compounds as a function of pressure. (c) YSH2 (relative to YSH + YSH5) and (d) YSH5 (relative to YSH + H2).

YSH compound was found to undergo the following complicated phase transitions at 0 K as a function of pressure (Figure b)At ambient pressure, it is predicted that the hexagonal P6̅m2 YSH is stable. With increasing pressure, this phase becomes unstable and transforms to the P63/mmc structure at 48 GPa (Figures a and 3b). It is noteworthy that both P6̅m2 and P63/mmc contain S-sharing YS6 units, while the only difference lies in the stacking pattern of the YS6 units. For example, in the P6̅m2 structure, the YS6 units contain the same Y–S bond length (2.86 Å at 0 GPa) aligned along the (0 0 1) direction, whereas for P63/mm, the YS6 units (Y–S 2.48–2.51 Å at 80 GPa) are centrosymmetric with the point of the S atom in the unit cell (Figure b).

Figure 3

Crystal structures of the energetically stable YSH system. YSH: (a) P6̅m2 at 0 GPa, (b) P63/mmc at 80 GPa, (c) Pnma at 150 GPa, and (d) C2/m at 200 GPa; (e) YSH2: Imm2 at 200 GPa; and (f) YSH5: Cmc21 at 200 GPa. The large, medium, and small colored spheres represent Y, S, and H atoms, respectively. Nonequivalent H atoms are labeled with numbers in different colors.

The stacking pattern of YS6 building blocks in YSH is similar to the MoS6 units in the corresponding P6̅m2 and P63/mmc structures of MoS2,[36] respectively. Upon compression, orthorhombic Pnma symmetry (Figure c), also consisting of YS6 units with Y–S (2.37–2.50 Å) becomes stable above 125 GPa. Eventually, YSH is stabilized as a monoclinic C2/m at 175 GPa (Figure d), which is composed of YS7 units, and the Y–S bonds have a bond length of 2.37–2.40 Å at 200 GPa. All H atoms exist as atomlike hydrogen in the YSH structures, which is well explained in ref (37) by introducing an effective additional electron.

Besides YSH, YSH2 and YSH5 emerge at the convex hull with increasing pressure. YSH2 is stable against decomposition to YSH and YSH5 at 143 GPa with the symmetry space group Imm2 (Figures c and 3e). The compound contains two layers of YS8 bridged by Y atoms, forming four Y–S bonds. The YS8 units are similar to those found in the YS CsCl structure. However, at 200 GPa, the Y–S bond lengths in YSH2 are slightly different (four bonds are 2.36 Å and the rest are 2.40 Å), whereas the Y–S bonds in YS have the same length of 2.40 Å.

The unit cell with Imm2 symmetry contains two molecular H2 units and four monoatomic H atoms. The H2 units are oriented along the [1 0 0] direction with the bond length of 0.87 Å at 200 GPa. The electron localization function of the intermolecular bond has a rather high value of (0.92), indicating the strong covalent feature of H–H bonds (Figure S1e). The H–H bond lengths are longer than those of a typical hydrogen molecule (0.74 Å) at ambient condition. The mixture of atomlike and molecular hydrogen has also been reported in binary Ca–H compounds[37,38] and Mg–H compounds.[39]

YSH5 with a symmetry space group Cmc21 becomes energetically stable at 87 GPa and remains stable at least up to 200 GPa (Figures d and 3f). The unit cell contains four YS5 units with S-sharing atoms, eight H2 molecules, and four monoatomic hydrogen atoms. Unlike YSH2, half of the H2 molecules in YSH5 are equivalent H atoms (blue, labeled 4 in Figure f) with an H–H length of 0.836 Å along the [1 0 0] direction, and the rest (labeled 1 and 3 in Figure f) are parallel to the bc planes with a longer H–H length (0.862 Å) at 200 GPa.

To better understand the electronic properties of predicted structures, we have performed the electronic band structures and projected density of states for these stable compounds as summarized in Figures and 5. The results reveal that YSH is a semiconductor with an indirect band gap of 1.62 eV at ambient pressure (Figure a). With increasing pressure, the gap gradually narrows to a direct band gap of 1.41 eV (Figure b) at 50 GPa, then to 0.17 eV at 130 GPa (Figure c), eventually, followed by a metallic C2/m phase (Figure d).

Figure 4

Electronic band structures and projected density of states (PDOS) of (a) P6̅m2–YSH at 0 GPa, (b) P63/mmc–YSH at 50 GPa, (c) Pnma–YSH at 130 GPa, and (d) C2/m–YSH at 180 GPa.

Figure 5

Electronic band structures and projected density of states (PDOS). Band structures of Cmc21–YSH5 at (a) 90 and (b) 235 GPa. (c) Band structure of Imm2–YSH2 at 150 GPa. (d) Band gap of YSH5 as a function of pressure.

To investigate the possible phase transition, we perform the structure prediction of YSH5 from ambient pressure to 300 GPa. The Cmc21 structure, which is the stable phase of YSH5 over the studied pressure range, is initially semiconducting with an indirect band gap of 1.44 eV at 90 GPa (Figure a) and metallized at 235 GPa (Figure d). Further prediction of the structure of YSH5 confirmed that Cmc21 is the stable phase at least up to 300 GPa. The metallic Imm2 nature of YSH2 can be determined by one band, mainly from the Y 4d orbital, crossing the EF, indicating a weak metallic nature, which is confirmed by the low value (∼0.020 states/eV) occupation at the EF of the density of states (DOS) (Figure c). The weak metallic nature is also found in metallic YSH (Figure d) and YSH5 (Figure b) with negligible occupation of states at EF.

The dynamic stability of these structures is confirmed by the absence of imaginary frequencies in their calculated phonon dispersions[40] (Figure ). The frequencies in YSH compounds are well-distinguished between H atoms and Y/S atoms; i.e., the heavier S and Y atoms contribute lower frequencies and higher frequencies are related to H atoms. The stretching vibrations (>80 THz) are assigned to the H2 units in YSH2 and YSH5 compounds and lower frequencies correspond to the H bending vibrations.

Figure 6

Phonon dispersion curves and phonon density of states (PHDOS) projected on Y, S, and H atoms of YSH. (a) P6̅m2–YSH at 0 GPa, (b) P63/mmc–YSH at 50 GPa, (c) Pnma–YSH at 130 GPa, (d) C2/m–YSH at 180 GPa, (e) Imm2–YSH2 at 150 GPa, and (f) Cmc21–YSH5 at 90 GPa.

Given the high Tc of binary Y–H and S–H compounds, we also performed electron–phonon coupling calculations within the framework of BCS theory. However, the estimated Tc is less than 1 K (Table S2), which is much lower than those of H3S (200 K[2]), YH10 (300 K[4,5]), and YH6 (250 K[29]). In fact, it is not unreasonable that a low value of DOS occupation exists at EF. The S–H and Y–H bonding in the YSH compounds is investigated further by plotting the electron localization functions (Figure S1). No electron localization in YSH is found between H and S (Y) atoms in Figure S1a–d, ruling out the strong covalent feature in H–S (Y) bonding, which has been reported to be responsible for the high Tc of H3S.[23] The possible charge transfer is explored by calculating the charge density difference (Figure ). The charge density is depleted on the Y atoms and increased on the S and H atoms in all the YSH compounds, which reflects their ionic nature. By calculating the Bader charge using the quantum atoms in molecular[41] analysis (Table S3), we find that the Y atoms donate 1.87 e– per atom at ambient pressure, from which S atoms gain 1.27 e– and H atoms accept the rest, 0.60 e–, in YSH. The amount of transferred charge decreases slightly when the pressure increases (1.5 and 1.34 e– at 150 and 200 GPa, respectively), but the ionic nature of S (Y)–H does not change. In contrast, there is almost no charge transfer (−0.05 e–) between H2 and Y atoms in YSH2. Generally, metals with small charge transfer are not expected be good superconductors because the metallization comes from the broadening of the H– and H2 δ* antibonding orbital,[36] which is also found in the I4/mmm symmetry compound, CaH4.[37,38] For YSH5, the charge transfer between H2 and Y atoms increases to 0.18 e– and Tc slightly increases to 0.70 K; however, the superconductivity is still weak due to low value of DOS occupation at EF.

Figure 7

Charge density difference with an isosurface value of 0.009 e/bohr for YSH. The structures (a)–(f) correspond to those in Figure . The gain and loss of charge are denoted by yellow and cyan, respectively.

Conclusions

We have systematically investigated the crystal structures and stabilities of a YSH ternary system under high pressure using swarm-intelligence structure prediction methodology within the first-principles electronic structure framework. Three stable ternary hydrides, YSH, YSH2, and YSH5, were identified by structural prediction under high pressure. Only atomlike H species were found in YSH compounds. However, the stable structures of YSH2 and YSH5 contained mixed atomic H and molecular H2. YSH, YSH2, and YSH5 can be metallized at pressures of 168, 143, and 232 GPa, respectively. The electron–phonon coupling calculations reveal that YSH, YSH2, and YSH5 have weak superconductivities due to the low value of DOS occupation at EF. The high symmetry of the structures is favorable for achieving a high Tc superconductivity compared with the high Tc of the corresponding binary hydrides, fcc YH10 and cubic SH3. Our work provides a new guidance for future experimental work on the Y–S–H ternary system.

Computational Details

A crystal structure search was performed with the CALYPSO code[42,43] based on a particle swarm optimization algorithm whose validity has been verified by correctly predicting various crystal structures under high pressure.[37,44−51] To investigate the properties of the YS–H system, first, we performed systematic structure searches of H-rich concentration of YSH (n = 1–10) with a maximum four formula units per simulation cell at 10, 50, 100, 150, and 200 GPa. Each generation contains 50 structures. The first generation of the crystal structures is generated randomly with some symmetry constraints and subsequent optimizations. For the subsequent generations, 60% of the structures with the lowest enthalpy are selected in the previous generation to form the next generation through the particle swarm optimization algorithms, while the rest 40% are generated randomly. The structure search was considered converged when ∼1000 successive structures were generated after a lowest energy structure was found. The underlying ab initio structural relaxations were performed using density functional theory with the Perdew–Burke–Ernzerhof functional of the generalized gradient approximation[52] as implemented in the Vienna ab initio simulation package.[53] The all-electron projector-augmented wave (PAW) method was used with the PAW potentials,[54] where 4s24p65s24d1, 3s23p4, and 1s1 are treated as valence electrons for the Y, S, and H atoms, respectively. A cutoff energy for the expansion of the wave function into the plane wave basis was set to 1000 eV. The Monkhorst–Pack k-point meshes[55] with a grid density of 0.20 Å–1 were chosen to ensure that the total energy convergence is better than 1 meV per atom. The electron–phonon coupling calculations were performed within the framework of the linear response theory through Quantum-ESPRESSO code.[56] Ultrasoft pseudopotentials for Y, S, and H were used with a kinetic cutoff energy of 80 Ry. The crystal structures and ELF are plotted using the VESTA software.[57]