Synthesis of molecular metallic barium superhydride: pseudocubic BaH12

Following the discovery of high-temperature superconductivity in the La–H system, we studied the formation of new chemical compounds in the barium-hydrogen system at pressures from 75 to 173 GPa. Using in situ generation of hydrogen from NH3BH3, we synthesized previously unknown superhydride BaH12 with a pseudocubic (fcc) Ba sublattice in four independent experiments. Density functional theory calculations indicate close agreement between the theoretical and experimental equations of state. In addition, we identified previously known P6/mmm-BaH2 and possibly BaH10 and BaH6 as impurities in the samples. Ab initio calculations show that newly discovered semimetallic BaH12 contains H2 and H3– molecular units and detached H12 chains which are formed as a result of a Peierls-type distortion of the cubic cage structure. Barium dodecahydride is a unique molecular hydride with metallic conductivity that demonstrates the superconducting transition around 20 K at 140 GPa.

The manuscript reports on the first experimental synthesis and detection of metallic superconducting Ba hydride under high pressure. This discovery is very important because it can shed light on the mechanisms behind the chemistry and formation of high temperature superhydrides, and introduces a newly experimentally verified family of binary hydrides in the periodic table.
In spite of the interest and the importance of the findings reported in the paper, I found several flaws which prevent the manuscript to be published in the present status.
These are the major points: -the authors should show a rigorous comparison of the X-ray diffraction pattern between the most stable BaH12 symmetries (Cmc2_1, P2_1, P1) and experimental data. Only the Cmc2_1 pattern is shown in the manuscript.
-Why Cmc2_1 is the one detected experimentally even if the theoretical calculations clearly predict lowers symmetry structures as the most stable? Anharmonicity together with the nuclear quantum effects (NQE) are the most likely reasons. The authors should comment on that in the paper. NQE with anharmonic potentials can stabilize different symmetries than the ones obtained by a harmonic approach.
-The effect of impurities in the sample are not well discussed. According to Fig.3 the impurities are attributed to BaH12 stoichiometry, while in the abstract and in the conclusions BaH10 and BaH6 are cited as impurities, based on the convex hull diagram in Fig.1(c). This is confusing, and must be clarified.
-The synthesis of the "B" samples/cells is very well detailed, while for the "E" cells no description is reported. Please, add more information also for the "E" cells.
-In the theoretical analysis of superconductivity, which are the phonon modes that carry the largest el-ph coupling? In Fig. 5(b), reporting the physical values for different smearings is useless. One can systematically check the convergence as a function of smearing, at a given q-mesh. Only the converged results are of interest. Moreover, the 39-53 K range is reported in the text for the superconducting critical temperature at 150 GPa. The last sentence of the paragraph is not clear: "... and at 150 GPa the expected Tc may reach 59K", which is out of range. The authors should report in the main text at which pressure I4/mmm and Fm-3m yield the theoretically predicted superconducting Tc.
As a general comment, I found that the results in the paper are presented in a quite fragmented way. An effort to make them more homogeneously and uniformly organized must be done by the authors.
Other points: In the Supporting Information, it is explained that the electron-phonon coupling calculations are done with LDA, while all other calculations in PBE. Why the functional has been changed? The phonon and electron-phonon coupling calculations must be done at the relaxed structures. It is possible that PBE and LDA give different equilibrium structures and so different electron-phonon couplings and Tc. Please, verify.
In the S1 convex hull diagrams, one would expect to find not only the Cmc2_1 symmetry, but also the P2_1 and P1. Moreover, a direct comparison the the convex hull diagrams with and without ZPE would be useful, to study the impact of NQE at least in the harmonic approximation.
Page S26. Please, verify the cross references.
Reviewer #2 (Remarks to the Author): In the manuscript entitled "Synthesis of Molecular Metallic Barium Superhydride: Pseudocubic BaH12", Wuhao Chen et al. present a combined experimental and theoretical study to reveal the formation of a new superhydride BaH12 structure at pressures ranging from 75 to 173 GPa. In contrast with recently synthesized high-Tc superhydrides such as LaH10, YH6, ThH10, CeH9, and so on, BaH12 contains the molecular units of H2 and H3 as well as detached H12 chains. Interestingly, they argue that the latter one-dimensional chains are formed as a result of the Peierls-type distortion of a cage-like structure. Moreover, this superhydride is observed to exhibit a superconducting transition of ~20 K at 140 GPa, which is much lower than those of other superhydrides with cage structures.
Unfortunately, I do not see sufficient novelty and significance which can warrant publication of these results in Nature Communications and I cannot find this work to be interesting for a general audience of Nature Communications. In this referee's opinion, the current work is well suited for a more specialized journal. But I find a few deficiencies in the paper which are listed below: 1. The authors claimed that "The computed equation of state of Fm-3m BaH12 (Fig.1d) corresponds well to the experimental volume-pressure dependence." In Fig. 1d, the computed equation of states of Fm-3m BaH12 shows a phase transition, but it seems that there is no phase transition in the experiment results. I cannot find a good agreement between theory and experiment. What is the difference between the phases before and after the phase transition? How about this kind of phase transition in Cmc21 or P21 phase? 2. The authors claimed that the semimetallic Cmc21 phase of BaH12 explains well the experimental results. However, it is dynamically unstable (see Fig. 2). How does this unstable structure correspond to the experimental structure?

Reviewer #1 (Remarks to the Author):
The manuscript reports on the first experimental synthesis and detection of metallic superconducting Ba hydride under high pressure. This discovery is very important because it can shed light on the mechanisms behind the chemistry and formation of high temperature superhydrides, and introduces a newly experimentally verified family of binary hydrides in the periodic table.
In spite of the interest and the importance of the findings reported in the paper, I found several flaws which prevent the manuscript to be published in the present status.
These are the major points: -the authors should show a rigorous comparison of the X-ray diffraction pattern between the most stable BaH12 symmetries (Cmc2_1, P2_1, P1) and experimental data. Only the Cmc2_1 pattern is shown in the manuscript.
REPLY: We thank the reviewer for his interest to this research. This comparison was added to the Supporting Information. We also added discussion of this comparison in the main text. In fact, all these structures differ only in the structure of hydrogen sublattice, while the X-ray diffraction patterns come from the sublattice of barium atoms. Thus, XRD patterns of these structures are similar (pseudocubic) and practically cannot be distinguished from each other.

Fig. R1.
Comparison of the predicted XRD patterns of DFT relaxed (PAW_PBE) structures of Cmc2 1 -, P2 1and P1-BaH 12 at 150 GPa (before refinement). All considered structures have a pseudocubic diffraction pattern and a slight distortion of these structures in experimental conditions can transform the patterns to each other.
-Why Cmc2_1 is the one detected experimentally even if the theoretical calculations clearly predict lowers symmetry structures as the most stable? Anharmonicity together with the nuclear quantum effects (NQE) are the most likely reasons. The authors should comment on that in the paper. NQE with anharmonic potentials can stabilize different symmetries than the ones obtained by a harmonic approach. REPLY: The Cmc2 1 modification was chosen for the best fit with the observed experimental propertiesmetallic conductivity, superconductivity and absence of Raman signals. It is possible that the correct structural solution for the hydrogen sublattice is a combination of the found H-nets in the Cmc2 1 -, P2 1 -and P1-, and can only be found within supercells size > 100 atoms. We believe that such complex calculations, together with a detailed analysis of the impact of anharmonic effects on the structure, electronic properties and superconductivity of the compound, should be the subject of a separate work.
At the moment, there is no experimental technique to establish the exact structure of the hydrogen sublattice at pressures above 100 GPa. Thus, the solution found theoretically cannot be strictly justified experimentally, even for the famous H 3 S and LaH 10 superconductors.
We have studied the influence of anharmonicity in the framework of molecular dynamics. It confirms that the most stable modification at 300 K is also a pseudocubic P1-BaH 12 . However, as already was mentioned, the most thermodynamically stable phase is semiconducting, whereas in all experiments our samples were good metals even at pressures below 100 GPa.
-The effect of impurities in the sample are not well discussed. According to Fig.3 the impurities are attributed to BaH12 stoichiometry, while in the abstract and in the conclusions BaH10 and BaH6 are cited as impurities, based on the convex hull diagram in Fig.1(c). This is confusing, and must be clarified.
REPLY: discussion of these impurities has been moved to the Supporting Information, section "Synthesis at 173 and 154 GPa: Side Products". In fact, the XRD reflections of potentially existing BaH10 and BaH6 overlap with the BaH12 reflections and, therefore, we have insufficient information for identification of the impurities. BaH6 and BaH10 are proposed as possible candidates on the basis of theoretical modeling, simple indexing of the reflections in hexagonal space group (i.e. 'h-BaH 12 ') and calculations of the unit cell volumes at corresponding pressures. In Fig. 3 intensity of side reflections is not enough for a confident interpretation, but the peaks marked as (*) can be indexed in P63/mmc space group and corresponding unit cell volume is close to volume of BaH12.
-The synthesis of the "B" samples/cells is very well detailed, while for the "E" cells no description is reported. Please, add more information also for the "E" cells.
REPLY: Description of the "E"-series of diamond anvil cells was added to the Supporting Information ("Methods").
-In the theoretical analysis of superconductivity, which are the phonon modes that carry the largest el-ph coupling? In Fig. 5(b), reporting the physical values for different smearings is useless. One can systematically check the convergence as a function of smearing, at a given q-mesh. Only the converged results are of interest. Moreover, the 39-53 K range is reported in the text for the superconducting critical temperature at 150 GPa. The last sentence of the paragraph is not clear: "... and at 150 GPa the expected Tc may reach 59K", which is out of range. The authors should report in the main text at which pressure I4/mmm and Fm-3m yield the theoretically predicted superconducting Tc.
REPLY: The phonon modes corresponding to the largest el-ph coupling are low-frequency soft modes associated with both barium and hydrogen atoms. We have changed Fig. 5 (b) in the proposed manner. "59 K" -is a misprint, should be 53 K. Pressures (120-135 GPa) for which we calculated Tc of I4/mmm and Fm-3m were added.
As a general comment, I found that the results in the paper are presented in a quite fragmented way. An effort to make them more homogeneously and uniformly organized must be done by the authors.
REPLY: in the revised version the text was rewritten and its coherence improved. Newly added material is highlighted in blue.

Other points:
In the Supporting Information, it is explained that the electron-phonon coupling calculations are done with LDA, while all other calculations in PBE. Why the functional has been changed? The phonon and electronphonon coupling calculations must be done at the relaxed structures. It is possible that PBE and LDA give different equilibrium structures and so different electron-phonon couplings and Tc. Please, verify. REPLY: We are sorry for misleading, this was a misprint. All calculations were performed within the same functional (PBE).
In the S1 convex hull diagrams, one would expect to find not only the Cmc2_1 symmetry, but also the P2_1 and P1. Moreover, a direct comparison the convex hull diagrams with and without ZPE would be useful, to study the impact of NQE at least in the harmonic approximation.
REPLY: the direct comparison of Ba-H convex hulls with and without ZPE at 0 K was added to the Supporting Information (Fig. S4). At 150 GPa ZPE stabilizes Immm-BaH12, however, this compound has not been detected. At 100 GPa and below, Cmc21-BaH12 is close to the convex hull without accounting of ZPE. Discrepancies between the experiment and results of theoretical calculations may point to an insufficient accuracy of the known pseudopotentials of Ba and H in the studied range of pressures.
Page S26. Please, verify the cross references.
REPLY: We fixed this issue.

Reviewer #2 (Remarks to the Author):
In the manuscript entitled "Synthesis of Molecular Metallic Barium Superhydride: Pseudocubic BaH12", Wuhao Chen et al. present a combined experimental and theoretical study to reveal the formation of a new superhydride BaH12 structure at pressures ranging from 75 to 173 GPa. In contrast with recently synthesized high-Tc superhydrides such as LaH10, YH6, ThH10, CeH9, and so on, BaH12 contains the molecular units of H2 and H3 as well as detached H12 chains. Interestingly, they argue that the latter onedimensional chains are formed as a result of the Peierls-type distortion of a cage-like structure. Moreover, this superhydride is observed to exhibit a superconducting transition of ~20 K at 140 GPa, which is much lower than those of other superhydrides with cage structures.
Unfortunately, I do not see sufficient novelty and significance which can warrant publication of these results in Nature Communications and I cannot find this work to be interesting for a general audience of Nature Communications. In this referee's opinion, the current work is well suited for a more specialized journal.
BaH12 combines key features of both types of superhydrides: molecular structure with metallic properties and superconductivity. In the same time, the discovered here barium superhydride has one of the highest hydrogen content of all known hydrides. With 12 atoms of hydrogen per each Ba it is stable even below 100 GPa. Our work opens prospects for the synthesis of even more hydrogen rich compounds, such as predicted LaH16 and ErH15, and new ternary high-Tc polyhydrides in such systems as Ba-Y-H, Ba-La-H. But I find a few deficiencies in the paper which are listed below: 1. The authors claimed that "The computed equation of state of Fm-3m BaH12 (Fig.1d) corresponds well to the experimental volume-pressure dependence." In Fig. 1d, the computed equation of states of Fm-3m BaH12 shows a phase transition, but it seems that there is no phase transition in the experiment results. I cannot find a good agreement between theory and experiment. What is the difference between the phases before and after the phase transition? How about this kind of phase transition in Cmc21 or P21 phase? REPLY: The equation of state of the Fm-3m-BaH12 was compared to the experiment only above 100 GPa where the agreement is satisfactory. The phase transition below 100 GPa is irrelevant as we ruled out Fm-3m-BaH 12 because of its thermodynamic instability. Possible phase transitions in low-symmetry modifications of BaH 12 were also studied. There should be P2 1 -BaH 12  Immm-BaH 12 transition at ~190 GPa (Fig. R2). However, this pressure is beyond the experimentally studied region and Immm-BaH 12 was not detected experimentally. Fig. R2. Enthalpy-pressure diagram for low-symmetry modifications of BaH 12 at 100-300 GPa, 0 K.
2. The authors claimed that the semimetallic Cmc21 phase of BaH12 explains well the experimental results. However, it is dynamically unstable (see Fig. 2). How does this unstable structure correspond to the experimental structure?
REPLY: XRD pattern of Cmc2 1 -BaH 12 best fits to experimental X-ray diffraction. Electronic properties of Cmc2 1 -BaH 12 correspond well to observed metallic and superconducting properties of the synthesized barium superhydride. As we demonstrated, within DFT approach the Cmc2 1 -BaH 12 should undergo a distortion to P1. However, this distortion is not observed experimentally. Additional factors related to the questions, which are beyond the scope of this work: 1) anharmonic effects, 2) limitations of available Ba pseudopotentials.
3. How do you calculate the superconducting Tc of the pseudocubic Cmc21-BaH12, which has the imaginary phonon modes.
REPLY: Imaginary phonon modes were excluded from the calculations of isotropic Eliashberg spectral function performed via averaging of ω qv λ qv over the BZ.
4. The observed Tc values show a large difference between 20 and 7 K at 140 GPa and 132 GPa, respectively. Why does such large difference of Tc occur? REPLY: Because BaH 12 is near the metallization pressure (Fig. 2c, Fig. 4h). Even a small change in pressure in this region (120-140 GPa) leads to a relatively large change in the density of electronic states at the Fermi level and, therefore, in the superconducting properties. 5. How do the predicted Tc values of Cmc21-BaH12 vary as a function of pressure? Do they agree well with the experimental data? REPLY: We have calculated Tc at 2 points of pressure: 140 and 150 GPa (see revised Fig. 5), and results point to a substantial increase of the critical temperature along with the pressure (dTc/dP = +0.7 K). The available experimental data confirm this trend: we observed superconducting transition at about 5-7 K (132 GPa) and ~20 K at 140 GPa.
6. The authors claimed that "The low electronic density of state in semimetallic Cmc21 BaH12 looks typical for one-dimensional …H-H-H… chains, which are divided into H2, H3 fragments due to the Peierls-type distortion. In fact, all of the discussed structures of BaH12 can be viewed as a result of Peierls-type distortion." I cannot find the proper origin for this Peierls-distortion. Can you provide more detailed explanation for the Peierls-distortion mechanism?
REPLY: 1D chain of hydrogen atoms provides a classic example of Peierls distortion. The result of the distortion is changing distances between atoms in the chain. This leads to consequent decomposition of the chain into H 2 molecules with formation of stable non-metallic molecular hydrogen from unstable metallic modification. The Peierls effect is opposed by repulsive nearest neighbor forces that can keep the structure from distortion. Under high pressure, these forces become more pronounced, suppressing Peierls distortion and stabilizing the metallic state.
(2) Regarding Comment 2, the authors explained the stability of the P1 structure in terms of anharmonic effects and Ba pseudopotentials. However, I don't understand how these reasons influence the energetics between the Cmc21 and P1 phases.