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Prediction of Stable Ground-State Lithium Polyhydrides under High Pressures

Hydrogen-rich compounds are important for understanding the dissociation of dense molecular hydrogen, as well as searching for room temperature Bardeen-Cooper-Schrieffer (BCS) superconductors. A recent high pressure experiment reported the successful synthesis of novel insulating lithium polyhydrides when above 130 GPa. However, the results are in sharp contrast to previous theoretical prediction by PBE functional that around this pressure range all lithium polyhydrides (LiHn (n = 2-8)) should be metallic. In order to address this discrepancy, we perform unbiased structure search with first principles calculation by including the van der Waals interaction that was ignored in previous prediction to predict the high pressure stable structures of LiHn (n = 2-11, 13) up to 200 GPa. We reproduce the previously predicted structures, and further find novel compositions that adopt more stable structures. The van der Waals functional (vdW-DF) significantly alters the relative stability of lithium polyhydrides, and predicts that the stable stoichiometries for the ground-state should be LiH2 and LiH9 at 130-170 GPa, and LiH2, LiH8 and LiH10 at 180-200 GPa. Accurate electronic structure calculation with GW approximation indicates that LiH, LiH2, LiH7, and LiH9 are insulative up to at least 208 GPa, and all other lithium polyhydrides are metallic. The calculated vibron frequencies of these insulating phases are also in accordance with the experimental infrared (IR) data. This reconciliation with the experimental observation suggests that LiH2, LiH7, and LiH9 are the possible candidates for lithium polyhydrides synthesized in that experiment. Our results reinstate the credibility of density functional theory in description H-rich compounds, and demonstrate the importance of considering van der Waals interaction in this class of materials.


Introduction
High pressure stability of hydrogen-rich compounds has attracted a lot of attention because of the richness of these materials in physics and chemistry that has been revealed by recent theoretical and experimental works [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . Some of them (e.g., H3S was predicted theoretically and then confirmed by experiment) would be possible candidates of "high temperature" Bardeen-Cooper-Schrieffer (BCS) superconductors [18][19][20][21] , and some others (e.g., LiHn) have important applications in the field of hydrogen storage and energy industry. Direct laboratory synthesis of hydrogen rich compound LiHn (n > 1) is difficult, and may be hindered by kinetic barriers when LiH and H2 are mixed together. It is well known that LiH keeps stable up to 160 GPa at 300 K, and has no chemical reaction with the molecular hydrogen 22 . Using laser to heat LiH+H2 mixture in a diamond anvil cell (DAC) is helpful to overcome this barrier, and this method provided the first preliminary experimental evidence of the formation of lithium polyhydrides that containing H2 units (referred to as LiHx-II). It indicated that LiHx-II was synthesized at 5 GPa and 1800 K, which is transparent up to 62 GPa 23 . Nevertheless, possible chemical contamination is difficult to avoid in the heating process. Also, a recent similar experiment up to 50 GPa and 2000 K was not able to detect any polyhydrides of Li 24 . In that experiment, however, novel NaH3 and NaH7 have been successfully synthesized. This indicates higher pressure is required for LiHn synthesis. Indeed, it was reported recently that at 300 K the lithium polyhydrides containing H2 units have also been synthesized when above 130 GPa. The new phases were detected using a noninvasive probing technique of synchrotron infrared (IR) absorption that has a high sensitivity to chemical changes 25 . The experiment unequivocally showed that these polyhydrides remain insulating up to 215 GPa, and the shifts of vibron IR frequencies exhibit a positive pressure dependence. This experiment was inspired by previous prediction made using the density functional theory on the stability of LiHn (n = 2-8) with the Perdew-Burke-Enzerhof (PBE) functional 26 . The results of the theoretical calculation and experiment are consistent in the formation pressure of lithium polyhydrides. And the measured vibron frequencies also roughly coincide with the most intense frequencies calculated for LiH2 and LiH6. It was tentatively assumed that the synthesized polyhydrides are LiH6 and LiH2, which contain H2 units in the structure, unfortunately, the observed insulative character contradicts with the predicted metallic behavior of these phases sharply. This qualitative discrepancy stimulates us 4 to pursue further theoretical investigations on LiHn with more accurate exchange-correlation functionals.
It is well known that the results of density functional theory (DFT) depend on the exchange-correlation functional 27 . Most previous structure searching and electronic structure calculations for hydrogen and alkali and alkaline earth hydrides were performed using the semi-local generalized gradient approximation (GGA), usually in the parameterization of PBE. It gives a good description of the structural stability of lithium and sodium, as well as the melting curve of hydrogen 28-31 . However, it was found very recently that PBE is poor when describing the dissociation of H2 molecules, and the correction from the van der Waals interaction is essential 32 , which was demonstrated by comparison to the most accurate quantum Monte Carlo (QMC) calculation, and the vdW-DF functional was shown to provide the most consistent bond length of the molecular phase of hydrogen with respect to QMC 32 . Since many hydrogen-rich compounds also contain H2 units, and some even involve H2 dissociation, it is expected that van der Waals interaction might play a significant role in the structural stability of these compounds. But this contribution was completely ignored in most previous DFT calculations, which could be the origination of the discrepancy between the theory and experiment on lithium polyhydrides.
In this work, we combine the unbiased structural search using the particle-swarm optimization (PSO) algorithm 33, 34 and DFT calculation with the van der Waals functional (vdW-DF) 35 to systematically investigate the phase stability of lithium polyhydrides LiHn (n = 2-11, 13) under high pressures. Our results reveal that the van der Waals interaction indeed alters the relative stability of lithium polyhydrides greatly. Furthermore, the electronic structure and vibrational property are also modified with respect to the PBE functional. The compounds with stoichiometry of LiH, LiH2, LiH7 and LiH9 are predicted to have a band gap up to at least 208 GPa, which agrees well with the observed insulative characters in the experiment. The pressure dependence of their vibron frequencies also has a trend similar to the experimental data 25 . These results constitute a much better theoretical interpretation of the recent experimental data.

Computational Details
We searched for high pressure structures of lithium polyhydrides using the particle swarm optimization methodology as implemented in the CALYPSO code 33, 34 . This approach is unbiased 5 by any prior known structure information and has demonstrated good efficiency in predicting high pressure structures of hydrogen-rich compounds 7-9, 15, 16, 36 and other novel materials 37-41 . The size of the system in our structure searches contains 1-4 formula units per simulation cell. Each search generation contains 30-50 structures and the structure searching simulation is usually stopped after generates 900-1500 structures. The underlying ab initio total energy calculations and structural relaxations are carried out using the plane wave basis and projector-augmented-wave (PAW) using denser grids at a high level of accuracy. Lattice dynamics and phonon contributions are calculated to verify the dynamical stability of predicted phases by the small displacement method as implemented in the PHONOPY package 47 .

Structure and convex hull
We perform structure searches for LiHn (n = 2-11, 13) at pressures of 150 and 200 GPa using vdW-DF functional, respectively. Thermodynamic stabilities of the LiHn compounds under various pressures are then investigated by calculating the formation enthalpy (ΔH) with respect to decomposition into LiH and H2, as shown in Figures 1 and 2. It is necessary to point out that LiH is always the stable compound of LiHn when n<2 26 , therefore it is not necessary to study the stability of LiHn with respect to the constituent elements Li and H2. Our vdW-DF calculations predict that the stable stoichiometries of polyhydrides are LiH2 and LiH9 at 130-170 GPa, which then shift to LiH2, LiH8, and LiH10 at 180-200 GPa. LiH2 has the most negative formation enthalpy with respect to LiH and H2 within the whole pressure range we studied. These accurate results are in sharp contrast to the previous PBE predictions of LiHn (n = 2-8) 26 , which suggested that LiH2, LiH6, and LiH8 are the three most stable lithium polyhydrides at pressures between 150-200 GPa, and LiH6 was predicted to be the most stable one. The later phase, however, is always metastable at the level of vdW-DF. Additionally, we also recalculate the formation enthalpies of LiH16 with vdW-DF functional using the structure given in Ref.
[48] that was predicted by PBE functional, 6 and find that it shifts up to above the convex hull when the van der Waals interaction is included, indicating that LiH16 is actually unstable or metastable in energetics. A comparison of the phase stability of LiHn calculated by LDA, PBE, and vdW-DF is presented in Figure 1. It can be clearly seen that the van der Waals interaction has a dramatic impact on the stability of LiHn: It not only adds two new phases LiH9 and LiH10 to the ground states (their structures are presented in Figure   3), but also removes LiH6 away from the convex hull. This effect of van der Waals interaction is a combination result of the better description of the electronic structure by advanced vdW-DF functional and the subsequent modification on the atomic structures. Table S1 in the Supporting Information (SI) provides the shortest bond length (H-H, Li-H and Li-Li) in lithium polyhydrides and their relative deviations of PBE with respect to the results calculated by vdW-DF functional. It is found that the vdW-DF corrections are mainly on the H-H distance that leads to shorter H2 bond length, and this is fully in line with our initial expectation. The consequence is that the van der Waals correction leads to slightly larger lattice parameters (see Table S3 in the Supporting Information), and the formation enthalpies are significantly reduced, thus alters the relative phase stability of lithium polyhydrides greatly. Inclusion of the zero-point energy at 0 K or the finite temperature free energy at 300 K has a negligible influence on the convex hull (see Figure S2 in the Supporting Information).
It should be mentioned that although the vdW-DF functional 35 significantly modifies the relative stabilities of LiH2, LiH6, and LiH8, the re-optimized structures of these phases using vdW-DF still have the same space groups as those obtained by PBE 26 . The structure details of them are presented in Table S4 of the Supporting Information. In addition, it should be emphasized that it is the first time that LiH9 and LiH10 phases are predicted to be stable ground states in lithium polyhydrides. The newly discovered LiH9 has three distinct structures, each with two formula units per cell (see Figure 3b): the first one (space group Cmc21) stabilizes at  GPa, the second one (space group Cc) is stable up to 223 GPa, and then transforms to the third one (with space group P-1) when beyond 223 GPa. LiH10 stabilizes in a structure of C2/c with two formula units per cell. In order to examine the dynamical stability of the predicted LiHn compounds, lattice dynamics are calculated with quasi-harmonic approximation. The results show that all predicted structures have no imaginary phonon modes, except for LiH11 that is not on the convex hull. This indicates that these predicted compounds should be stable or at least be 7 meta-stable, and could be detected experimentally. In particular, LiH7 and LiH9 are meta-stable at 180-200 GPa, where they have a slightly higher formation enthalpy with respect to LiH2, LiH8, and LiH10 at this pressure range.
The structural elements in these stable or meta-stable phases can be divided into three categories (see Figure S3 in the Supporting Information): (i) Li + ions and H2 dimers; (ii) Li + ions, H2 dimers, and hydridic Hanions; and (iii) Li + ions, H2 dimers, and asymmetric H -3 clusters. Only the first two cases were observed in the previous PBE calculations of lithium polyhydrides 26 , which appear in LiH2, LiH6, and LiH8, respectively. The newly discovered phases LiH7 and LiH9 also contain asymmetric H -3 units. This is analogous to the newly synthesized NaH3 and NaH7, where the former contains H2 units and the latter also has H -3 motif 24 . Both phases are insulative, similar to the experimentally observed LiHn 25 . The observation of asymmertric H -3 anions is astonishing since it was believed that such motif cannot occur in LiHn 49 , though they are ubiquitous in heavy alkali polyhydrides 49-51 . As shown in Figure 1, the vdW-DF functional brings the LiH7 and LiH9 phases closer to the convex hull, in which the LiH9 phase locates exactly on the convex hull in comparison with those predicted by PBE, respectively. For lithium-rich hydrides and heavy alkali polyhydrides, van der Waals interaction might also affect their relative stabilities.
For this reason, we also employ the vdW-DF functional to recalculate the formation enthalpies for the previously predicted structures of LinH (n=3-9) at 90 GPa 52 and NaHx (x =3, 6-12) at 50, 100, and 300 GPa 24, 53 , respectively (see Figures S4 and S5 in the Supporting Information). It is found that the vdW-DF corrections in NaHx are smaller than those in LiHn, and keep their relative stabilities unchanged in comparison with those predicted by PBE. This is likely due to the stronger coulomb interaction between Na and H arising from the lower ionization potential and larger ionic radius of Na as compared with Li 53 . But in lithium polyhydrides, the van  units is driven by the tendency to form multi-centered bonding 54 , here it is preferred because of the enhanced van der Waals interaction between Hanions and H2 dimers, whereas it is supposed to be because of the softness of the cations in the heavy alkali polyhydrides 49-51 .

Electronic properties
The recent high-pressure experiment revealed an insulating state in the synthesized lithium polyhydrides up to at least 215 GPa 25 . This is quite unexpected and contradicts the previous theoretical predictions made by PBE, which suggested that all phases of LiHn (n = 2-8) are metallic from 100 to 300 GPa 26 . One possible reason of this discrepancy is that some stable or meta-stable structures have been omitted in previous structure searches, as our newly discovered

Vibron frequencies
The vibron frequencies of LiH2 and LiH6 in previous PBE calculations for LiHn (n = 2-8) 26 were lately employed to lithium polyhydrides, and matched the infrared spectra observed in the experiment roughly 25 . But the poor quality of PBE when describing the structures and energetics of lithium polyhydrides greatly undermines its credibility, not to mention that the predicted metallic behavior of these two phases is completely in disagreement with the insulating feature up to 215 GPa observed in the experiment 25 . Based on our predicted phase stability of insulating LiH  Another possibility of the discrepancy might be that the experimentally observed ν1 and ν2 IR frequencies come from the influence of carbon (of DAC) on the vibron properties of LiHn, which is still a topic requires further exploration. According to above predicted insulative characters and vibron frequencies of lithium polyhydrides with vdW-DF calculations, we conclude that the possible candidates for the majority of the lithium polyhydrides that were synthesized in the recent experiment should be LiH2, LiH9, or the meta-stable LiH7, with LiH9 has the highest possibility.

Conclusions
The phase stability of LiHn (n = 2-11, 13) at high pressures are investigated using the particle-swarm optimization algorithm in combination with first-principles calculations using vdW-DF functional to take the van der Waals interaction into account. We found that the van der Waals correction significantly alters the relative stabilities of lithium polyhydrides, predicting that LiH2 and LiH9 are stable at 130-170 GPa, and LiH2, LiH8, and LiH10 become stable at 180-200 GPa. Most importantly, we discovered that besides LiH, polyhydrides LiH2, LiH7, and LiH9 also keep the insulating feature up to at least 208 GPa, which is in sharp contrast to the metallic behavior of LiH2, LiH6, and LiH8 predicted by PBE, but is in good accordance with the recent experimental results. Furthermore, the calculated vibron frequencies of these insulating phases agree qualitatively with the experimental infrared (IR) data, revealing that LiH9 could compose the major bulk of the synthesized polyhydrides, with very tiny amount of metastable LiH6 or LiH8.
Our calculation completely revised the phase stability of lithium polyhydrides, and brought the state-of-the-art ab initio predictions for the electronic properties and vibron frequencies of lithium polyhydrides to a high level with a much better agreement with the experiment than the previous theoretical assessment. It is worthwhile to note that the hydrogen content in LiH9 reaches a significant 57 wt %, about one order higher than the industrial use requirements. Knuo's experiment hinted that this polyhydride could be synthesized at a much low pressure and high temperature 23 , indicative of the attractive prospect of lithium polyhydrides in the application of hydrogen storage.

Supporting Information Available:
Phase         into LiH and H2 calculated using the vdW-DF functional at 150 GPa (with and without zero-point energies (ZPE)), and the Gibbs free energy of formation of LiHn at 300 K, respectively. The abscissa x is the fraction of H2 in the structures, and the filled symbols represent the stable ground-state compounds under the corresponding pressure.   Auxiliary Table S1. The shortest bond length in LiHn (n = 2, 6-10) at 150 GPa and their relative errors in PBE results with respect to those of the vdW-DF functional.