The Li–F–H ternary system at high pressures

The incorporation of hydrogen in materials is of both fundamental and technological interest. Hydrogen undergoes compound formation with elements across the periodic table and can adopt various bonding schemes varying from ionic to covalent to van der Waals when present in the molecular form. Technologically, hydrides have been employed in nuclear reactor applications, but their formation can precipitate corrosion and embrittlement.¹ More recently, a wide variety of hydrides have been considered for energy applications such as for hydrogen storage² and in battery materials.³ 

High pressure has been explored as a route to increase the amount of hydrogen that may be stored in materials,^4,5 and to synthesize novel materials such as high temperature superconductors.⁶ A broad range of structures can form under pressure, many of which can be very hydrogen rich. Hydrogenic motifs that have been identified include quasimolecular H₂ units and atomic H⁻, as well as extended hydrogenic lattices.^7–9 Many of the hydrogen-rich phases could be very high-temperature superconductors, as first established for H₃S and LaH₁₀. These phases were predicted^10–12 and synthesized^13,14 under pressure, with measured superconducting critical temperatures, T_cs, as high as 203 K¹³ at 150 GPa and 250–260 K around 200 GPa,^15,16 respectively. The theoretical studies of compressed binary hydrides have paved the way to investigations of more complex ternary systems including LiPH₆,¹⁷ LiP₂H₁₄,¹⁸ Li₂MgH₁₆,¹⁹ CH₄ intercalated H₃S,^20,21 SH₃–SeH₃,²² MgCH₄,²³ H₃P_0.15S_0.85,²⁴ CaSH₃,²⁵ and CaYH₁₂,²⁶ which are predicted to possess T_c values of 100–473 K at pressures ranging from 100 to 230 GPa. In fact, recently, a T_c of 288 K has been reported experimentally in a phase (or phases) in the C–S–H ternary system near 270 GPa.²⁷ 

The ionic solid LiF has been employed as a radiation dosimeter in molten salt coolants for nuclear reactors, and it is a test system for models of ionic solids. With its large bandgap, LiF has the lowest refractive index of all common infrared materials. It also possesses the highest UV transmission of any material, being able to transmit significantly into the VUV region. The properties of LiF render it important for a wide range of applications in high pressure research, and its properties under static high pressures have been widely studied (see Refs. 28 and 29). This includes the use of LiF as a pressure standard and pressure-transmitting medium in diamond anvil cell experiments.^30,31 Moreover, because LiF is observed to remain optically transparent to at least 900 GPa,³² it has been employed extensively as a window material in dynamic compression experiments,³³ e.g., for interferometric velocimetry (VISAR) diagnostics. Because of the importance of LiF in these experiments, its high pressure properties continue to be of great interest.^{28,29,32,34–45}

The interaction of LiF with hydrogen under pressure has not been explored in detail experimentally or theoretically. Early on, it was suggested that LiH₂F, where a hydrogen atom or H₂ molecule is placed in the pseudo-octahedral holes in the B1 structure of LiF, might be a way to achieve the metallization of hydrogen and concomitant superconductivity as discussed above.⁴⁶ In addition, possible pressure-induced chemical reactions between hydrogen and LiF windows in dynamic compression experiments near 300 GPa^44,45 could affect the interpretation of the results. Given the above data and the propensity for formation of stable and metastable hydrides under pressure, we were motivated to apply crystal structure prediction techniques to the Li–F–H ternary system at multimegabar pressure. By now, the phase diagrams of the elemental (Li,⁴⁷ H,⁴⁸ and F⁴⁹) and binary (Li–H,^50,51 H–F,^52,53 and Li–F^40,41) systems have been studied computationally up to 300 GPa, providing the basis for us to explore the high pressure phases of the ternary system.

Using evolutionary crystal structure prediction techniques, we find a number of metastable phases that are within 50 meV/atom of the convex hull and are therefore potentially synthesizable. Common structural motifs present in these phases include $HnFn+1−$ anions of various lengths and Li⁺ counter-cations. Most of these crystalline lattices are calculated to be wide-gap insulators, with the exception of LiF₃H, which is predicted to be metallic and superconducting below 0.1 K. Li₃F₄H is found to be thermodynamically and dynamically stable at atmospheric pressure.

Crystal structure prediction searches were performed using density functional theory (DFT) coupled with the evolutionary algorithm (EA), XtalOpt, release 9.^54–56 Duplicate structures were detected via the XtalComp algorithm.⁵⁷ EA runs were carried out on LiFH_n (n = 2, 3), LiF₂H_n (n = 1–2), LiF₃H_n (n = 1–3), LiF₄H_n (n = 1, 4), Li₂F_mH (m = 1–3), Li₂FH₂, Li₃F_mH (m = 1–4), Li₄FH₄, Li₄F₃H, and Li₄F₄H stoichiometries at 300 GPa employing 2–3 formula units (FUs) within the simulation cells. The lowest enthalpy structures obtained from each search were relaxed at 300 GPa.

Geometry optimizations and electronic structure calculations were performed using DFT as implemented in the Vienna Ab Initio Simulation Package (VASP) version 5.4.1,⁵⁸ with the gradient-corrected exchange and correlation functional of Perdew, Burke, and Ernzerhof (PBE).⁵⁹ The projector augmented wave (PAW) method⁶⁰ was used to treat the core states along with a plane-wave basis set with an energy cutoff of 700 eV. The F 2s²2p⁵, H 1s¹, and Li 1s²2s¹ electrons were treated explicitly using the PAW-PBE F, PAW-PBE H, and PAW-PBE Li_sv POTCARs. In the EA searches, only the Li 2s¹ electrons were considered as valence because exploratory EA runs for LiF₄H₃ with the two sets of POTCARs found the same lowest enthalpy structures, and their volumes differed by less than 0.5%. The k-point grids were generated using the Γ-centered Monkhorst–Pack scheme, and the number of divisions along each reciprocal lattice vector was chosen such that the product of this number with the real lattice constant was 30 Å in the structure searches and 50 Å otherwise. The crystal orbital Hamiltonian populations (COHPs)⁶¹ and the negative of the COHPs integrated to the Fermi level (−iCOHPs) were calculated using the LOBSTER package.⁶² Phonon calculations were performed using VASP combined with the Phonopy⁶³ package under the harmonic approximation. The supercells were chosen such that the number of atoms within them was always greater than 100. Infrared (IR) spectra were simulated using the Phonopy-Spectroscopy package.^64,65

Density functional perturbation theory (DFPT), as implemented in the Quantum Espresso (QE)⁶⁶ program, was used to obtain the dynamical matrix of the LiF₃H phase. The Li, F, and H pseudopotentials, obtained from the GRBV pseudopotential library, adopted used the 1s²2s^0.55, 2s²2⁵, and 1s¹ valence configurations, respectively. The plane-wave basis set cutoff energies were set to 90 Ry, and the Brillouin-zone sampling scheme of Methfessel and Paxton⁶⁷ using a smearing of 0.002 Ry and a 12 × 12 × 12 k-point grid was employed. The electron phonon coupling (EPC), λ, was calculated using a Gaussian broadening of 0.012 Ry and a 3 × 3 × 3 q-grid. The critical superconducting temperature, T_c, was estimated using the Allen–Dynes modified McMillan equation,⁶⁸ 

where ω_log is the logarithmic average frequency and μ^* is the Coulomb pseudopotential, often assumed to be between ∼0.1 and 0.13.

The geometry optimization of the (F–H–F)⁻ anion in the gas phase was performed using the Amsterdam Density Functional (ADF) software package.^69,70 The basis functions consisted of an all electron triple-ζ Slater-type basis set with polarization functions (TZP) from the ADF basis set library,⁷¹ and the PBE⁵⁹ functional was employed.

At 300 GPa and 0 K, the thermodynamically stable phases located on the three-dimensional convex hull are the elemental and binary phases: Li, H₂, F₂, LiF, HF, LiH, LiH₂, and LiH₆. However, all of the ternary Li–F–H phases uncovered here are dynamically stable. Among them, LiF₃H₂, LiF₂H, Li₃F₄H, LiF₄H₄, and Li₂F₃H are within 41 meV/atom of the hull (Fig. S3 and Table S1), while LiF₃H₃, Li₃FH, LiF₃H, Li₄F₃H, Li₄FH₄, LiF₄H, Li₂FH, Li₂F₂H, and Li₃F₂H are within 58–91 meV/atom of the hull. All other phases are less stable with the most unfavorable candidate that was identified, LiFH₃, lying 222.5 meV/atom above the hull. As described in Fig. S5, the LiH₂F phase found in the EA searches was considerably more stable than those proposed previously by Gilman.⁴⁶ 

When the zero-point-energy (ZPE) was taken into consideration, LiF₃H joined the aforementioned five phases to lie less than 50 meV/atom from the hull (Fig. S4 and Table S2). The reaction enthalpies, ΔH_F, of the decomposition of LiF₃H₂, LiF₂H, Li₃F₄H, and Li₂F₃H into LiF and HF were computed to be −13.3 (−10.9), −29.3 (−28.5), −33.1 (−33.8), and −40.5 (−41.1) meV/atom when the ZPE was neglected (taken into consideration), consistent with the fact that they lie above the convex hull. Other reactions that thermodynamically destabilize two additional phases of interest and their computed reaction enthalpies are $LiF4H4→LiF+3HF+12H2$ [ΔH_F = −33.4 (−37.0) meV/atom] and $LiF3H→LiF+HF+12F2$ [ΔH_F = −62.5 (−49.0) meV/atom].

A recent data-mining study found that the 90th percentile of the 0 K DFT-calculated metastability of all of the compounds within the Inorganic Crystal Structure Database (ICSD) was ∼70 meV/atom.⁷² For matter under pressure, the choice of the synthetic pathway, including the precursors and temperatures employed, might be able to produce kinetically stable phases. Several examples of metastable hydrides that have been synthesized under pressure include C_xS_yH_z,^20,21,27 PH_n,^73–76 and CaH_2.5.⁷⁷ Moreover, anharmonic and quantum nuclear effects, not considered here, can be important in determining the stability of compounds, in particular those containing light elements.⁷⁸ Therefore, we chose to analyze the structure, bonding, and properties of phases that were within 50 meV/atom of the convex hull at 0 K.

Our first-principles based crystal structure prediction searches predicted that $P1¯LiF3H2$⁠, shown in Fig. 1(a), is the closest phase to the 300 GPa convex hull. A prominent structural motif within LiF₃H₂ is the V-shaped (FH–F–HF)⁻ anion, whose H–F_middle–H bond angle measures 110.0°, and F_terminal–H–F_middle bond angles measure 160.3° and 165.7°. The F_terminal–H bonds comprising this building block are shorter than the H–F_middle bonds (0.998 and 1.004 Å vs 1.107 and 1.099 Å, respectively). Each lithium cation is coordinated to six fluorine atoms at distances ranging from 1.587 to 1.638 Å, and each fluorine atom is coordinated to two lithium cations. One of the Li–F_terminal contacts in each (FH–F–HF)⁻ unit measures 1.587 Å, and the fluorine involved in this contact forms the shortest H–F_terminal bond with the largest F_terminal–H–F_middle bond angle.

The phase that is second closest to the convex hull, $P1¯LiF2$H, shown in Fig. 1(b), resembles LiF₃H₂, but the (FH–F–HF)⁻ units are replaced by bifluoride, (F–H–F)⁻, anions. This phase is characterized by layers containing Li⁺ and (F–H–F)⁻ units that are stacked in an ABCABC… fashion along the c-axis. The (F–H–F)⁻ molecules in layers A and B are bent with a bond angle of 165.3° and bond lengths of 1.034 and 1.067 Å. In going from one layer to the next, the orientation of the (F–H–F)⁻ units changes via a rotation of 180° around the c-axis. In layer C, the (F–H–F)⁻ anion is linear and symmetric, with both of the H–F bonds measuring 1.037 Å.

The gas phase bifluoride anion possesses D_∞h symmetry and is characterized by a strong three-center four-electron (3c–4e) bond where four electrons fill two molecular orbitals formed from linear combinations of the H 1s and F 2pσ atomic orbitals.⁷⁹ In crystals, the anion is often bent with two unequal F–H bond lengths, and in some cases it may better be described as (F⁻)(HF) with one formal H–F classic two-center two-electron (2c–2e) bond and one F⁻⋯H hydrogen bond.^80,81 A deformation from the ideal symmetry is often a result of the interaction with Lewis acids in the crystal lattice or with external hydrogen bonds. Although less common, an (FHF)⁻⋯HF structural motif, which may be treated as an $F3H2−$ ion when the bonds are nearly symmetric, has also been observed in various salts.^82–84 A few inorganic compounds containing other suprahalide anions with the general formula $HnFn+1−$ and n = 3–6 are also known.^81,85

The two molecular motifs present within $P1¯LiF3H2$ and $P1¯LiF3H2$⁠, (FH–F–HF)⁻ and (F–H–F)⁻, are also found in the other four compounds that are calculated to lie within 50 meV/atom of the 300 GPa convex hull [Figs. 1(c)–1(f)]. Bifluoride anions are present in all of these structures, and LiF₄H₄ also contains the longer five-atom chain. The smaller $HnFn+1−$ anion is the only molecular species found in phases where the H:Li ratio ≤1 and the H:F ratio ≤0.5.

We now examine the structural peculiarity of these phases, starting with those that only contain the bifluoride anion. The C2/m symmetry Li₃F₄H phase consists of layers of bifluoride anions that lie parallel to each other stacked along the c-axis. These are separated by a five atom thick LiF slab made from alternating Li and F layers, with Li comprising both the top and bottom layers. At ambient conditions, LiF crystallizes in the B1 (⁠$Fm3¯m$⁠) structure, and first-principles calculations have shown that it does not undergo a phase transition to the B2 structure to at least 1 TPa at 0 K.⁴⁰ Not surprisingly, the LiF layer in Li₃F₄H can be described as a slightly distorted slab cut out from the B1 phase. The segregation into distinct layers observed within Li₃F₄H is consistent with the finding that its decomposition into LiF and HF is preferred.

The slightly less stable C2/m symmetry Li₂F₃H phase can be constructed from Li₃F₄H by removing two layers (one of lithium and one of fluorine) from the LiF slab. In both of these compounds, the (F–H–F)⁻ units are linear and symmetric with H–F bond lengths of 1.041 Å, and the fluorine atom is coordinated to three lithium ions in the LiF slab. P2₁/m LiF₃H also contains layers of linear (F–H–F)⁻ anions; however, they are not symmetric with H–F bond lengths of 1.079 and 1.014 Å, and each one of the fluorine atoms within them is coordinated to two lithium ions in the outer most layer of the LiF slab. It is conceivable that phases with these same stoichiometries, but different numbers of atoms in the unit cell, or different stoichiometries that are composed of a single layer of bifluoride anions separated by LiF layers of varying thickness may also be metastable, with enthalpies of formation falling within the realm of synthesizability.

The most complex structure identified, P1 LiF₄H₄, contains both the short (F–H–F)⁻ and the long (FH–F–HF)⁻ anions, along with triangular $H3+$ cations. This compound can also be viewed as a layered phase, with bifluoride anions and $H3+$ cations comprising one set of layers. Each one of the fluorine atoms in these (F–H–F)⁻ units is coordinated to a single lithium ion within the next layer, which also contains (FH–F–HF)⁻ motifs wherein both of the terminal fluorines are coordinated to two lithium ions. Thus, each Li⁺ is coordinated to seven fluorines, three belonging to (F–H–F)⁻ and four belonging to (FH–F–HF)⁻, at distances ranging from 1.601 to 1.662 Å.

The bifluoride anion linkages in LiF₄H₄ are not linear, with a bond angle of 175.5°, nor are they symmetric, with bond lengths measuring 1.035 and 1.042 Å. The $H3+$ molecular units resemble the trihydrogen cation, one of the most abundant interstellar molecules,⁸⁶ which assumes an equilateral triangle and forms a three-center two-electron (3c–2e) bond. However, the $H3+$ molecule found here is not quite a perfect equilateral triangle, with bond angles of 58.4°, 60.4°, and 61.2°, and bond lengths of 0.805, 0.782, and 0.799 Å. This structural motif has been predicted to exist in H₅Cl^52,87,88 as well as H₂F, H₃F, and H₅F⁵² phases under pressure. The geometric parameters of the (FH–F–HF)⁻ molecules resemble those in the LiF₃H₂ phase, with bond angles of 107.9° (H–F_middle–H), as well as 160.1° and 166.4° (F_terminal–H–F_middle), and bond lengths of 0.997 and 1.002 Å (H–F_terminal), as well as 1.110 and 1.098 Å (H–F_middle). Similar to what was found in $P1¯LiF3H2$⁠, the terminal fluorine atom that is closest to a lithium ion has a smaller F–H–F bond angle and shorter H–F bond length.

Because of the difficulties inherent in measuring the position of hydrogen atoms in crystals, the geometry of the bifluoride anion in simple salts such as KHF₂⁸⁹ and NaHF₂⁹⁰ has been debated. Two types of bonding scenarios are possible: a delocalized 3c–4e bond in the symmetric structure vs one 2c–2e bond and one extremely strong hydrogen bond in the unsymmetric geometry. In more complex salts, hydrogen bonding with other moieties or electrostatic interactions with strong Lewis acids can lead to a deviation from linearity.⁸⁰ As discussed above, examples of both of these scenarios are present within the phases predicted here. A recent study employed a combination of two-dimensional femtosecond infrared spectroscopy coupled with high-level quantum calculations to probe the crossover from hydrogen to chemical bonding in an (F–H–F)⁻ anion dissolved in water.⁹¹ In the strongly hydrogen bonded regime, the delocalization of the proton in a flat potential was shown to lead to the phenomenon of superharmonicity, where the spacing between vibrational states increases analogous to what is found for the particle in a box. Moreover, a detailed analysis of the bonding suggested that the 3c–4e bonded species can better be characterized as a hydrogen-mediated donor–acceptor bond between the fluorine atoms.

It is also instructive to consider the evolution of the low temperature phases of HF under pressure. At ambient conditions, the Cmc2₁ symmetry HF phase contains planar zigzag chains of hydrogen-bonded molecules that are held together via van der Waals forces.⁹² Between 25 and 143 GPa, a Cmcm symmetry structure where each fluorine atom is symmetrically bonded to two hydrogen atoms is preferred.^53,93 First principles calculations have predicted a further transition to a Pnma symmetry structure with nearly symmetric H–F⁵³ bonds that is stable until at least 900 GPa.⁹⁴ 

In order to better understand the bonding within the (F–H–F)⁻ and (FH–F–HF)⁻ anions, we calculated the negative of the crystal orbital Hamilton populations between select atoms integrated to the Fermi level (-iCOHP) because they can be used to gauge the bond strength. The results obtained for the Li–F–H phases can be compared with the values calculated for a symmetric (F–H–F)⁻ molecule optimized in the gas phase at 0 GPa and Pnma HF optimized at 300 GPa (Table I).

LiF₂H, Li₃F₄H, and Li₂F₃H contain linear bifluoride anions with equivalent F–H bond lengths, and therefore, they can be considered 3c–4e bonded species. Because the neighboring Li⁺ cations are arranged symmetrically about the (F–H–F)⁻ anions, the geometry of these molecular motifs is not distorted via electrostatic interactions. The F–H bond lengths in these species are shorter than in the bifluoride anion in the gas phase, and the bond strengths, as measured by the -iCOHPs, are therefore almost twice as large, in line with the bond strengthening that is expected to occur because of increased orbital overlap under pressure.⁹⁵ The calculated F–H bond strengths and lengths in the Li–F–H ternaries are not too different from those found in solid HF at the same pressure. In addition to the D_∞h symmetry (F–H–F)⁻ unit, LiF₂H also contains a bifluoride anion that is bent and asymmetric because of electrostatic interactions with neighboring Li⁺ cations and other (F–H–F)⁻ species. Both sets of H–F bonds are stronger and shorter than in the gas phase molecule. Asymmetric (F–H–F)⁻ also comprises LiF₄H₄, whose bifluoride anion is slightly bent, and LiF₃H, where it remains linear. The bond strengths in the ternaries typically increase with decreasing bond lengths.

Although the asymmetric H–F bonds within the 1D zigzag chains in HF do not have a significantly different bond length, their different chemical environments affect their strengths with calculated -iCOHPs of 7.46 and 7.09 eV/bond. Generally speaking, the H–F bond distances in Pnma HF are slightly longer than in the ternaries, but the -iCOHPs are also larger. This suggests that the complicated chemical environment in the ternary phases with the presence of Lewis acid species destabilizes the bifluoride anions.

Figure 2 illustrates the H–F bond lengths and associated −iCOHPs in the more complicated (FH–F–HF)⁻ units that are present in LiF₃H₂ and LiF₄H₄. In both cases, the H–F_terminal bonds are shorter and stronger than in HF or in any of the ternaries, whereas the H–F_middle bonds are longer and weaker (∼1 Å and 7.9–8.3 eV/bond vs ∼1.1 Å and 5.4–5.7 eV/bond). This coincides with the 1 atm picture where the (FH–F–HF)⁻ motifs are viewed as being composed of two HF units hydrogen bonded to a central F⁻.⁸⁰ 

Bader charges were calculated to verify the formal charges assigned. The results, provided in Table S3, show that in all of the Li–F–H phases, the Bader charge on Li fell between +0.83 and +0.86, in line with a formal +1 oxidation state. The charges on the fluorine and hydrogen atoms within the $HnFn+1−$ anions typically ranged from −0.74 to −0.80 and +0.73 to +0.76, respectively, which is close to the values computed for HF at the same pressure, ±0.75. Generally speaking, the overall charges on the $HnFn+1−$ anions fell between −0.76 and −0.85, and the charges on the fluorine atoms comprising the LiF slabs were somewhat more negative than in the molecular motifs, −0.82/−0.83. Only one phase, LiF₃H, deviated from these trends. The reason for this turns out to be key for the metallicity of this phase, as described below.

Figure 3 plots the electron localization functions (ELFs) of LiF₃H₂, LiF₂H, and LiF₄H₄ because they are representative of all of the structural motifs observed. LiF₃H₂ and LiF₄H₄ contain the (FH–F–HF)⁻ anion; LiF₄H₄ also accommodates the $H3+$ unit and asymmetric (F–H–F)⁻, and LiF₂H contains both symmetric and asymmetric (F–H–F)⁻. Because the planes of the contours chosen do not necessarily coincide with planes passing through the bifluoride anions and $H3+$⁠, and because a single plane cannot pass through (FH–F–HF)⁻, some discontinuities are present in the ELF contour maps. Therefore, isosurface plots are also provided in Figs. S7–S9. Nonetheless, the ELF plots clearly show high regions of localization around the fluorine atoms, with slightly more density localized along the F–H contacts that are shorter as compared to those that are longer. Moreover, the ELF is high around the $H3+$ molecule because of its 3c–2e bond.

The electronic band structure and density of states (DOS) plots of LiF₃H₂, LiF₂H, Li₃F₄H, LiF₄H₄, Li₂F₃H, and LiF₃H at 300 GPa are provided in Fig. 4. As expected, the F p orbitals contribute the most to the occupied DOS. The bottom of the conduction band, on the other hand, contains almost equal contributions from F 2p, H 1s, and Li 2s states, which is consistent with the Bader charges, indicating that both H and Li transfer electrons to the most electronegative element present. Except for LiF₃H, all of the Li–F–H phases considered here have large bandgaps, which are listed in the DOS plots, ranging from 10.4 to 14.4 eV within the PBE functional. The bandgap for the B1 LiF phase calculated at this level of theory is 15.9 eV at 300 GPa, suggesting that the presence of hydrogen in the ternary phases reduces the bandgap slightly. The large bandgaps of these ternary hydrides suggest that they remain transparent at 300 GPa.

Only one phase, P2₁/m LiF₃H, was calculated to be metallic at 300 GPa, and its DOS at the Fermi level, E_F, was almost completely due to the F 2p orbitals (Fig. 4). The metallicity of this phase is not a result of pressure-induced band broadening but rather a result of the dissociation of F₂ molecules and the electron count in the compound, as verified by calculations with the hybrid HSE06 functional (Fig. S6). Between 70 and 2500 GPa, diatomic fluorine is predicted to adopt the Cmca structure, followed by a transformation to a novel metallic phase with P4₂/mmc symmetry.⁴⁹ In contrast, experiments have shown that iodine becomes monoatomic, metallic, and superconducting with a T_c of 1.2 K already at 28 GPa.^96–98 In the full ionic picture, the formula of P2₁/m LiF₃H can be written as Li⁺(FHF⁻)F⁰. This phase could be insulating if fluorine were present as a diatomic molecule. However, the Bader charges yield Li^+0.85(FHF^−0.52)F^−0.33, and the nearest neighbor distance between two fluorine atoms in the LiF slab separating the bifluoride layers measures 1.610 Å, as compared to the F–F bond length of 1.393 Å in Cmca F₂ at the same pressure. Since F₂ molecules are not found in P2₁/m LiF₃H, an extra electron per formula unit would be required to render it a wide-gap insulator. The DOS as calculated with the HSE-06 hybrid functional (Fig. S6) supports the metallicity of this phase.

Because P2₁/m LiF₃H is metallic, we calculated its electron–phonon coupling (EPC) parameter, λ, and estimated its T_c using the Allen–Dynes modified McMillan equation given in Eq. (1).⁶⁸ Both the small EPC parameter, 0.27, and the small ω_log, 695 K, resulted in a low estimated T_c of 0.092–0.007 K. Thus, in contrast with Gilman’s prediction,⁴⁶ none of the low-lying metastable Li–F–H ternary phases at 300 GPa is a good candidate for pressure-induced hydride based superconductivity. Finally, to aid future characterization of these phases, should they ever be synthesized, we present the calculated infrared spectra for HF, LiF₃H₂, LiF₂H, Li₃F₄H, LiF₄H₄, Li₂F₃H, and LiF₃H in Figs. S31–37.

High P − T synthesis techniques are powerful tools to access novel stoichiometries and materials with unique electronic structures and properties. It may be possible to quench materials made at high pressures to atmospheric conditions, provided that the kinetic barriers toward their decomposition are sufficiently high. Although synthesized as early as 1956,⁹⁹ the crystal structure of LiF₂H, which easily decomposes into hydrogen fluoride and lithium fluoride at room temperature and 1 atm, was not solved until 1962.¹⁰⁰ It is therefore of interest to examine if any of the high pressure phases predicted here could be dynamically stable at 1 atm (effectively zero pressure in our calculations).

The zero pressure phase diagram, not including the ZPE contributions, is provided in Fig. 5. The previously synthesized LiF₂H phase having $R3¯m$ symmetry is dynamically stable (Fig. S38), and it lies on the convex hull. Because the $P1¯$ symmetry LiF₂H phase we identified at 300 GPa is 33 meV/atom less stable than $R3¯mLiF2$H at 0 GPa, we did not attempt to calculate its phonons at this pressure. Remarkably, Li₃F₄H was found to be thermodynamically stable at zero pressure, and phonon calculations confirmed that it was dynamically stable (Fig. S39). LiF₃H₂, Li₂F₃H, LiF₃H, and LiF₄H₄ were found to lie 3.8, 1.6, 149.8, and 33.7 meV/atom above the convex hull, respectively. Thus, our computations hint that novel Li–F–H ternary compounds containing $HnFn+1−$ anions are awaiting discovery and suggest Li₃F₄H as an immediate target for synthesis.

Using evolutionary crystal structure searches, we predict a number of metastable phases, LiF₃H₂, LiF₂H, Li₃F₄H, LiF₄H₄, Li₂F₃H, and LiF₃H, that are within 50 meV/atom of the ternary convex hull within the static-lattice approximation. These potentially synthesizable phases contain the bifluoride anion, (F–H–F)⁻, or the longer (FH–F–HF)⁻ molecular motif along with Li⁺ cations. LiF₄H₄ additionally features an $H3+$ counter-cation, and LiF slabs are present within Li₃F₄H. The bonding within the $HnFn+1−$ motifs encountered here is analyzed, and it ranges from multi-centered interactions to those containing classic two-centered two-electron bonds and H⋯F⁻ hydrogen bonds. With the exception of LiF₃H, all of the low-lying predicted compounds are computed to be wide-gap insulators.

Due to the computational cost involved in crystal structure prediction, it is not feasible to carry out an EA search for every plausible stoichiometry. Nonetheless, our study has unveiled the structural features associated with the low-lying metastable species in the Li–F–H ternary system. Our calculations suggest that other analogous phases containing $HnFn+1−$ motifs and n > 2 could potentially be metastable near 300 GPa. For example, exploratory calculations on the LiF₄H₃ stoichiometry predict a structure that contains bent and asymmetric bifluoride anions, as well as infinite HF chains with nearly equal bond lengths, whose enthalpy lies 21.7 meV/atom above the convex hull. Moreover, Li₃F₄H was predicted to be thermodynamically and dynamically stable at zero pressure, suggesting that other Li–F–H compounds with unique $HnFn+1−$ could be synthesized and quenched to ambient conditions. This study provides the basis for future work exploring the finite temperature stability of Li–F–H phases with the inclusion of anharmonic effects, which are known to be important for light element systems, especially at high pressures.

See the supplementary material for additional computational details, enthalpic comparisons, structural coordinates, and results of electronic structure calculations.

E.Z. and T.B. acknowledge the NSF (Grant No. DMR-1827815), and R.H. acknowledges the NSF (Grant No. DMR-1933622) for financial support. We acknowledge the U.S. Department of Energy, National Nuclear Security Administration, through the Chicago-DOE Alliance Center under Cooperative Agreement No. DE-NA0003975. Calculations were performed at the Center for Computational Research at SUNY Buffalo.¹⁰⁴ We are grateful to Sebastien Hamel for useful discussions. This work was, in part, performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. This work was prepared, in part, as an account of work sponsored by an agency of the United States Government. Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof and shall not be used for advertising or product endorsement purposes. A.S. notes No. LLNL-JRNL-817757.

The data that support the findings of this study are available from the corresponding author upon reasonable request.