Unexpected Trend in Stability of XeâF Compounds under Pressure

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Unexpected Trend in Stability of Xe–F Compounds Under Pressure Driven by Xe–Xe Covalent Bonds Feng Peng, Jorge Botana, Yanchao Wang, Yanming Ma, and Mao-Sheng Miao J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b01922 • Publication Date (Web): 24 Oct 2016 Downloaded from http://pubs.acs.org on October 25, 2016

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The Journal of Physical Chemistry Letters

Unexpected Trend in Stability of Xe–F Compounds Under Pressure Driven by Xe–Xe Covalent Bonds Feng Peng,†‡§ Jorge Botana,§ Yanchao Wang,† Yanming Ma,†* and Maosheng Miao#§* †

‡

State Key Lab of Superhard Materials, Jilin University, Changchun 130012, P. R. China College of Physics and Electronic Information, Luoyang Normal University, Luoyang 471022, P. R. China § Beijing Computational Science Research Center, Beijing 10084, P. R. China # Department of Chemistry and Biochemistry, California State University Northridge, CA 91220, USA * Corresponding author. Email: [email protected] and [email protected] Abstract: Xenon difluoride is the first and the most stable of hundreds of noble-gas (Ng) compounds. These compounds reveal the rich chemistry of Ngs. No stable compound that contains a Ng–Ng bond has been reported previously. Recent experiments have shown intriguing behaviors of this exemplar compound under high pressure, including increased coordination numbers and an insulator-to-metal transition. None of the behaviors can be explained by electronic-structure calculations with fixed stoichiometry. We therefore conducted a structure search of xenon–fluorine compounds with various stoichiometries, and studied their stabilities under pressure using first principles calculations. Our results revealed, unexpectedly, that pressure stabilizes xenon–fluorine compounds selectively, including xenon tetrafluoride, xenon hexafluoride, and the xenon-rich compound Xe2F. Xenon difluoride becomes unstable above 81 GPa, and yields metallic products. These compounds contain xenon–xenon covalent bonds, and may form intercalated graphitic xenon lattices, which stabilize xenon-rich compounds and promote the decomposition of xenon difluoride.

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Predicted phase diagram and stable phases of Xe-F compounds.

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(vdW) interactions were examined using the PBE and vdWDF2 density functional and found to have only minor effects (in the order of meV/atom) on the energetics of XeFx at high pressures (> 50 GPa), and the vdW corrections are negligible under such conditions. To ensure the validity of the pseudopotentials used here, we also performed full-potential allelectron calculations for the equation of states of the XeF2 compound using the WIEN2K code22. Our all-electron calculations yield almost identical results to the Vienna Ab-initio Simulation Package (Figure S1), which validates our pseudopotentials.

Since the first discovery of noble gases (Ngs) by Ramsey in 19041, the synthesis of compounds that contain them has presented a significant challenge to chemists. These elements are inert to chemical reactions because their outermost shells are filled. The reaction of xenon (Xe) with fluorine (F) was first predicted by Pauling, and was realized in the laboratory, to form xenon difluoride (XeF2), by Bartlett and Hoppe2 some 30 years later. Since then, a few hundred Ng compounds and species have been obtained. In these compounds, Ng elements are oxidized and share their outer-shell electrons to form covalent or ionic bonds. Among them, XeF2 is the most stable and the best studied. Under ambient conditions, it is a crystalline insulator consisting of linear XeF2 molecules. Pressure may affect the atomic and electronic structure of matter. Early research suggested that the low-pressure structure of XeF2 remained stable to 50 GPa1,2. A recent experiment revealed that XeF2 may transform into two- and three-dimensional extended solids and become metallic when a higher pressure is applied3,4. However, such transitions cannot be explained by using recent density-functional theory (DFT) calculations and structure searches of XeF2, which show that the ambient-pressure I4/mmm structure persists as the thermodynamically most stable phase of XeF2 up to 105 GPa5. Above 105 GPa, the I4/mmm structure transforms to a Pnma structure that contains bent F–Xe–F molecules. Two Ng atoms that both have a filled valence shells do not engage in chemical bonding. However, once electrons have been depleted from the outer shell, they may be capable of forming chemical bonds. Drews et al.6 isolated a salt of cationic Xe2+ containing a Xe–Xe bond with an interatomic distance of 3.087(1) Å. Stein et al.7 also identified Xe2+ experimentally. Seidel et al.8 detected and characterized by calculations a blue Xe4+ cation with a linear, symmetric structure. Fernández and Frenking9 proposed the viability of a metastable HXeXeX (X = F to I) molecule with an energy barrier of 13 kcal mol−1. They predicted that it could be synthesized and studied in a low-temperature Xe matrix.9,10 Recently, Somayazulu et al. studied the Xe–H2 binary system under high pressure.11 They found that the nearest neighbor Xe–Xe distance at 4.9 GPa is close to that of neutral dimers in the gas phase (3.84 Å)12. In this work, we studied the structures and stabilities of selected stoichiometric XeFx (x = 1/4, 1/3, 2/3, and 1–8) compounds using an accurate first-principles method and an automatic structure search based on a particle swarm optimization algorithm implemented in the CALYPSO method13,14. The crystal structure predictions were performed under various pressures, including 0, 50 100, and 200 GPa. The CALYPSO method has been benchmarked in many well-studied systems, including elements and binary and ternary compounds15,16. Total-energy calculations were performed in the DFT framework within the Perdew–Burke–Ernzerhof17 parameterization of generalized gradient approximation18 as implemented in the Vienna Ab-initio Simulation Package code19. The projector-augmented wave method20 was used to describe the ionic potential. 4d105s25p6 and 2s22p5 were treated as valence electrons in the Xe and F atoms, respectively. A plane-wave kinetic energy cutoff of 1200 eV and dense k-point samplings gave excellent convergence of total energies. Phonon calculations were performed for all relevant structures using the phonopy code21. The van der Waals

Figure 1. Phase stabilities of Xe–F compounds. (a) Enthalpies of formation of XeFx under a series of pressures. The dotted lines connect the data points, and the solid lines denote the convex hull. (b) Stable pressure range for XeFx.

Our calculations reveal that Xe–F compounds with unusual stochiometries, such as XeF and Xe2F, can be stabilized under elevated pressure and temperature. We also found a number of new structures that are governed by novel chemical bonding and include the Xe–Xe covalent bonds and the intercalated Xe honeycomb lattices. These structures are dynamically stable in their respective pressure ranges by phonon calculations (Supporting information). We investigated the stabilities of the Xe–F compounds by calculating and comparing the formation enthalpies of each compound in the structure with lowest enthalpy from 0 to 200 GPa. The most efficient way to compare the stabilities of the binary compounds with variable stoichiometry is to construct a convex hull (Fig. 1a). The compounds that are located on the hull are stable; whereas those that are located above the hull are unstable, and will decompose to form the compounds on the hull23-25.


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covalent bond in Xe2F. Bader analysis28 reveals a charge transfer of 0.37 e from Xe to F. To characterize the bonding nature including Xe-Xe and Xe-F bonds, we calculated the Crystalline Orbital Hamiltonian Population (COHP) and the integrated COHP (ICOHP) for Xe-Xe and Xe-F pairs Xe2F at 200 GPa (Figure 3a). The results clearly revealed the bonding nature of neighboring Xe-Xe pairs in Xe2F. It shows that Xe-Xe pairs in Xe2F are form its covalent bonds. The COHP plots (Figure 3a) also reveal fully occupied bonding states and partially occupied anti-bonding states, leading to net covalent bonding between the two neighboring Xe atoms. We also calculated the electron localization function (ELF) 29-32 (Fig. 4a). As a rule, a typical covalent bond has an ELF value larger than 0.7. However some covalent bonds have lower ELF value (even less than 0.5)33-37. Indeed, for a covalent bonding molecule I2, the ELF value is about 0.6 as calculated by the same method (Fig. 4c). The large ELF value of ~0.5 between neighboring Xe atoms confirms the presence of covalent bonds. This is the first example of compounds that possess covalent bonds between Ng atoms. Furthermore, the nearest Xe–F (2.35 Å) and F–F (2.28 Å) distances are both much larger than the covalent Xe–F and F–F bond lengths of 2.00 Å in the XeF2 molecule38 and 1.56 Å in F2 respectively39. This suggests that Xe and F or F and F do not bond covalently in Xe2F. The calculated COHP (Figure 3b) shows that the Xe-F bonds between the nearest neighboring Xe-F pairs have smaller COHP values than Xe-Xe (Figures 3a and 3b), indicating weaker covalent bonding. It confirms the ionic character of F atoms, as shown by the Bader charge analysis and the high coordination number 8 of F atoms. In addition, the spherical ELF distribution (Fig. 4b) also confirms the states with closed-shell electron configurations of F atoms. The projected density of states (PDOS) (Fig. 4e) reveals that Xe2F is metallic. The Xe 5p and F 2p orbitals contribute substantially to the DOS at the Fermi level. a

Figure 2. Most stable structures of various Xe-F compounds at selected pressures. (a) Xe2F in an I4/mcm structure at 200 GPa; (b) Xe3F2 in a P21/c structure at 50 GPa; (c) XeF4 in an I4/m structure at 200 GPa; (d, e, f) XeF6 in C2/c structure at 50 GPa, Cmcm structure at 100 GPa, and R-3 structure at 200 GPa, respectively. The smaller green spheres are F atoms and the larger purple ones are Xe atoms.

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As shown by the convex hull, XeF2, xenon tetrafluoride (XeF4), and xenon hexafluoride (XeF6) are the only stable compounds at ambient pressure. These results compare well with experimental observations and general knowledge on Xe chemistry: Xe is stable in the +2, +4, and +6 states at ambient pressure. Although other Xe–F compounds do not locate on the convex hull at 0 GPa, the energy difference is small and is of the order of a few meV. By taking xenon trifluoride (Xe2F6) as an example, we calculate the relative enthalpies of formation at 0 GPa, including the van der Waals interaction. The results (Figure S2) show that the inclusion of this interaction can stabilize Xe2F6. The relative enthalpies of formation per atom for XeF2, Xe2F6, and XeF4 are almost identical (less than 2 meV difference), which indicates that all three compounds may become stable at 0 GPa. Pressure can change the stability of the Xe–F compounds significantly. Figure 1 shows that Xe2F and Xe3F2 become stable at 60 GPa and 25 GPa, respectively. Surprisingly, pressure destabilizes XeF2, which is the first synthesized and the best-known Ng compound26. Above 81 GPa, XeF2 decomposes to XeF4 + Xe2F. Our calculations show that Xe3F, XeF, xenon pentafluoride, xenon heptafluoride (XeF7), and xenon octafluoride (XeF8) are unstable throughout the studied pressure range (0–200 GPa).

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Xe–F compounds exhibit interesting structural features and electronic properties. Figure 1b shows that Xe2F is stable in the structure with I4/mcm symmetry above 60 GPa. In this structure, Xe atoms form intercalated graphitic layers (honeycomb lattice) in two perpendicular directions. The distance between neighboring layers is 3.90 Å at 100 GPa. The intercalated layers form parallel channels, in which chains of F atoms are located. At 200 GPa, all in the graphitic layer Xe-Xe distances have the same value 2.63 Å. This value is close to the summation of the covalent radius of two Xe atoms (1.31 Å)27, and suggests the formation of a Xe–Xe

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C2/m structure (Figure 5d) has the lowest XeF energy. In this structure, Xe atoms can be divided into two categories: isolated Xe ions (Xe1) and Xe–Xe dimers (Xe2). At 100 GPa, the shortest Xe-F distance is 2.45 Å, which is much larger than the covalent Xe–F bond length of 2.00 Å in the XeF2 molecule38. Bader charge analysis reveals the large charge transfer from Xe2 to F indicates that XeF consists of Xe+ and F− ions, while Xe1 atoms have almost no charge transfer to F atoms. Different from most other Xe–F compounds, the F atoms do not form covalent bonds with Xe and remain as isolated anions. Xe+(Xe2) ions have seven electrons, including two that occupy 5s and five that occupy 5p orbitals. They are isoelectronic to I atoms. The bond length of Xe–Xe dimers is 2.54 Å at 100 GPa, which is smaller than two times the covalent radius of 1.31 Å for the Xe atoms27. The calculated COHP and the ICOHP for Xe-Xe pairs (Figure 3c) reveal the covalent bonding nature of neighboring Xe-Xe pairs in XeF. The calculated COHP (Figure 3d) shows that the Xe-F bonds between the nearest neighboring Xe-F pairs have smaller COHP values than Xe-Xe (Figure S3a), indicating weaker covalent bonding, which is consistent with the observation that F atoms are strongly ionic and bind with Xe atoms mainly by electrostatic forces, as shown by the Bader charge analysis. The Xe–Xe covalent bonding character of XeF is also revealed by the ELF (Figure 5c) and the charge-density difference (Figure 5d). The PDOS (Figure S5) reveals that the C2/m structure of XeF is metallic at 100 GPa.

Figure 3. Plots of the COHP and ICOHP of Xe2F and XeF. For Xe2F at 200 GPa, (a) Xe-Xe pairs separate by 2.62 Å. (b) Xe-F pairs separate by 2.38 Å. For XeF at 100 GPa, (c) Xe-Xe pairs separate by 2.59 Å. (d) Xe-F pairs separate by 2.13 Å.

Figure 1 shows that Xe3F2 is stable above 25 GPa. It is predicted to adopt a P21/c structure with two formula units per unit cell (Fig. 2b) throughout its stable pressure range (25–55 GPa). Xe3F2 is a typical molecular crystal, is composed of a linear XeF2 molecule (Xe atom named Xe1) and two isolated Xe atoms (Xe2) in a formula unit. At 50 GPa, the shortest Xe1–F distance is 1.98 Å, which is the same as that of XeF2, whereas, the next nearest Xe2–F distance is 2.55 Å, No covalent bond exists between F atoms and the Xe2 atoms. The shortest F–F distance is 2.67 Å, which is much larger than that of the F–F bond length (1.56 Å) in F2,31 and suggests that no covalent bond forms between F atoms. The calculated ELF (Fig. 4d) reveals that the Xe–F bond in the XeF2 molecule is covalent, whereas the interaction between F atoms and isolated Xe2 atoms shows no covalent bonding. Bader analysis reveals a charge transfer of 0.6 e from Xe1 to F atoms, and no charge transfer from Xe2 to other atoms. The PDOS of Xe3F2 (Fig. 4f) reveals it as a semiconductor, with a gap of 0.72 eV. This is a natural result of the fact that Xe3F2 consists of XeF2 molecules and Xe atoms, both of which have filled highest occupied molecular or atomic orbitals.

Figure 4. Electronic properties of Xe2F and Xe3F2. (a, b) Calculated ELF plots in (-1 1 0) and (1 1 0) sections of of Xe2F at 200 GPa (c, d) Calculated ELFs of I2 at 0 GPa and Xe3F2 at 50 GPa, respectively. (e, f) Electronic PDOS per atom of Xe2F at 200 GPa and Xe3F2 at 50 GPa, respectively. The dashed line indicates the Fermi energy.

Figure 5. Predicted structures, synthesis conditions and bonding properties of XeF. (a) Predicted R-3m structure for XeF at 50 GPa. (b) Gibbs free energy of formation of XeF at different temperatures at 100 GPa. (c) ELF plots in (1 0 2.41) section of C2/m structure of XeF within one unit cell at 100 GPa. (d) Calculations of charge density difference of XeF in a C2/m structure at 100 GPa.

XeF remains unstable below 200 GPa at 0 K. It tends to decompose to other Xe–F compounds, such as Xe2F and XeF4. However, the enthalpies of XeF are quite close to the convex hull. Several recent studies of other Xe compounds indicate that elevated temperature has a significant effect and may alter the stability40,41. We therefore performed quasiharmonic free-energy calculations from the phonon spectra computed using the finite-displacement method. As shown in Figure 5b, increasing the temperature suppresses the decomposition of XeF to Xe2F and XeF4. At T = 140 K, XeF becomes stable. A structure search shows that a monoclinic

XeF2 adopts a I4/mmm structure (Figure S6a) throughout its stable pressure range (0–100 GPa). In this structure, linear XeF2 molecules that are oriented along the c axis occupy a body-centered tetragonal lattice. The Xe–F bond lengths of the linear XeF2 units are 1.98 Å at 0 GPa. These results are in good agreement with the experimental results42 and pervi-


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ous theoretical result5. Above 110 GPa, XeF2 is stabilized in a Pnma structure (Figure S6b), which consists of bent F–Xe– F molecules with unequal Xe–F bond lengths. At 150 GPa, a new closely related structure (Cmcm) (Figure S6c) approaches the enthalpy of the Pnma structure. Our results agree well with previous theoretical calculations5. However, the geometry change and the corresponding electronicstructure evolution of XeF2 under pressure cannot explain the recent experimental observations.4 Figure S7 shows the proposed Pnnm-2 and Fmmm structures to explain that the experiments are quite high in enthalpy as calculated by DFT. The Pnnm-2 and Fmmm structures exhibit substantial phonon instabilities (i.e., imaginary phonon frequencies), which suggest dynamic instability5. The resistance measurement of XeF2 under pressure showed that XeF2 became metallic above 70 GPa4. We therefore performed DFT calculations using the Heyd–Scuseria– Ernzerhof hybrid functional43 for the electron-exchange energy to investigate the electronic structure of XeF2 in the I4/mmm structure at 100 GPa. The resultant DOS (Figure 6c) shows a gap, which remains for XeF2, throughout the studied pressure range. This obvious disagreement with experiments and the inconsistency of the atomic structures between DFT and the experiments may be resolved by the trend in stability of the Xe–F compounds under pressure. The convex hull (Figure 1a) shows that XeF2 becomes unstable above 81 GPa, and decomposes to Xe2F and XeF4, of which Xe2F is metallic, and thus might contribute to the significant decrease in resistance in reduction of the XeF2 under pressure.

cal reaction. Although ∆U is constant with pressure, the ∆PV term is reduced substantially more than the constant ∆U value because of the volume reduction that is associated with a higher packing efficiency in the Xe2F and XeF4 mixture. The stability of Xe2F6 is at a critical point under atmospheric conditions. With a slight increase in pressure, Xe2F6 becomes unstable (Figure 1) and decomposes to XeF2 and XeF4. Calculations show that Xe2F6 adopts a monoclinic P21/c structure at atmospheric pressure, which is in good agreement with experimental observations44. Xe2F6 can be viewed as a molecular complex that consists of linear XeF2 molecules and planar XeF4 molecules in a 1:1 ratio. The Xe– F bond lengths in the XeF2 and XeF4 molecules are 1.99 Å and 1.93 Å, respectively. They are both slightly larger than those of pure XeF2 (1.98 Å) and XeF4 (1.91 Å) molecular crystals at atmosphere pressure. XeF4 remains stable throughout the studied pressure range up to 200 GPa. Pressure stabilizes XeF4 considerably, and is the main reason that the other compounds become unstable. A structure search at 0 GPa showed a monoclinic structure with P21/c symmetry (Figure S8), which agrees well with the experimental results45,46. At ~30 GPa, this structure transforms to a tetragonal structure with a higher symmetry of I4/m (Figure 2c), and no further structural transformation occurred to 200 GPa. Both structures consist of XeF4 planar molecules. The Xe–F bond lengths in these two structures are almost identical, at 1.91 Å at 100 GPa. The Xe–F bond length increases with increasing pressure, which results because owing to the stronger inter-molecular interactions weakening the Xe–F covalent bonds. Similar to XeF4, XeF6 is also stable throughout the studied pressure range (from 0 GPa to 200 GPa). Because its structure at ambient pressure has been well studied, we only searched for structures from 50 to 200 GPa. Our results show that the monoclinic structure with C2/c symmetry (Figure 2d) remains stable up to 60 GPa. This structure consists of XeF6 octahedron molecules, which is similar to the ambientpressure phase. The Xe coordination number is 6. The monoclinic C2/c structure transforms to a Cmcm structure (Figure 2e) at 60 GPa, and the structure features chain-like polymerization of ⋯–F–Xe–F–Xe–F⋯, which results in the connection of neighboring XeF6 octahedrons. The Xe coordination number increases to 8. At 120 GPa, XeF6 transforms to a hexagonal structure with R-3 symmetry (Figure 2f). The F atoms bonded with two Xe to form a threedimensional network structure. The Xe coordination number increases from 6 to 8 with a structural change from C2/c to Cmcm, and then to 12 in the R-3 structure. The atomic and electronic structural features indicate that the oxidation state of Xe increases monotonically with the composition ratio of F. To examine this behavior further, we calculated the charges using Bader analysis for XeFx at 100 GPa, as shown in Figure 6b. For XeFx (x ≤ 6) compounds, the Xe charge increases almost linearly with F content. In contrast, for XeFx (x > 6), the Xe charge increases much less with an increasing number of F atoms. This occurs because the 5p electrons are easier to lose than the 5s electrons, and which is also the reason that XeF7 and XeF8 cannot form below 200 GPa. In this pressure range, Xe acts as a p-block element. While sharing its 5p electrons, Xe can bond covalently with F to form XeFx molecules or extended networks. Interestingly, many different bonding features, including inter-molecular, covalent, ionic as well as metallic, can be

Figure 6. Decomposition at high pressure, and electronic properties of XeF2. (a) Relationship between ∆H, ∆U, and ∆PV with pressure for 7XeF2 → 2Xe2F + 3XeF4. We define ∆H = 2H Xe2F + 3HXeF4 – 7HXeF2 , ∆U = 2UXe2F + 3UXeF4 – 7UXeF2, and ∆PV = 2PVXe2F + 3PVXeF4 – 7PVXeF2, where P and V are the pressure and volume per formula unit, respectively. (b) Calculated Bader charge of Xe in XeFx at 100 GPa. (c) Calculated electronic DOS of XeF2 used by normal Perdew–Burke– Ernzerhof and hybrid functional Heyd–Scuseria–Ernzerhof (HSE06) at 100 GPa, respectively.

We discuss the energetic driven mechanism on the reaction of 7XeF2 → 2Xe2F + 3XeF4 at high pressure through calculations of enthalpies (H = U + PV), PV terms, and static energies (U) of XeF2, Xe2F, and XeF4 as shown in Figure 6a. Competition between ∆U and ∆PV dominates the chemi-



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found in these compounds. Some bonds, for example the XeXe in Xe2F and XeF, show mixed features of covalent and metallic bonding; and Xe-F in Xe2F show mixed features of ionic and covalent bonding. In summary, using an unbiased structure-search method based on particle-swarm optimization algorithms in combination with DFT calculations, we investigated the phase stabilities and structural changes of various Xe–F systems under high pressure. We identified the formation of six stoichiometric Xe fluorides (Xe2F, Xe3F2, XeF, XeF2, XeF4, and XeF6) with unforeseen structural features. These fluorides may be synthesized experimentally over a wide range of pressures. Surprisingly, we found that XeF2 tends to decompose to XeF4 + Xe2F above 81 GPa. XeF4 remains as a molecular crystal up to 200 GPa, whereas XeF6 can polymerize with a higher coordination number under increasing pressure. On the Xe-rich side, Xe fluorides (Xe3F2, Xe2F, and XeF) with an ultralow oxidation state can form at lower pressure, and Xe–Xe dimers and graphite-like layers that contain the novel Xe–Xe covalent bond were discovered. Here, Xe behaves like a p-block element, and it can form compounds with molecular, covalent, ionic, and metallic features under pressure. Acknowledgements We thank the Natural Science Foundation of China under 11304141 and 11534003, China Postdoctoral Science Foundation under 2016M590033. This work is also sponsored by the Program for Science and Technology Innovation Talents in University of Henan Province Grant No. 17HASTIT015 and Open Project of the State Key Laboratory of Superhard Materials (Jilin University No. 201602). We also acknowledge the support of NSF-funded XSEDE resources (TG-DMR130005) including Stampede cluster maintained by Texas Advanced Computing Center (TACC). Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI:xxx. Equation of state, the enthalpies of formation, crystal structure, electronic properties, phonon dispersion curves, and ELF curves for various stoichiometry under different pressures.

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