Crystal Structures and Electronic Properties of Xe-Cl Compounds at

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Crystal Structures and Electronic Properties of Xe-Cl Compounds at High Pressure Niloofar Zarifi, Hanyu Liu, John S Tse, and Eva Zurek J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10810 • Publication Date (Web): 16 Jan 2018 Downloaded from http://pubs.acs.org on January 17, 2018

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The Journal of Physical Chemistry

Crystal Structures and Electronic Properties of Xe-Cl Compounds at High Pressure Niloofar Zarifi,† Hanyu Liu,‡,§ John S. Tse,¶ and Eva Zurek∗,† Department of Chemistry, State University of New York at Buffalo, Buffalo, NY 14260-3000, USA, Geophysical Laboratory, Carnegie Institute for Science, Washington, DC 20015, USA, and Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, Saskatchewan, S7N 5E2, Canada E-mail: [email protected]

∗

To whom correspondence should be addressed Department of Chemistry, State University of New York at Buffalo, Buffalo, NY 14260-3000, USA ‡ Geophysical Laboratory, Carnegie Institute for Science, Washington, DC 20015, USA ¶ Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, Saskatchewan, S7N 5E2, Canada § Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, Saskatchewan, S7N 5E2, Canada †

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Abstract Crystal structure prediction techniques coupled with enthalpies obtained at 0 K from density functional theory calculations suggest that pressure can be used to stabilize the chlorides of xenon. In particular, XeCl and XeCl2 were calculated to become metastable by 10 GPa and thermodynamically stable with respect to the elemental phases by 60 GPa. Whereas at low pressures Cl2 dimers were found in the stable phases, zigzag Cl chains were present in Cmcm XeCl at 60 GPa and atomistic chlorine comprised P 63 /mmc XeCl and F d¯3m XeCl2 at 100 GPa. A XeCl4 phase that was metastable at 100 GPa contained monomers, dimers and trimers of chlorine. XeCl, XeCl2 and XeCl4 were metallic at 100 GPa, and at this pressure they were predicted to be superconducting below 9.0 K, 4.3 K, and 0.3 K respectively. Spectroscopic properties of the predicted phases are presented to aid in their eventual characterization, should they ever be synthesized.

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Introduction Pauling and von Antropoff were the first to propose that the so-called “noble” gases could, in fact, be coerced to bond with other elements. 1–3 Yet, their reactivity was not observed in the laboratory until the synthesis of the first xenon compounds in the summer of 1962: XePtF6 was made by Bartlett, 4 XeF2 5 by Hoppe, 6 and XeF4 7 by Claassen. 8 The simple binary fluorides XeF2 , 9 XeF4 and XeF6 10 assume linear, square planar, and octahedral coordination. Despite their relative instability, binary compounds of xenon with a less electronegative halogen have also been made. For example, evidence for the formation of XeCl2 via infrared spectroscopy has been obtained after a xenon-chlorine mixture was subject to a microwave discharge, 11 and matrix isolation methods have been employed to produce XeCl2 . 12 Molecular calculations have explored the potential energy surface of XeCl2 as a stable linear molecule, a van der Waals (vdW) complex, or a bent intermediate. 13 Xenon halides with the formula XeX · , and their ionic counterparts have been studied extensively because of their importance in rare-gas halide excimer lasers. Theory and experiment have show that the monohalide radicals are weakly bound, with XeF · having the largest bond strength due to covalent bond formation in the neutral radical. 14 For further information about noble gas compounds we refer the reader to two excellent reviews that describe the richness of noble gas chemistry uncovered in the last half-century. 15,16 Pressure can alter the structure, electronic structure, and reactivity of extended systems. 17 A hierarchy of responses to increasing pressure has been proposed, which includes: increasing coordination via electron rich or electron poor multicenter bonding schemes, decreasing the size of anions, and valence electrons being “squeezed” into the interstitial space. 18 Density functional theory (DFT) calculations predicted that even though they are not stable at atmospheric pressures, phases such as XeNi3 , XeFe3 , 19 Xe7 O2 , Xe3 O2 , Xe2 O, XeO2 , and XeO3 20,21 become stable at conditions that are found in the Earth’s mantle and core. Experiments have shown that xenon reacts with water at conditions that are found in the interiors of giant planets, 22 and hydrogen-rich xenon-containing compounds such as Xe(H2 )7 have been synthesized under pressure. 23 XeF2 is the easiest noble-gas fluoride that can be handled and synthesized in high purity. 5 High 3



level quantum chemical calculations yield heats of formation of -23.3 kcal/mol and -23.9 kcal/mol at 0 K and 298 K, respectively, for the gas phase species. 24 However, XeCl2 , XeBr2 , and XeI2 have never been isolated outside of a matrix. Because the application of pressure is known to increase the strength of an oxidant, Grochala proposed that pressure could be used to coerce Br2 to oxidize Xe 0 to Xe II , thereby leading to the formation of XeBr2 . 15 Exploratory DFT calculations revealed that an XeBr2 phase would become stable with respect to decomposition into the solid elemental phases by 80 GPa. Furthermore, Grochala’s computational experiments hinted that XeCl2 and XeI2 could become stable at P < 80 GPa and P > 80 GPa, respectively. On the other hand, the high pressure chemistry of XeF2 has been explored in the lab 25,26 and on the computer. 26–28 Experimental studies on compressed XeF2 25 provided evidence for the existence of three distinct insulating phases below 23 GPa, followed by a transformation to a semiconducting structure, and finally to a metallic phase at 70 GPa. The ambient-pressure polymorph of XeF2 (phase I) contains linear F-Xe-F units arranged in a lattice with I4/mmm symmetry. Experiments suggested that phase I transforms to structures assuming the Immm and P nnm space groups, which differ from I4/mmm only by a slight modification of their lattice vectors. Phase IV was also indexed as having P nnm symmetry, but the linear XeF2 units were thought to be arranged in graphite-like layers. It was concluded that the metallic phase V assumed a fluorite-like three-dimensional structure with F mmm symmetry. Subsequent DFT calculations, 27 on the other hand, showed that the I4/mmm phase had the lowest enthalpy up to 105 GPa, and none of the experimentally observed phases were found to be dynamically stable. Above 105 GPa metallic phases wherein one Xe-F bond contracted, and another Xe-F bond was found to bend and elongate were preferred. Electronic structure calculations revealed that the phases that were stable up to 200 GPa could be thought of as ionic solids comprised of [XeF]+ F – motifs. A recent study that combined experiment and first-principles calculations found the following transition sequence, I4/mmm → Immm → P nma, and illustrated that non-hydrostatic conditions employed in the experiments are likely to have an impact on the structural transformations observed under pressure. Because Refs. 26,27 were limited to the XeF2 stoichiometry, structure prediction techniques coupled

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with DFT calculations have recently been used to study the Xe-F phase diagram up to 200 GPa. 28 Whereas XeF2 was calculated to become thermodynamically unstable past ∼80 GPa, phases with XeF4 , XeF6 and Xe2 F stoichiometries, some of which contained covalent Xe-Xe bonds, were found to stabilize above this pressure. Unfortunately, very little work has been carried out to test Grochala’s hypothesis that pressure could hasten the synthesis of the heavier halides of xenon. To date only one experimental study was performed, wherein pressures of 60 GPa, and temperatures of 300-2000 K were applied to XeCl2 mixtures. 29 Above 15 GPa spectroscopic evidence for the formation of a Xe/Cl2 solid solution was obtained, however further structural details could not be discerned. This motivated us carry out a systematic theoretical study of the high pressure phase diagram of xenon chlorides with the formula XeCl, XeCl2 and XeCl4 up to 100 GPa. In agreement with the proposition that chlorides of xenon should become stable below 80 GPa, 15 we find that phases with the XeCl and XeCl2 stoichiometries are thermodynamically and dynamically stable by 60 GPa. Moreover, in agreement with the aforementioned experimental investigations, 29 we find that these same stoichiometries, but with different structure types, become metastable by 10 GPa. By 100 GPa an XeCl4 phase becomes metastable. Atomistic Cl, molecular Cl2 and Cl3 motifs, along with one dimensional zigzag Cl chains are found in these high pressure phases. And, at 100 GPa P 63 /mmc XeCl, F d¯3m XeCl2 and P ¯6m2 XeCl4 are found to be superconducting below 9.0 K, 4.3 K and 0.3 K, respectively.

Computational Details Structure searches were carried out using the particle-swarm-optimization method as implemented in the CALYPSO code, 30 and evolutionary algorithms as implemented in the ASAP 31 program, and X TALOPT 32 version 10 wherein duplicate structures were removed using the X TAL C OMP algorithm. 33 The CALYPSO and ASAP searches were performed on supercells containing 8 formula units for XeCl and 4 formula units for XeCl2 . The X TAL O PT searches were carried out on 2-6 formula unit supercells for XeCl, XeCl2 and XeCl4 . To reduce the search space, minimum

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inter-atomic distance constraints were applied to generate the initial structures, and these were maintained during the structure searches. In all of the calculations on the Xe-Cl phases, the minimum distances between xenon-xenon, xenon-chlorine and chlorine-chlorine atoms were set to 2.9, ˚ respectively. We also carried out geometry optimizations of XeCl2 analogues of 1.9 and 1.2 A, the XeF2 structures proposed in the Refs. 25–27 at different pressures. As shown in the Supporting Information, SI, Table S3, all of their enthalpies were higher than those that were found via crystal structure prediction techniques. Geometry optimizations, as well as calculations of the optical spectra, and the electronic structure were performed with the VASP code. 34,35 The atomic potentials were described using the PAW method 36 with the PBE exchange-correlation functional, 37 and a plane wave basis energy cutoff of 600 eV. The valence electron configuration used for the halogens was s2 p5 , whereas for xenon s2 p6 was employed below 60 GPa, and d10 s2 p6 for P ≥ 60 GPa. In the structure searches, the ˚ −1 . Higher precision geometry optimizations, k-point meshes employed a grid spacing of 0.04 A and electronic structure calculations on promising structures were performed using a smaller grid ˚ −1 , and a tighter force criterion of less than 1 meV/A. ˚ The bonding was further spacing of 0.025 A analyzed by calculating the crystal orbital Hamilton populations (COHP) 38 and the negative of the COHP integrated to the Fermi level (-iCOHP) using the LOBSTER package. 39–41 To ensure that the results are valid within the pressure range studied the equation of states (EOS) of an XeCl2 phase calculated with the PAW potentials was compared to the results obtained using all electron calculations carried out with the WIEN2K code, 42 as shown in the SI, Figure S3. The effect of van der Waals (vdW) interactions was examined by comparing the EOS of two XeCl2 phases, and their relative enthalpies of formation above 10 GPa (see Figure S2) as calculated with the PBE, and the vdW-DF2 43 functionals. Because the results obtained with the vdW-DF2 functional agreed well with those obtained from PBE, we do not expect the inclusion of vdW effects to significantly affect the results and conclusions of our study. Moreover, the geometries of (i) XeCl: C2/m at 10 GPa, Cmcm at 60 GPa, P 63 /mmc at 100 GPa, and (ii) XeCl2 : Cmcm at 10 GPa, P 41 21 2 at 60 GPa, and F d¯3m at 100 GPa were optimized using the HSE06 screened

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hybrid functional. 44 The starting geometries were those obtained from PBE, but the symmetry was turned off in the optimization thereby allowing structural distortions to occur. The coordinates of the optimized structures, given in the SI section S1, reveal that the main difference between the HSE06 and PBE geometries was a small change in the lattice parameters, and symmetry breaking distortions did not occur. In addition, the HSE06 calculations confirmed the metallicity of XeCl and XeCl2 at 100 GPa (Figure S7). Phonon band structures, see section S6, were calculated using the supercell approach, 45,46 and/or DFT perturbation theory 47 (DFPT). In the former, Hellmann-Feynman forces were calculated from a supercell constructed from replicating the optimized structure, and dynamical matrices were computed using the PHONOPY code. 48 In select cases, the convergence of the phonon band structures with the supercell size were examined, and compared using the DFT linear response method. In the DFPT approach, the phonon spectra were calculated using either the VASP or the QUANTUM ESPRESSO (QE) codes. 49 The electron-phonon coupling (EPC) parameters were calculated using QE. The Xe and Cl pseudopotentials, obtained from the QE pseudopotential library, were generated by the method of Trouiller-Martins 50 with s2 p6 and s2 p5 valence configurations, along with the PBE generalized gradient approximation. Plane-wave basis set cutoff energies were set to 80 Ry for all systems. The Brillouin-zone sampling scheme of Methfessel-Paxton 51 and 8×8×4/8×8×8/8×8×8 k-point grids for XeCl/XeCl2 /XeCl4 were employed. The EPC parameter, λ, was calculated using a set of Gaussian broadenings in steps of 0.05 Ry from 0-0.300 Ry and 4×4×2/2×2×2/2×2×2 q-meshes for XeCl/XeCl2 /XeCl4 (Figure S11). The broadening for which λ was converged to within 0.05 was between 0.055 and 0.170 Ry for all structures. The critical superconducting temperature, Tc , has been estimated using the Allen-Dynes modified McMillan equation, 52 where the renormalized Coulomb potential, µ∗ , was assumed to be 0.1. This equation was chosen because it has been shown to provide reasonable estimates of the Tc of materials whose λ < 1.5. In addition, it has been employed to estimate the Tc of elemental Cl2 53 and Xe 54 under pressure with µ∗ = 0.1. Accurate electronic band structures of the Xe-halides were calculated with the GW method. 55,56

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The ‘single-shot’ GW calculations were carried out on structures optimized with PBE, and the results were compared with those obtained using the PBE approximation (Figure S6). Calculations have been carried out that compare the band structure of compressed AlH3 computed with screened hybrid functionals and GW methods. 57 In the DFT perturbation approach, self-energy corrections are added to the Kohn-Sham eigenvalues at selected k-points. In the calculation of the self-energy matrix, the number of unoccupied bands was increased to at least twice the number of occupied bands. The band structure was then constructed from the interpolation of the corrected GW eigenvalues at each k-point using the Wannier function technique. 58,59 Optical absorption spectra, Figure S10, were obtained by solving the Bethe-Salpeter equation (BSE) using the GW eigenvalues, 60,61 and the Raman intensities, Figure S9, were calculated from derivatives of the macroscopic dielectric tensor with respect to the normal mode coordinate. 62 The molecular calculations on the charged and neutral chlorine dimers and trimers were performed using the Amsterdam Density Functional (ADF) 63,64 software package, a triple-ζ Slatertype basis set with polarization functions (TZP) and a 2p frozen core from the ADF basis set library, 65 along with the PBE functional. 37

Results and discussion XeCl2 : The Lowest Point on the Convex Hull Figure 1 provides the enthalpies of formation, ∆HF , of the XeCln , n > 1, compounds that were found via crystal structure prediction techniques in a pressure range of 10-100 GPa, and lists their spacegroups. The ∆HF were computed using the face centered cubic (fcc) structure of Xe, which is stable at room temperature up to pressures of at least 55 GPa, 66,67 the hexagonal close-packed (hcp) Xe structure above 70 GPa, 68–70 and the molecular structure of Cl2 with the Cmca space group, which is stable up to 142 GPa. 53 At 10 and 20 GPa all of the binary compounds were computed to be thermodynamically unstable with respect to decomposition into the elemental phases. However, as discussed later, some of them were dynamically stable. In good agreement with Grochala’s 8


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prediction 15 XeCl2 and XeCl lie on the convex hull at 60 GPa and 100 GPa, whereas XeCl4 is metastable at 100 GPa. XeCl

0.1

XeCl2

XeCl4

C2/m P1 P1

0.05

∆HF (meV/atom)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


P21/m

C2/m 0

P-6m2

Cmcm Cmcm P43212

-0.05

P-6m2 -0.1 10 GPa 20 GPa 60 GPa 100 GPa

-0.15 P63/mmc Fd-3m -0.2

0.4

0.5

0.6

0.7

0.8

0.9

1

mole fraction Cl Figure 1: The enthalpy of formation, ∆HF , for the reaction Xe + n2 Cl2 → XeCln and n = 1, 2, 4 versus the Cl composition in the binary compound at different pressures. The enthalpies of Cmca Cl2 (10-100 GPa), fcc Xe (10-60 GPa) and hcp Xe (100 GPa) were used to calculate ∆HF . The phases whose enthalpies fall on the convex hull, denoted by the solid lines, are thermodynamically stable.

At 10 GPa, the two binary structures closest to thermodynamic stability had the XeCl2 stoichiometry, and their enthalpies were within 3 meV/atom of each other. These phases, assuming the P 21 /m and Cmcm spacegroups, were comprised of molecular Cl2 , but their Xe sublattices differed. Even though the formation of these structures from the elemental phases was computed to be endothermic by ∼16 meV/atom, they were dynamically stable. Finite temperature effects are nearly negligible for the stability of these phases, whose formation remains endergonic by ∼ 2.2 meV/atom at 1000 K. However, because these systems are metastable and their ∆HF are within kB T , they could potentially be accessed experimentally. In fact, these may be candidate structures for the phases that were synthesized when Xe-Cl2 mixtures were compressed above 15 GPa at 9



temperatures of 300-2000 K. 29 The structures of the Cmcm and P 21 /m XeCl2 phases are markedly different from the ambient pressure polymorph of XeF2 that has I4/mmm symmetry, and consists of linear F-Xe-F motifs that lie along the c-axis. The Cmcm structure is base-centered orthorhombic with four formula units per unit cell, and it was found to be the lowest enthalpy XeCl2 phase at pressures lower than 40 GPa. As shown in Figure 2a, it contains layers of Cl2 and Xe atoms wherein the Cl2 bond lengths ˚ which compares well with our optimized bond length within molecular solid Cl2 , measured 2.02 A, ˚ at 1 atm and 2.03 A ˚ at 10 GPa. Since a nominal Xe-Cl bond at ambient pressure is between 2.01 A ˚ 15 the Xe-Cl distances of 2.99 A ˚ suggests little interaction. The Xe-Xe, Xe-Cl and Cl2.31-2.85 A, Cl distances for all of the phases studied herein at select pressures are provided in the SI in Table S1. The monoclinic P 21 /m phase illustrated in Figure 2b also contained 12 atoms in its primitive cell, and consisted of layers of Xe atoms and Cl2 molecules wherein the Cl-Cl bond lengths ranged ˚ and the nearest neighbor Xe-Cl contacts measured 2.92 and 2.98 A. ˚ The main from 2.02-2.04 A, difference between the two phases is in the structures assumed by the Xe sublattices: whereas the Cmcm phase contained a flat square net, in the P 21 /m phase the planes were puckered. In ˚ to each other Figure 2 connections are drawn between xenon atoms that are closer than 4.0 A to more clearly illustrate the noble gas sublattice. For comparison, experiments indicate that the ˚ 71 whereas at nearest neighbor distance in solid fcc xenon at 4 K and ambient pressure is ∼4.34 A, ˚ 72 Even though both of these phases were room temperature and 5 GPa it was found to be 3.83 A. dynamically stable at 10 GPa, at 0 GPa phonon calculations revealed instabilities suggesting they cannot be quenched to atmospheric conditions. To better analyze the bonding in these phases we calculated the negative of the crystal orbital Hamilton populations integrated to the Fermi level (-iCOHP) for various atom pairs, as shown in Table S4. The -iCOHPs can be used to gauge the bond strength, especially when compared with the results obtained for the elemental phases. Between 10-100 GPa the -iCOHPs between neighboring atoms in elemental Xe were computed to be 0 eV, as expected for PBE-GGA. For elemental Cl2 they decreased from 5.44 eV at 1 atm to 4.59 eV at 100 GPa. The -iCOHPs between the atoms

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(a) XeCl2-Cmcm

c

(b) XeCl2-P21/m

c b

a

Figure 2: Optimized structures of XeCl2 at 10 GPa with the (a) Cmcm and (b) P 21 /m spacegroups. Chlorine atoms are green and xenon atoms are blue/purple. The sticks between two chlorine atoms represent bonds, whereas those joining xenon atoms are merely provided to emphasize the structure adopted by the xenon lattice, and they do not represent bonding interactions. comprising the chlorine dimers in the P 21 /m and Cmcm XeCl2 structures at 10 GPa, 4.9 eV, were nearly the same as those computed for elemental chlorine at the same pressure, 4.84 eV. The Xe-Cl -iCOHPs were 0.44 and 0.32 eV for P 21 /m and Cmcm XeCl2 and 0 eV for Xe-Xe in both structures. Because the difference between the 0 K enthalpies of the two aforementioned phases is very small, calculations were carried out to determine if zero-point-energy (ZPE) corrections and the effect of vdW interactions could affect their relative stabilities at 10 GPa. Since both Xe and Cl are heavy atoms, and since the structural motifs found in the two phases were similar, it was not surprising that the ZPE corrections did not stabilize one structure over the other (see Table S2). Furthermore, the EOS curves from 10-60 GPa obtained with the PBE and vdW-DF2 functionals ˚ 3 /atom suggesting that dispersion were nearly identical with volumes differing by less than 0.04 A interactions are not significant in these systems (Figure S2). The P 21 /m phase was found to have a slightly higher enthalpy than Cmcm-XeCl2 above 10/15 GPa with the vdW-DF2/PBE functionals, again highlighting that the inclusion of vdW effects is not crucial in DFT calculations on the high pressure chlorides of xenon. At 60 GPa, the lowest point on the convex hull had the XeCl2 stoichiometry, and it was ther-

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modynamically preferred over the elemental phases by ∼26 meV/atom. Actually, our structure searches found two isoenthalpic dynamically stable phases that could be indexed as having the P 41 21 2, and the P 43 21 2 spacegroups. These two spacegroups, 92 and 96, are enantiomorphs, that is they are chiral mirror images of each other. Because their structure and electronic structure are the same, we only show the results for the P 41 21 2 phase. These were the most stable XeCl2 phases between 37-70 GPa. The unit cell of P 41 21 2-XeCl2 , see Figure 3a, contained four formula units, ˚ The -iCOHP for this bond pair, 3.93 eV, was over half an eV and Cl2 motifs that measured 2.04 A. smaller as compared to elemental Cl2 at the same pressure. The Xe sublattice was diamond-like ˚ which is similar to the distance in elemental Xe at this pressure, with Xe-Xe distances of 3.15 A, and each atom was nearly tetrahedrally coordinated with the angles (108.4 ◦ and 111.6 ◦ ) deviating ˚ Because the chlorine molecules were situated in the voids slightly from the ideal value of 109.5 A. within the diamond sublattice, the structure can be approximated as a cubic fcc Xe lattice wherein the Cl2 are found in the octahedral sites. Each chlorine molecule was surrounded by nine Xe atoms, ˚ somewhat longer than the distance of an wherein the Xe-Cl distances measured from 2.93-3.14 A, ˚ 15 The -iCOHP for the closest Xe-Cl bond at ambient conditions, which ranges from 2.31-2.85 A. Xe-Cl pair was 0.05 eV. The Xe atoms in turn, were surrounded by twelve Cl atoms. A Bader analysis revealed charge transfer from Xe to the more electronegative element, resulting in a net charge of −0.1e on each Cl atom. (a) XeCl2-P41212

c

(b) XeCl2-Fd-3m

b

b c

a

a

Figure 3: Optimized structures of XeCl2 at (a) 60 GPa with the P 41 21 2 spacegroup, and (b) 100 GPa with the F d¯3m spacegroup. 12


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Past 80 GPa the most stable XeCl2 phase assumed F d¯3m symmetry, see Figure 3b, and it was the lowest point on the 100 GPa convex hull. Comparison of Figure 3a and Figure 3b reveals that this phase is structurally related to the lower pressure P 41 21 2/P 43 21 2 structures. In fact, optimization of P 43 21 2 XeCl2 without symmetry at pressures larger than 80 GPa yielded the F d¯3m XeCl2 phase. In the F d¯3m structure, the Xe lattice assumed the diamond lattice type with angles ˚ which is too long for covalent of 109.5◦ . The closest Cl-Cl contacts at 100 GPa measured 2.42 A, bond formation, as confirmed by the Electron Localization Function (ELF) shown in Figure S12 and the -iCOHPs of 0.58 eV. For comparison, the molecular dissociation of Cl2 units in solid chlorine to yield the monoatomic phase was calculated to occur at pressures greater than 157 GPa. 53 Each Xe atom within F d¯3m XeCl2 was surrounded by 12 Cl atoms with all of the Xe-Cl contacts ˚ with -iCOHPs of 0.11 eV. A Bader analysis yielded a charge of less than -0.2e measuring 2.84 A on each Cl at 100 GPa. Interestingly, F d¯3m XeCl2 is isotypic with the MgCu2 Laves structure that is adopted by many intermetallic phases. This suggests that pressure can coerce two elements, which are not metallic at ambient conditions, to form structures that are typically observed in intermetallics.

XeCl: From Cl2 Molecules, to Zigzag Cl∞ Chains, to Kagome Lattices Comprised of Chlorine Atoms The most stable phase with the XeCl stoichiometry assumed the C2/m spacegroup between 1034 GPa. Phonon calculations confirmed it was dynamically stable by 10 GPa even though it was not thermodynamically stable with respect to the elemental phases; ∆HF was calculated as being 74 meV/atom at this pressure. As illustrated in Figure 4a this phase can be viewed as a host Xe ˚ act as guests in channels that lie lattice within which Cl2 molecules with bond lengths of 2.03 A along the c-axis. The Cl2 molecules are arranged so that the Xe-Cl2 -Xe angle is 180◦ with Xe˚ This phase resembles a structure that was predicted to become Cl distances measuring 2.99 A. stable above 90 GPa, Cmcm H2 I, wherein H2 molecules are arranged in a zigzag fashion through channels formed by an iodine host. 73 13



(a) XeCl-C2/m

b

(d) XeCl-P63/mmc

b a

(b) XeCl-Cmc21

c

a

(c) XeCl-Cmcm

b

a

a

b

Figure 4: Optimized structures of XeCl at (a) 10 GPa with the C2/m spacegroup, (b) 40 GPa with the Cmc21 spacegroup, (c) 60 GPa with the Cmcm spacegroup, and (d) 100 GPa with the P 63 /mmc spacegroup. A Cmc21 symmetry arrangement, found in structure searches carried out at 40 GPa, was the most stable XeCl phase between 35-55 GPa. Its crystal lattice, show in Figure 4b, could also be perceived as a host-guest structure. The arrangement of Xe atoms resembled the host lattice of the incommensurate Ba-IVa structure 74 in the sense that both of these systems possess octagonal channels that point along the c-axis. However, the way in which the channels are interconnected in the two structures differed slightly. Moreover, whereas the guest lattice in Ba-IVa is comprised of linear atomic chains, in the high pressure XeCl phase it contained Cl2 molecules arranged in a zigzag fashion within the channels. The inter- and intramolecular Cl-Cl distances measured 2.36 ˚ respectively, with angles of 75.4◦ between adjacent molecules. By 60 GPa the Cmcm and 2.05 A, phase shown in Figure 4c, which is structurally related to Cmc21 and was dynamically stable at 60 and 100 GPa, had the lowest enthalpy. The main difference between the two structures is that the distances between Cl atoms are equalized within Cmcm XeCl, so that one can no longer ˚ distinguish between inter- and intramolecular contacts with each Cl-Cl distance measuring 2.18 A at 60 GPa. The ‘bent’ Cl-Cl-Cl angle changes only slightly to 73.1◦ . The Cmc21 phase was

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calculated to be dynamically stable at 40 and 60 GPa, whereas Cmcm XeCl did not display any imaginary phonon modes at 60 GPa. The individual Xe and Cl sublattices within the Cmcm phase both had the same symmetry as the XeCl binary compound. Within the Cmc21 structure only the Cl sublattice maintained this symmetry, whereas the Xe sublattice was identified as having Cmcm symmetry. This again illustrates that the main difference between the two phases lies in the arrangement of the Cl atoms. By 100 GPa a P 63 /mmc XeCl phase, see Figure 4d, became nearly isoenthalpic with Cmcm, with ∆HF differing by ∼2 meV/atom, and at this pressure both structures were dynamically stable. The Xe sublattice of P 63 /mmc XeCl consisted of an AAA stacking of slightly puckered hexagonal nets wherein an atom caps the center of each hexagon and ˚ (the shortest Xe-Xe distances in the elemental phase the Xe-Xe distances measured 2.97-3.10 A ˚ at this pressure). The Cl atoms formed sheets that stack in the c-direction and measure 3.02 A ˚ P 63 /mmc XeCl resembles the assumed a Kagome lattice with Cl-Cl contacts of 2.39 and 2.66 A. MgZn2 Laves structure, however whereas in the former Cl is found on the 6h Wyckoff site and Xe on the 4f and 2a sites, in the latter Mg occupies the 4f site and Zn the 6h and 2a sites. Figure 5 more clearly illustrates the chlorine lattices in these three XeCl phases, along with contour plots of the ELF, which shows the presence of Cl2 molecules at 40 GPa. By 60 GPa the ELF values between Cl atoms that form zigzag chains with equalized distances in the Cmcm phase are ∼0.6, indicative of weak bonding between adjacent Cl atoms. By 100 GPa, however, there is no evidence of Cl-Cl bond formation within P 63 /mmc XeCl (or in F d¯3m XeCl2 , see Figure 3b). The -iCOHPs, provided in the caption of Figure 5, also illustrate the evolution of the Cl-Cl bond strength under pressure. Thus, our results suggest that in comparison to elemental chlorine, for which PBE-GGA calculations found that the monoatomic phase becomes preferred above 157 GPa, 53 bond dissociation occurs at a lower pressure in XeCl2 and XeCl. A Bader analysis found that the charge transferred from the Xe to Cl atoms is, on average, -0.10e for the Cmc21 phase at 40 GPa, -0.21e and -0.11e on the “terminal” and “central” Cl atoms comprising the zigzag chain in the Cmcm phase at 60 GPa, and -0.39e in the P 63 /mmc structure at 100 GPa, suggesting that increasing pressure results in a larger charge buildup on the electronegative chlorines. The

15



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Xe-Cl -iCOHPs in these phases are small, < 0.15 eV. (a) Cmc21 40 GPa

(c) P63/mmc 100 GPa

(b) Cmcm 60 GPa

2.39

1.0

0.4

Figure 5: Contour maps of the electron localization function (ELF) in the (100) planes for XeCl at (a) 40 GPa with the Cmc21 spacegroup, (b) 60 GPa with the Cmcm spacegroup, and (c) 100 GPa with the P 63 /mmc spacegroup. The -iCOHPs for the Cl-Cl contacts whose distances are given in ˚ 1.13 eV (2.36 A), ˚ (b) 2.16 eV (2.18 A), ˚ the brackets were computed to be: (a) 3.81 eV (2.05 A), ˚ (c) 0.44 eV (2.39 A).

XeCl4 : Metastable at 100 GPa Crystal structure prediction techniques were also employed to find the most stable structures with the XeCl4 stoichiometry. At P ≤ 60 GPa, the predicted phases were thermodynamically unstable with respect to decomposition into the elemental phases. At 100 GPa our structure searches found a dynamically stable P ¯6m2 symmetry phase shown in Figure 6a whose enthalpy lay only ∼ 40 meV/atom above the convex hull, suggesting that this metastable phase may be experimentally accessible. This structure is unlike any we have witnessed till now. It consisted of an almost diamondoid Xe lattice, where each angle lies close to the one found in an ideal tetrahedron (108.3˚ and 3.02 A ˚ (cf. 3.02 A ˚ in elemental xenon). As 110.6◦ ) and the Xe-Xe distances measured 2.98 A illustrated by the ELF plots in Figure 6b and c, the chlorine atoms that were found in the same layer as the xenon atoms, and in a layer between them, did not form bonds with any other atoms.

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The Bader charges of +0.33e to +0.47e on the xenon atoms were indicative of charge donation from the noble gas to the halogen atoms, with the largest amount, -0.21e to -0.25e, residing on the chlorines within the xenon lattice. The layers containing both Xe and Cl atoms were separated with ones made up solely of chlorine atoms that formed Cl2 and linear symmetric Cl3 molecules ˚ and 2.04 A, ˚ respectively. The bonding was confirmed by the with Cl-Cl bond lengths of 1.97 A ELF, as illustrated in Figure 6d, and the -iCOHPs that were calculated to be 4.09 eV and 3.09 eV for the Cl-Cl bonds within the dimers and trimers, respectively. Despite the fact that one would expect the dimer to be neutral, and the trimer to have a charge of -1e, the Bader analysis was suggestive of the following charges: Cl−0.28 and Cl−0.03 to Cl−0.07 . 2 3 3 In the trimer the middle atom had a slight positive charge of around +0.11e, whereas the end −0.05 atoms ranged from -0.06e to -0.1e. A gas phase molecular optimization on Cl− yielded 3 and Cl3

charges of -0.07e and +0.18e on the central chlorine atom, respectively, whereas the terminal chlorines had charges of -0.47e and -0.11e, respectively. The larger negative charge on the terminal atoms in the molecular trimer is expected based upon simple molecular orbital considerations. Thus, the charge distribution found in the trimer in P ¯6m2 XeCl4 is consistent with that expected for a Clx− 3 molecule. To determine the effect of pressure on the electron transfer from the xenon to the chlorine lattice, the structure was reoptimized at 0 GPa. Even though this structure is likely not dynamically stable at this pressure, it is instructive to consider how pressure affects the charge transfer between the halogen and the noble gas atoms. According to the Bader charges, at 0 GPa both the chlorine dimer and trimer were nearly neutral. The xenon atoms assumed a charge of +.07e on average, whereas the chlorines in the xenon plane had a charge of -0.15e and those situated between the xenon atoms were nearly neutral. This shows that pressure enhances the amount of charge transfer from the xenon to the chlorine atoms.

Electronic Structure and Properties Unsurprisingly, the projected densities of states (PDOS) plots of the different XeCl and XeCl2 phases calculated with the PBE functional at 15, 60 and 100 GPa, which are provided in Figure 17



(a) XeCl4 P-6m2 b

(b)

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1.0

c

(d)

d (c)

c a

0.5

b

Figure 6: (a) Optimized structure of XeCl4 at 100 GPa with the P ¯6m2 spacegroup. (b-d) ELF contour maps of the regions indicated in (a). 7, show that both the xenon and chlorine p states furnish the main contributions to the DOS right below the Fermi level, EF . Above EF the main contributions are typically the chlorine 3p, with a slight admixture of the xenon 5p states. These results are in line with the Bader charges, which indicate charge transfer from xenon to the more electronegative chlorine atoms. Within PBE XeCl and XeCl2 were found to have a band gap of 1.65 eV and 1.97 eV, respectively, at 15 GPa. As show in Figure S6, the more accurate GW calculations yielded gaps of over 4 eV, instead. The large band gaps illustrate that the crystalline structures could be transparent. Pressure decreases the band gap, so that by 60 GPa the most stable phases of XeCl and XeCl2 have gaps of 0.05 and 0.71 eV within PBE (they are at least 0.75 eV larger within GW), respectively. The experimental estimate of the metalization pressure of XeF2 is still under debate: a 2010 study observed band gap closure by 70 GPa, 25 whereas a more recent work found evidence of a gap of 1.83 eV at 82 GPa. 26 For comparison, in this pressure regime we find that P 41 21 2 XeCl2 still has a fairly large band gap and the color of the compound would be blue-green. As illustrated in Figure 8, at 100 GPa the PDOS of the metastable P ¯6m2 XeCl4 structure is also dominated by the Cl p and Xe p states near EF , and this phase is metallic. At 100 GPa P 63 /mmc XeCl and F d¯3m XeCl2 were calculated to be metallic with both the PBE and HSE06 functionals (calculations on XeCl4 were prohibitively expensive). All three of the 100 GPa phases were metallic at 1 atm within PBE. The metallicity is likely due to the presence of 18


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Figure 7: The PBE band structure and projected densities of states (PDOS in units of states/eV/cell) of (a) C2/m XeCl at 15 GPa, (b) Cmcm XeCl at 60 GPa, (c) P 63 /mmc XeCl at 100 GPa, (d) Cmcm XeCl2 at 15 GPa, (e) P 421 21 XeCl2 at 60 GPa, and (f) F d¯3m XeCl2 at 100 GPa.

Figure 8: The PBE band structure and PDOS of P ¯6m2 XeCl4 at 100 GPa.

19



monoatomic chlorine, and not because of pressure induced band overlap. This mechanism of metalization is not unprecedented: both experiments and theory have confirmed that the metalization of iodine under pressure is a result of pressure induced dissociation of the I2 molecules, 75,76 and superconductivity has been measured below 1.2 K at 28 GPa in the monoatomic phase. 77 Therefore, electron-phonon calculations were carried out on the metallic Xe-Cl phases and their superconducting critical temperatures, Tc s, were estimated using the Allen-Dynes modified McMillan equation and a µ∗ value of 0.1. The electron-phonon coupling was calculated to be λ = 0.64, 0.50 and 0.32, and the average logarithmic frequencies, ωlog , were found to be 319, 345 and 331 K leading to a Tc of ∼9.0, ∼4.3 and ∼0.3 K for XeCl, XeCl2 and XeCl4 , respectively. These values are somewhat higher than the Tc of 0.04 K calculated for the close-packed phase of xenon at 215 GPa, 54 but lower than the max Tc calculated for solid Cl2 , 13 K at 380 GPa. 53 Finally, the Raman and optical properties of these structures are presented for future comparison with experimental measurements in Figure S8 and S9. The results of the BSE calculations yielded band gaps of ∼4 eV for both C2/m XeCl and Cmcm XeCl2 at 15 GPa, in agreement with the GW results. Moreover, the reflectivities of these two phases were found to be very low as expected for insulators. At 60 GPa, the reflectivity of both stoichiometries increased somewhat due to the smaller energy gaps in these crystals.

Conclusion The reactivity of the “noble” gases has fascinated chemists ever since the first synthesis of xenon containing compounds over half a century ago. However, the only noble gas halide that has been isolated outside of a matrix is XeF2 as a molecule, and in the solid state. The chemistry of crystalline XeF2 has been explored up to pressures of 200 GPa. Grochala proposed that pressure could be employed to stabilize the heavier halides of xenon, and in particular XeCl2 would become stable below 80 GPa. 15 Our theoretical calculations, which combined crystal structure prediction techniques and 0 K DFT calculations, confirmed Grochala’s suggestion by showing that extended phases with the XeCl and XeCl2 stoichiometries will become stable with respect to the elemental 20


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phases by 60 GPa. Moreover, these two stoichiometries were found to be dynamically stable by 10 GPa, in agreement with recent experiments, which showed that a Xe/Cl2 solid solution formed at pressures larger than 15 GPa. 29 Our calculations also identified a metastable XeCl4 phase at 100 GPa. At low pressures the stable XeCl and XeCl2 phases contained Cl2 dimers, whose bonds equalized forming zigzag Cl∞ chains in Cmcm XeCl by 60 GPa, and Cl atoms were found in P 63 /mmc XeCl and F d¯3m XeCl2 by 100 GPa. In elemental chlorine, on the other hand, the transition from diatomic to monoatomic chlorine motifs was computed to occur at a slightly higher pressure, 157 GPa. 53 In addition to monoatomic and diatomic chlorine motifs, at 100 GPa P ¯6m2 XeCl4 also contained Cl3 units. A Bader charge analysis revealed that, in general, a slight transfer of charge from xenon to the more electronegative chlorine atoms occurs. Both the PBE functional, and GW calculations indicated that the XeCl and XeCl2 phases are semiconductors at 60 GPa. By 100 GPa all of the studied stoichiometries were found to be metallic, with the metallicity arising from the presence of monoatomic chlorine within the structures. The Allen-Dynes modified McMillan equation predicted a superconducting critical transition temperature, Tc , of 9.0 K, 4.3 K and 0.3 K for XeCl, XeCl2 and XeCl4 at this pressure, respectively. The Raman vibrational modes, as well as the optical properties and reflectivity of select phases were calculated to aid their eventual experimental identification. Finally, we note in passing that exploratory calculations were carried out on the heavier halides of xenon, XeBrn and XeIn with n = 1, 2, 4 up to 60 GPa (see section S12 ). In agreement with Grochala’s study 15 we did not find any stable iodides of xenon at P ≤ 60 GPa, and the most stable phases recovered contained segregated regions of xenon and iodine. Such layered structures indicate that for the given stoichiometry and pressure the elements favor phase separation. A stable XeBr2 phase was found at P > 40 GPa that was metallic and superconducting below 1.4 K at 60 GPa. This phase was isotypic with F d¯3m XeCl2 , and at 60 GPa it’s enthalpy was 0.328 eV/atom lower than the previously studied I4/mmm XeBr2 structure. 15 We look forward to the eventual synthesis of these phases, and further computational exploration of the phase diagram of the xenon

21



halides under pressure with varying stoichiometries.

Supporting Information Available: Structural parameters using PBE and HSE06, results of calculations carried out with the vdW-DF2 functional, enthalpies with and without ZPE corrections, EOS obtained with WIEN2K, electronic band structures, results of GW and HSE06 calculations, phonon band structures, supplemental ELF plots and -iCOHP table, spectroscopic and optical properties, results for the Tc calculations, and computations on XeBrn and XeIn . This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgments: E.Z. and N.Z. acknowledge the NSF (DMR-1505817) for financial support, and the Center for Computational Research (CCR) at SUNY Buffalo for computational support. Part of the calculations have been performed by the use of computing resources provided by WestGrid and Compute Canada. J.T. and H.L. acknowledge support from the University of Saskatchewan research computing group and the use of the HPC resources (Plato machine). H.L. acknowledges support by EFree, an Energy Frontier Research Center funded by the DOE, Office of Science, Basic Energy Sciences under Award No. DE-SC-0001057.

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Table of Contents Graphic P 6 3 /m m c X e C l a t 1 0 0 G P a T

F d -3 m

31

c

= 9 K

X e C l2 a t 1 0 0 G P a T

c

= 4 .3 K


Crystal Structures and Electronic Properties of Xe-Cl Compounds at

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