DOI: 1.138/NCHEM.2528 Synthesis and stability of xenon oxides Xe 2 O 5 and Xe 3 O 2 under pressure Agnès Dewaele, 1 Nicholas Worth, 2 Chris J. Pickard, 3, 4 Richard J. Needs, 2 Sakura Pascarelli, 5 Olivier Mathon, 5 Mohamed Mezouar, 5 and Tetsuo Irifune 6, 7 1 CEA, DAM, DIF, F-91297 Arpajon, France 2 TCM Group, Cavendish Laboratory, J J Thomson Avenue, University of Cambridge, United Kingdom 3 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom 4 Department of Materials Science & Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge, CB3 FS, United Kingdom 5 European Synchrotron Radiation Facility, BP22, 3843 Grenoble Cedex, France 6 Ehime University, 2 5 Bunkyo-cho, Matsuyama 79-8577, Japan 7 Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo 152-85, Japan (Dated: April 8, 216) NATURE CHEMISTRY www.nature.com/naturechemistry 1
Contents Page 1. Synthesis conditions... 3 2. Summary of stable xenon oxides... 3 3. Comparison with previous work... 4 4. Full convex hull plots... 5 5. Raman spectra... 6 6. Equations of state of Xe 2 O 5 and Xe 3 O 2... 7 7. Charge density analysis...... 8 8. Xe orbitals... 1 9. Treatment of Xe 4d electrons... 11 1. Higher-pressure structures... 13 11. Bandstructures and densities of states... 14 12. Structural data of xenon oxides... 17 13. Band gaps...... 18 14. X-ray absorption spectroscopy (XAS)... 19 15. Xe-O stoichiometries searched... 21 NATURE CHEMISTRY www.nature.com/naturechemistry 2
1. SYNTHESIS CONDITIONS TABLE SI: Conditions of synthesis of xenon oxides. The starting mixtures (composed of three phases: Xe with O 2 impurities, Xe(O 2 ) 2 and O 2 ) were laser-heated for several minutes at the pressures indicated. The products were observed in coexistence with the reactants. Xe 2 O 5 and Xe 3 O 2 are the only observed products. During the second experiment, the sample was laser-heated on pressure increase starting from 4 GPa, with 5 GPa pressure steps; the reaction was observed at 77 GPa. Run number Composition Heating P Measurements Products 1 33 % Xe 67 % O 2 83 GPa PXRD + Raman Xe 2 O 5 2 4 % Xe 6 % O 2 77 GPa Raman Xe 2 O 5 3 49 % Xe 51 % O 2 9 GPa PXRD Xe 2 O 5 4 36 % Xe 64 % O 2 82 GPa PXRD + XAS Xe 2 O 5 5 75 % Xe 25 % O 2 92 GPa PXRD Xe 3 O 2 + Xe 2 O 5 6 89 % Xe 11 % O 2 95 GPa PXRD + Raman Xe 3 O 2 + Xe 2 O 5 2. SUMMARY OF STABLE XENON OXIDES TABLE SII: Stable xenon oxides predicted using DFT at pressures of 83 GPa, 15 GPa and 2 GPa. Pressure Stable Structures 83 GPa Xe 2 O 5 -P 4/ncc, Xe 3 O 2 -Immm, Xe 2 O-C2/m 15 GPa Xe 2 O 5 -P 4/ncc, Xe 3 O 2 -Immm, Xe 2 O-C2/m, XeO 3 -P 2 1 2 1 2 1 2 GPa Xe 3 O 2 -Immm, XeO 3 -P 2 1 2 1 2 1, XeO 2 -P nma NATURE CHEMISTRY www.nature.com/naturechemistry 3
3. COMPARISON WITH PREVIOUS WORK a Zhu et al. Hermann and Schwerdtfeger This study b Zhu et al. Hermann and Schwerdtfeger This study Formation Enthalpy (ev/atom) -.2 -.4 Formation Enthalpy (ev/atom) -.2 -.4 -.6 -.8 -.6 Xe 2 O Xe 3 O 2 XeO.2.4.6.8 1 x in Xe 1-x O x Xe 2 O 5-1. -1.2 Xe 2 O Xe 3 O 2 XeO XeO 2 Xe 2 O 5 XeO 3.2.4.6.8 1 x in Xe 1-x O x c Zhu et al. Hermann and Schwerdtfeger This study Formation Enthalpy (ev/atom) -.2 -.4 -.6 -.8-1. -1.2-1.4 Xe 2 O Xe 3 O 2 XeO.2.4.6.8 1 x in Xe 1-x O x FIG. S1: Convex hull diagrams for xenon oxides showing the enthalpies of formation per atom from the elements calculated in Refs. 1 and 2, and in the current work, at three pressures. a, 1 GPa, b, 15 GPa, c, 2 GPa. The different symbols and lines correspond to the different studies (dotted lines and diamonds: Ref. 1, dashed lines and squares: Ref. 2, continuous lines and circles: current work). The enthalpies calculated in Refs. 1 and 2 agree with each other. The Xe 3 O 2 and Xe 2 O stoichiometries were considered in Ref. 2 but not in Ref. 1. In contrast to the current work, neither Ref. 1 nor Ref. 2 explicitly included the Xe 4d electrons in their calculations. Including the Xe 4d electrons results in lower enthalpies of formation (greater stability) for all xenon oxides and in changes to the relative stabilities of structures (see Fig. S7). XeO 2 XeO 3 NATURE CHEMISTRY www.nature.com/naturechemistry 4
4. FULL CONVEX HULL PLOTS a b -.1 Formation Enthalpy (ev/atom) -.1 -.2 -.3 -.4 Xe 2 O C2/m Xe 3 O 2 Immm Xe 2 O 5 P4/ncc.1.2.3.4.5.6.7.8.9 1 x in Xe 1-x O x Formation Enthalpy (ev/atom) -.2 -.3 -.4 -.5 -.6 -.7 -.8 -.9 Xe 2 O C2/m Xe 3 O 2 Immm XeO 3 Xe 2 O 5 P4/ncc P2 1 2 1 2 1-1.1.2.3.4.5.6.7.8.9 1 x in Xe 1-x O x Formation Enthalpy (ev/atom) c -.1 -.2 -.3 -.4 -.5 -.6 -.7 -.8 -.9-1 -1.1-1.2 Xe 3 O 2 Immm XeO 2 Pnma XeO 3 P2 1 2 1 2 1.1.2.3.4.5.6.7.8.9 1 x in Xe 1-x O x FIG. S2: Convex hull plots for the xenon-oxygen system at three pressures. a, 83 GPa, b, 15 GPa, c, 2 GPa. Black circles with red centres lying on the convex hull represent structures stable to decomposition. Red dots denote structures generated by AIRSS that are either higher in enthalpy than other structures of the same stoichiometry, or unstable to decomposition into structures of other stoichiometies. 5 NATURE CHEMISTRY www.nature.com/naturechemistry 5
5. RAMAN SPECTRA a 8 6 Raman frequency (cm -1 ) 4 2 XeO 2 XeO 3 XeO 4 b Intensity (arbitrary units) Xe 2 O 5 after decompression XeO 4 XeO 3 XeO 2.8 V/V.9 1. 2 3 4 5 6 Raman shift (cm -1 ) 7 8 FIG. S3: Raman data measured on pressure decrease for Xe 2 O 5. a, Raman frequencies plotted as a function of compression. The pressure was measured using the high frequency Raman edge of the diamond anvil [3], and the compression was evaluated using data from Fig. S4. Comparisons are made with the Raman or infrared absorption lines of XeO 4 [8], XeO 3 [9] and XeO 2 [1] measured at ambient pressure. b, Raman spectrum recorded at ambient pressure before opening the diamond anvil cell, compared with frequencies and intensities reported in Refs. [8 1]. NATURE CHEMISTRY www.nature.com/naturechemistry 6
6. EQUATIONS OF STATE OF Xe 2 O 5 AND Xe 3 O 2 a 75 2.5 b.58 c/a 2. 1.95 18 c/a.57.38 4 6 8 1 V/f.u. (Å 3 ) 7 65 6 4 Xe 2 O 5 Exp. data Vinet fit DFT-PBE α Xe (ref. [1]) Vinet fit 6 P (GPa) 8 1 synthesis pressure V/2 f.u. (Å 3 ) 16 14 b/a.36 Xe 3 O 2 Exp. data Vinet fit DFT-PBE α Xe (Ref [1]) Vinet fit 4 6 P (GPa) 8 1 synthesis pressure 4 6 P (GPa) 8 1 4 6 P (GPa) 8 1 FIG. S4: Lattice parameters of Xe 2 O 5 (a) and Xe 3 O 2 (b) measured on pressure decrease at 3 K. The pressure was measured using the diffraction lines of a gold pressure marker [4] for Xe 2 O 5 and unreacted xenon diffraction lines [5] for Xe 3 O 2. The pressure has also been calculated using the PBE exchange-correlation density functional [6]. Both curves have been fitted with a Rydberg-Vinet equation of state [7] (blue dashed and black dashdotted lines). The agreement between the experimental and theoretical EoS parameters is very good near to the synthesis pressures, but the EoS parameters gradually diverge from the theoretical data with decreasing pressure. Such behaviour is not surprising on pressure release at room temperature because 1) the pressure distribution may become heterogeneous and 2) because we predict that xenon oxides are unstable below about 5 GPa. The grey dashed lines correspond to a volume proportional to the atomic volume of xenon [5]. NATURE CHEMISTRY www.nature.com/naturechemistry 7
7. CHARGE DENSITY ANALYSIS TABLE SIII: Atomic charges for Xe 2 O 5, with assigned oxidation states. (a) Mulliken population analysis Species Number s p d Charge (e) Oxidation state O1 16 1.92 5.5. -.96 2 O2 4 1.93 5.9. -1.2 2 Xe1 4 1.73 3.3 1. 2.98 6+ Xe2 4 2.15 3.96 1. 1.89 4+ (b) Hirshfeld charge analysis Species Number Charge (e) Oxidation state O1 16 -.27 2 O2 4 -.33 2 Xe1 4.8 6+ Xe2 4.61 4+ (c) Bader charge analysis Species Number Charge (e) Oxidation state O1 16-1. 2 O2 4-1.12 2 Xe1 4 2.96 6+ Xe2 4 2.16 4+ NATURE CHEMISTRY www.nature.com/naturechemistry 8
TABLE SIV: Atomic charges for Xe 3 O 2, with assigned oxidation states. (a) Mulliken population analysis Species Number s p d Charge (e) Oxidation state O 4 1.93 5.1. -1.3 2 Xe1 4 2.6 5.76 1..18 Xe2 2 1.92 4.38 1. 1.71 4+ (b) Hirshfeld charge analysis Species Number Charge (e) Oxidation state O 4 -.31 2 Xe1 4.8 Xe2 2.46 4+ (c) Bader charge analysis Species Number Charge (e) Oxidation state O 4-1. 2 Xe1 4.22 Xe2 2 1.57 4+ NATURE CHEMISTRY www.nature.com/naturechemistry 9
8. Xe ORBITALS.4.2 4d 5s 5p r ψ (Å -1/2 ). -.2 -.4 -.6 1 2 3 4 r (Å) FIG. S5: Hartree-Fock orbitals for an isolated Xe atom. The cut-off radius of the pseudopotential used is shown with the dotted vertical line. Note the significant extension of the 4d orbital beyond the cut-off radius of the pseudopotential. NATURE CHEMISTRY www.nature.com/naturechemistry 1
9. TREATMENT OF Xe 4d ELECTRONS 6 55 5 5s5p 4d5s5p 4s4p4d5s5p Cynn et al. Dewaele et al. Unit cell volume (Å 3 ) 45 4 35 3 25 2 4 6 8 1 12 14 16 18 2 22 24 26 Pressure (GPa) FIG. S6: Equation of state of HCP Xe using three different pseudopotentials and data from two experimental studies. The pseudopotentials treat explicitly the 5s5p electrons (green curve; core radius 2. bohr); the 4d5s5p electrons (red curve; core radius 2.2 bohr); and the 4s4p4d5s5p electrons (blue curve; core radius 2. bohr). The 4d, 5s, 5p pseudopotential was used in the main calculations. Experimental data points are included for comparison [5, 11]. The EOS obtained with the 4d5s5p and 4s4p4d5s5p pseudopotentials are almost identical, but the EOS for the 5s5p pseudopotential is significantly different. NATURE CHEMISTRY www.nature.com/naturechemistry 11
.3 Formation Enthalpy (ev/atom).2.1 -.1 -.2 -.3 Xe 2 O Xe 3 O 2 -.4 Xe 2 O 5.1.2.3.4.5.6.7.8.9 1 x in Xe 1-x O x FIG. S7: Diagram showing calculated enthalpies of formation per atom from the elements for xenon oxides at 83 GPa, calculated both with and without explicit treatments of the d-electrons. The lowest-enthalpy structures for each stoichiometry, with the 4d electrons calculated explicitly, are shown. Green points denote formation enthalpies calculated with an explicit treatment of the d electrons (4d5s5p pseudopotential), and purple points denote formation enthalpies without the explicit treatment of the d electrons (5s5p pseudopotential). Points marked with squares represent structures stable against decomposition into other structures; structures unstable to decomposition are marked with circles. x = corresponds to pure xenon and x = 1 to pure oxygen. NATURE CHEMISTRY www.nature.com/naturechemistry 12
1. HIGHER-PRESSURE STRUCTURES FIG. S8: XeO 3 -P 2 1 2 1 2 1 has a compact extended structure consisting of Xe atoms, all in a 6+ oxidation state, bonding to six O atoms, each of which is shared with another Xe atom. FIG. S9: XeO 2 -P nma consists of XeO 2 chains, with each Xe atom bonded to four O atoms. The Xe atoms have an oxidation state of +4. Unlike in Xe 3 O 2 -Immm, in which the Xe atoms lie along straight lines; the Xe atoms zig-zag between two parallel lines along the direction of the chain. The XeO 2 chains form layers, with the chains in alternate layers offset from, and at an angle to, each other. NATURE CHEMISTRY www.nature.com/naturechemistry 13
11. BANDSTRUCTURES AND DENSITIES OF STATES E - E f (ev) -2-4 -6 Γ M A Z R X Γ FIG. S1: Bandstructure of Xe 2 O 5 -P 4/ncc at 83 GPa. The electronic bands are shown in blue and the Fermi level is shown as a horizontal black dashed line. The orange line shows the d electron density of states (rescaled to fit on the axes), the red shows the s density of states, and the green shows the p density of states. The s and p densities of states include contributions from both Xe and O. Note the appearance of a band gap and that the d levels are about 3 ev below the s bands. DOS calculations were performed using OptaDOS [12 14]. 25 2 O s O p Xe s Xe p edos (ev -1 V u.c. -1 ) 15 1 5-2 -1 E - E f (ev) FIG. S11: Density of states for Xe 2 O 5 at 83 GPa, projected by both chemical species and angular momentum. Note the significant transfer of charge from the Xe 5p to the O 2p orbitals. V u.c. denotes the unit cell volume. NATURE CHEMISTRY www.nature.com/naturechemistry 14
E - E f (ev) -2-4 -6 S W R Γ X T W Γ FIG. S12: Bandstructure of Xe 3 O 2 -Immm at 83 GPa. The colouring is the same as for Fig. S1. 6 O s O p Xe s Xe p edos (ev -1 V u.c. -1 ) 4 2-2 -1 E - E f (ev) FIG. S13: Density of states for Xe 3 O 2 at 83 GPa, projected by species and angular momentum. The transfer of charge from Xe 5p to O 2p is much smaller than for Xe 2 O 5. This is primarily because two-thirds of the Xe atoms in this structure are in the zero oxidation state and are only very weakly involved in chemical bonding. V u.c. denotes the conventional unit cell volume. NATURE CHEMISTRY www.nature.com/naturechemistry 15
E - E f (ev) -2-4 -6 Γ X S Y Γ Z TR UZ FIG. S14: Bandstructure of XeO 3 -P 2 1 2 1 2 1 at 15 GPa. The colouring is the same as for Fig. S1. E - E f (ev) -2-4 -6 Γ Z T Y S X U R FIG. S15: Bandstructure of XeO 2 -P nma at 2 GPa. The colouring is the same as for Fig. S1. NATURE CHEMISTRY www.nature.com/naturechemistry 16
12. STRUCTURAL DATA OF XENON OXIDES TABLE SV: Structural information for stable xenon oxides. Calculated properties are listed in the first part of the table; experimental data are listed in the second part. P gauge stands for the pressure gauge (Refs. [4, 5]). Run numbers correspond to those listed in Table SI. Calculated structures Stoichiometry Space group Pressure (GPa) Lattice parameters Atomic co-ordinates Xe 2 O 5 P 4/ncc 83 Xe 3 O 2 Immm 83 Xe 2 O C2/m 83 XeO 3 P 2 1 2 1 2 1 15 a=4.983 Å c=9.955 Å a=8.536 Å b=3.217 Å c=4.964 Å a=1.1 Å b = 3.26 Å c=11.81 Å β=93.32 a=7.654 Å b=3.289 Å c=4.528 Å XeO 2 P nma 2 a=3.561 Å b=5.799 Å c=4.45 Å Experimentally observed structures Xe (4a)...25 Xe (4c)..5.45 O (4c)..5.266 O (16g).334.311.43 Xe (2c).5.5. Xe (4e).196.. O (4j).5..246 Xe (4i).643..923 Xe (4i).83..688 Xe (4i).634..458 Xe (4i).638..193 O (4i).27..29 O (4i).69..99 Xe (4a).16.195.491 O (4a).699.751.715 O (4a).65.251.74 O (4a).375.256.272 Xe (4c).34.25.965 O (8d).757.73.92 Oxide P gauge Pressure (GPa) Run number Lattice parameters Xe 2 O 5 Xe 83 1 a=4.98 Å, c=9.97 Å Au 93 3 a=4.949 Å, c=9.887 Å Xe 82 4 a=4.979 Å, c=9.96 Å Xe 87 5 a=4.965 Å, c=9.94 Å Xe 3 O 2 Xe 87 5 a=8.516 Å, b=3.186 Å, c=4.985 Å Xe 97 6 a=8.457 Å, b=3.166 Å, c=4.94 Å NATURE CHEMISTRY www.nature.com/naturechemistry 17
13. BAND GAPS TABLE SVI: Minimum and minimum direct band gaps in ev calculated with the PBE exchange-correlation functional [6] for stable xenon oxides at several pressures. (a) Minimum Pressure (GPa) Xenon oxide 83 1 15 2 Xe 2 O 5 1.48 1.38 1.4.77 Xe 3 O 2.... XeO 3.37.26.31.64 XeO 2.... (b) Minimum direct Pressure (GPa) Xenon oxide 83 1 15 2 Xe 2 O 5 1.8 1.76 1.65 1.55 Xe 3 O 2.1.2.7.2 XeO 3.42.35.66 1.18 XeO 2.4.8.12.7 NATURE CHEMISTRY www.nature.com/naturechemistry 18
14. X-RAY ABSORPTION SPECTROSCOPY (XAS) XAS has been performed on sample 4 (see Table SI). In order to reduce as much as possible the portion of unheated (unreacted) sample in the probed volume, the sample was laser heated on both sides. After heating, XAS data was measured near the Xe edge on a grid of points to map out the reacted zone (see Fig. S16). The XAS measurement presented in Fig. 2 was performed at the centre of a Xe-oxide area. In addition, a PXRD pattern was collected at the same spot on the same beamline (BM23 [15]) and on another beamline (ID27). The PXRD spectra are presented in Fig. S17. The PXRD data show a small amount of unreacted Xe on this spot (of the order of 6% on the basis of PXRD peak areas). FIG. S16: Left: microphotograph of the sample characterized with XAS after laser heating at 82 GPa. The reacted zone appears in black. Right: mapping of the sample chamber based on XAS measurements. The colourscale of the map is based on the ratio between the absorption peak measured just above the Xe K-edge (E=34.57 kev), characteristic of oxidized Xe, and the absorption at E=34.6 kev, characteristic of Xe in any oxidation state. The map has 31 34 pixels of 2 2 microns. The reacted zone appears in red. The XAS data was analysed with standard procedures using the Athena and Artemis softwares [16]. The Fourier transform parameters are: k-range = 3.-18. Å 1, Hanning window with dk =1Å 1, R-range =.9-3.2 Å, Hanning window with dr =.2 Å. Table SVII lists the parameters for two models used to least-squares fit the data: one with two shells (oxygen and xenon nearest neighbours) and no assumed structure, and the second with the Xe 2 O 5 structure found with AIRSS. For the latter model, the different oxygen shells have been fitted using only two δr parameters: one for the small distances (subscripted S), one for the large distances (subscripted L), and the number of neighbours has been fixed. In both models, the amplitude parameter S 2 was set to.9 and the energy offset parameter E was left free. NATURE CHEMISTRY www.nature.com/naturechemistry 19
(a) BM23 same spot as XAS Intensity Intensity 4 6 (b) ID27 8 1 12 2θ (deg.) 14 Xe 2 O5 Xe Xe 3 O 2 Re 16 18 4 6 8 1 12 2θ (deg.) 14 16 18 FIG. S17: PXRD spectra taken on the reacted zone in the sample used for XAS measurements, at 82 GPa. The two very intense (cut) peaks are the PXRD signal from the nanopolycrystalline diamond anvils. The most intense PXRD peaks from the sample correspond to Xe 2 O 5 (blue ticks and stars) with a=4.979 Å, c=9.96 Å. Around 6% of unreacted xenon (red ticks and stars) remain in the sample. Traces of Xe 3 O 2 (dark green ticks) can also be detected. A third fitting model has been tried, which is based on the two-shells model but includes a third Xe-Xe shell with fixed R corresponding to the separation for pure xenon at 82 GPa (3.16 Å [5]). The number of neighbours is not constrained in the fit. The fitted number of neighbours should be proportional to the amount of unreacted xenon in the zone probed with X-rays. The least-squares fit of the XAS data yielded a negligible number of neighbours for this shell. We thus conclude that the presence of unreacted Xe does not affect the analysis of the XAS data. NATURE CHEMISTRY www.nature.com/naturechemistry 2
TABLE SVII: Parameters of fit of X-ray absorption spectroscopy data. The parameters for the two models are listed in the first part of the table. The values of fitted parameters are listed in the second part of the table. E: energy offset parameter; N number of neighbours, R distance to neighbours, σ 2 mean squared relative displacement. Reduced χ 2 is the statistical mean square deviation between the data and fit. The error bars correspond to a 67% confidence level in the least-square fit. Models Two-shells fit Xe 2 O 5 fit Free fitting parameters E, δr O, δr Xe, σo 2, σ2 Xe, N O, N Xe E, δr OS, δr OL, δr Xe, σo 2, σ2 Xe Number of free parameters Degrees of freedom 7 14 6 15 Fitted parameters values Two-shells fit Xe 2 O 5 fit Reduced χ 2 55 38 E (ev) 1(1) 1.(9) N R (Å) σ 2 N R (Å) σ 2 ( 1 3 Å 2 ) ( 1 3 Å 2 ) Xe-O S.5 1.814(8) 3.5(7) Xe-O S 3.(5) 1.93(1) 3(1) 4 1.95(8) 3.5(7) Xe-O S 2 2.269(8) 3.5(7) Xe-O L 2 2.4(2) 3.5(7) Xe-O L 2 2.65(2) 3.5(7) Xe-Xe 5.(6) 3.165(5) 2.7(5) 4 3.162(4) 2.(2) 15. Xe-O STOICHIOMETRIES SEARCHED Structure searches were performed for the following Xe-O stoichiometries: Xe 7 O 2, Xe 3 O, Xe 5 O 2, Xe 2 O, Xe 3 O 2, Xe 4 O 3, XeO, Xe 4 O 5, Xe 3 O 4, Xe 2 O 3, XeO 2, Xe 2 O 5, XeO 3, XeO 4, Xe 2 O 9, XeO 5, XeO 11. [1] Zhu, Q. et al. Stability of xenon oxides at high pressures. Nat. Chem. 5, 61 65 (213). [2] Hermann, A. & Schwerdtfeger, P. Xenon suboxides stable under pressure. J. Phys. Chem. Lett. 5, 4336 (214). [3] Akahama, Y. & Kawamura, H. Pressure calibration of diamond anvil Raman gauge to 41 GPa. J. Phys.: Conf. Series 215, 12195 (21). [4] Dewaele, A., Loubeyre, P. & Mezouar, M. Equations of state of six metals above 94 GPa. Phys. Rev. B 7, 94112 94119 (24). [5] Dewaele, A., Loubeyre, P., Dumas, P. & Mezouar, M. Oxygen impurities reduce the metallization pressure of xenon. Phys. Rev. B 86, 1413 1417 (212). NATURE CHEMISTRY www.nature.com/naturechemistry 21
[6] Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 477, 3865 (1996). [7] Vinet, P., Ferrante, J., Rose, J. & Smith, J. Compressibility of solids. J. Geophys. Res 92, 9319 9325 (1987). [8] Huston, J. L. & Claassen, H. H. Raman spectra and force constants for OsO 4 and XeO 4. J. Chem. Phys. 52, 5646 5648 (197). [9] Claassen, H. H. & Knapp, G. Raman spectrum of xenic acid. J. Chem. Soc. 86, 2341 (1964). [1] Brock, D. S. & Schrobilgen, G. J. Synthesis of the missing oxide of xenon, XeO 2, and its implications for Earth s missing xenon. J. Am. Chem. Soc. 133, 6265 6269 (211). [11] Cynn, H. et al. Martensitic fcc-to-hcp transformation observed in xenon at high pressure. Phys. Rev. Lett. 86, 4552 4555 (21). [12] Morris, A. J., Nicholls, R. J., Pickard, C. J. & Yates, J. R. OptaDOS: A tool for obtaining density of states, core-level and optical spectra from electronic structure codes. Comp. Phys. Comm. 185, 1477 1485 (214). [13] Nicholls, R. J., Morris, A. J., Pickard, C. J. & Yates, J. R. OptaDOS - a new tool for EELS calculations. J. Phys.: Conf. Ser. 371, 1262 (212). [14] Yates, J., Wang, X., Vanderbilt, D. & Souza, I. Spectral and Fermi surface properties from Wannier interpolation. Phys. Rev. B 75, 195121 (27). [15] Mathon, O. et al. The time-resolved and extreme conditions XAS (TEXAS) facility at the European Synchrotron Radiation Facility: the general-purpose EXAFS bending-magnet beamline BM23. J. Synchrotron Rad. 22, 1548 1554 (215). [16] Ravel, B. & Newville, M. ATHENA, ARTEMIS, HEPHAESTUS: Data analysis for X-ray absorption spectroscopy using IFEFFIT. J. Synchrotron Rad. 12, 537 541 (25). NATURE CHEMISTRY www.nature.com/naturechemistry 22