A stable compound of helium and sodium at high pressure

Journal name:
Nature Chemistry
Year published:
Published online


Helium is generally understood to be chemically inert and this is due to its extremely stable closed-shell electronic configuration, zero electron affinity and an unsurpassed ionization potential. It is not known to form thermodynamically stable compounds, except a few inclusion compounds. Here, using the ab initio evolutionary algorithm USPEX and subsequent high-pressure synthesis in a diamond anvil cell, we report the discovery of a thermodynamically stable compound of helium and sodium, Na2He, which has a fluorite-type structure and is stable at pressures >113 GPa. We show that the presence of He atoms causes strong electron localization and makes this material insulating. This phase is an electride, with electron pairs localized in interstices, forming eight-centre two-electron bonds within empty Na8 cubes. We also predict the existence of Na2HeO with a similar structure at pressures above 15 GPa.

At a glance


  1. Thermodynamics of the Na–He system, which shows the enthalpic stability between Na2He and the mixture of elemental Na and He.
    Figure 1: Thermodynamics of the Na–He system, which shows the enthalpic stability between Na2He and the mixture of elemental Na and He.

    a, Predicted convex hulls of the Na–He system, based on the theoretical ground states of Na and He at each pressure13, 18, 22, 50. Here, ΔHformation(NaxHe1−x) = xH(Na) + (1−x)H(He)−H(NaxHe1−x), which can be considered as a criterion of thermodynamic stability. b, Enthalpy of formation of Na2He as a function of pressure. Our calculated pressures of the cI16–tI19 and tI19–hP4 transitions of Na are 151 and 273 GPa, respectively, similar to previous calculations13.

  2. Crystal structure of Na2He at 300 GPa.
    Figure 2: Crystal structure of Na2He at 300 GPa.

    a,b, Ball-and-stick representation (a, pink and grey atoms represent Na and He, respectively) and polyhedral representation (b), where half of the Na8 cubes are occupied by He atoms (shown as polyhedra) and half by 2e (shown as red spheres). c, Electron localization function (ELF, which measures the spatial localization of electrons) plotted in the [110] plane at 300 GPa. This structure has space group Fm-3m with lattice parameter a = 3.95 Å at 300 GPa and Na atoms occupying the Wyckoff position 8c (0.25,0.25,0.25) and He atoms occupying the 4a (0,0,0) position.

  3. Experimental data on Na2He: XRD at 140 GPa.
    Figure 3: Experimental data on Na2He: XRD at 140 GPa.

    a, Integrated XRD patterns before heating and after the second and third heating to ∼1,200 and >1,500 K, respectively. Vertical ticks correspond to expected positions and intensities of XRD peaks of Na2He, tI19-Na (ref. 18), Re (gasket) and W (pressure gauge). b, Two-dimensional image after the third heating, in radial coordinates, showing single-crystal reflections of tI19-Na and Na2He, marked by light blue circles and white rectangles, respectively. This pattern was obtained during a continuous rotation of the DAC along the ω axis to collect as many single-crystal reflections of tI19-Na as possible. Semi-continuous lines are from the Re gasket. Diffraction from Na2He and W consists of many small, almost uniformly spaced spots. After the third heating, a new almost continuous line appeared near 10.5°, which we assigned to yet unidentified reaction products. The X-ray wavelength is 0.31 Å. c, Equation of state (EOS) of Na2He synthesized in a DAC at 113–155 GPa in comparison with the EOS of Na. Filled circles: experimental unit cell volumes of Na2He. Open blue circles: volumes per two Na atoms. Error bars correspond to the experimental pressure uncertainty due to pressure gradients and pressure measurements. Pressure was determined from XRD measurements of the W marker in one experiment and using Raman shift of the stressed diamonds51. The solid blue line corresponds to a superposition of the EOS of Na and He (2Na + He) determined from experimental data52. Dashed and solid lines are the results of our GGA and LDA calculations, respectively. Dotted line: extrapolated EOS of fcc Na from ref. 19. Open red circles: volumes of Na phases reported in ref. 18.

  4. Electronic structure of Na2He.
    Figure 4: Electronic structure of Na2He.

    a, Density of states (DOS) of Na2He and its Na-sublattice, showing that the insertion of He opens a bandgap (the pure Na sublattice is metallic). The vertical line is the Fermi level. b, Band structure and bandgap as a function of pressure. GW gaps (where G is the Green’s function and W is the screened Coulomb interaction) are typically accurate to within 5–10% of experimental values53. It shows that both Na and Na2He have a wide gap that increases with pressure. c, Electron density change (defined as ρ(Na2He)−ρ(Na sublattice)−ρ(He sublattice)) induced by insertion of the He sublattice. (100) sections passing through He atoms (above) and Na atoms (below) are shown at 300 GPa. NNA (non-nuclear attractors) corresponds to interstitial electron localizations. The insertion of He pushes electron density out, causing its interstitial localization.


  1. Stevenson, D. J. Metallic helium in massive planets. Proc. Natl Acad. Sci. USA 105, 1103511036 (2008).
  2. Huheey, J. E., Keiter, E. A., Keiter, R. L. & Medhi, O. K. Inorganic Chemistry: Principles of Structure and Reactivity (Harper & Row, 1983).
  3. Hotop, H. & Lineberger, W. C. Binding energies in atomic negative ions: II. J. Phys. Chem. Ref. Data 14, 731750 (1985).
  4. Hiby, J. W. Massenspektrographische untersuchungen an wasserstoff- und heliumkanalstrahlen (H3+, H2, HeH+, HeD+, He). Annalen der Physik 426, 473487 (1939).
  5. Wong, M. W. Prediction of a metastable helium compound: HHeF. J. Am. Chem. Soc. 122, 62896290 (2000).
  6. Grochala, W. On chemical bonding between helium and oxygen. Pol. J. Chem. 83, 87122 (2009).
  7. Tariq, N., Taisan, N. A., Singh, V. & Weinstein, J. D. Spectroscopic detection of the LiHe molecule. Phys. Rev. Lett. 110, 153201 (2013).
  8. Loubeyre, P., Jean-Louis, M., LeToullec, R. & Charon-Gérard, L. High pressure measurements of the He-Ne binary phase diagram at 296 K: evidence for the stability of a stoichiometric Ne(He)2 solid. Phys. Rev. Lett. 70, 178181 (1993).
  9. Liu, H., Yao, Y. & Klug, D. D. Stable structures of He and H2O at high pressure. Phys. Rev. B 91, 014102 (2015).
  10. Hermann, A. & Schwerdtfeger, P. Xenon suboxides stable under pressure. J. Phys. Chem. Lett. 5, 43364342 (2014).
  11. Zhu, Q. et al. Stability of xenon oxides at high pressures. Nat. Chem. 5, 6165 (2013).
  12. Miao, M.-s. et al. Anionic chemistry of noble gases: formation of Mg–NG (NG = Xe, Kr, Ar) compounds under pressure. J. Am. Chem. Soc. 137, 1412214128 (2015).
  13. Ma, Y. et al. Transparent dense sodium. Nature 458, 182185 (2009).
  14. Zhang, W. et al. Unexpected stable stoichiometries of sodium chlorides. Science 342, 15021505 (2013).
  15. Lyakhov, A. O., Oganov, A. R. & Valle, M. in Modern Methods of Crystal Structure Prediction (ed. Oganov, A.R.) 147180 (Wiley-VCH 2010).
  16. Oganov, A. R. & Glass, C. W. Crystal structure prediction using ab initio evolutionary techniques: principles and applications. J. Chem. Phys. 124, 244704 (2006).
  17. Gerward, L. et al. X-ray diffraction investigations of CaF2 at high pressure. J. Appl. Crystallogr. 25, 578581 (1992).
  18. Gregoryanz, E. et al. Structural diversity of sodium. Science 320, 10541057 (2008).
  19. Hanfland, M., Loa, I. & Syassen, K. Sodium under pressure: bcc to fcc structural transition and pressure–volume relation to 100 GPa. Phys. Rev. B 65, 184109 (2002).
  20. Marqués, M. et al. Optical and electronic properties of dense sodium. Phys. Rev. B 83, 184106 (2011).
  21. Santamaría-Pérez, D., Mukherjee, G. D., Schwager, B. & Boehler, R. High-pressure melting curve of helium and neon: deviations from corresponding states theory. Phys. Rev. B 81, 214101 (2010).
  22. Gregoryanz, E., Degtyareva, O., Somayazulu, M., Hemley, R. J. & Mao, H.-k. Melting of dense sodium. Phys. Rev. Lett. 94, 185502 (2005).
  23. Somayazulu, M. et al. Pressure-induced bonding and compound formation in xenon–hydrogen solids. Nat. Chem. 2, 5053 (2010).
  24. Miao, M.-S. & Hoffmann, R. High pressure electrides: a predictive chemical and physical theory. Acc. Chem. Res. 47, 13111317 (2014).
  25. Miao, M.-S. & Hoffmann, R. High-pressure electrides: the chemical nature of interstitial quasiatoms. J. Am. Chem. Soc. 137, 36313637 (2015).
  26. Dye, J. L. Electrons as anions. Science 301, 607608 (2003).
  27. Shannon, R. D. & Prewitt, C. T. Effective ionic radii in oxides and fluorides. Acta Crystallogr. B 25, 925946 (1969).
  28. Rousseau, B. & Ashcroft, N. W. Interstitial electronic localization. Phys. Rev. Lett. 101, 046407 (2008).
  29. Pauling, L. The principles determining the structure of complex ionic crystals. J. Am. Chem. Soc. 51, 10101026 (1929).
  30. Bader, R. F. W. Atoms in Molecules – A Quantum Theory (Univ. Oxford Press, 1990).
  31. Henkelman, G., Arnaldsson, A. & Jónsson, H. A fast and robust algorithm for Bader decomposition of charge density. Comput. Mater. Sci. 36, 354360 (2006).
  32. Galeev, T. R., Dunnington, B. D., Schmidt, J. & Boldyrev, A. I. Solid state adaptive natural density partitioning: a tool for deciphering multi-center bonding in periodic systems. Phys. Chem. Chem. Phys. 15, 50225029 (2013).
  33. Zubarev, D. Y. & Boldyrev, A. I. Developing paradigms of chemical bonding: adaptive natural density partitioning. Phys. Chem. Chem. Phys. 10, 52075217 (2008).
  34. Dunnington, B. D. & Schmidt, J. R. Generalization of natural bond orbital analysis to periodic systems: applications to solids and surfaces via plane-wave density functional theory. J. Chem. Theory Comput. 8, 19021911 (2012).
  35. Foster, J. P. & Weinhold, F. Natural hybrid orbitals. J. Am. Chem. Soc. 102, 72117218 (1980).
  36. Dronskowski, R. & Blöchl, P. E. Crystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on density-functional calculations. J. Phys. Chem. 97, 86178624 (1993).
  37. Andersen, O. K. & Jepsen, O. Explicit, first-principles tight-binding theory. Phys. Rev. Lett. 53, 25712574 (1984).
  38. Winzenick, M., Vijayakumar, V. & Holzapfel, W. B. High-pressure X-ray diffraction on potassium and rubidium up to 50 GPa. Phys. Rev. B 50, 1238112385 (1994).
  39. Dye, J. L. Electrides: early examples of quantum confinement. Acc. Chem. Res. 42, 15641572 (2009).
  40. Vegas, Á. & Mattesini, M. Towards a generalized vision of oxides: disclosing the role of cations and anions in determining unit-cell dimensions. Acta Crystallogr. B 66, 338344 (2010).
  41. Oganov, A. R. et al. Ionic high-pressure form of elemental boron. Nature 457, 863867 (2009).
  42. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 38653868 (1996).
  43. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 1795317979 (1994).
  44. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 1550 (1996).
  45. Dovesi, R. et al. CRYSTAL14 User's Manual (Univ. of Torino, 2014).
  46. Gatti, C., Saunders, V. R. & Roetti, C. Crystal field effects on the topological properties of the electron density in molecular crystals: the case of urea. J. Chem. Phys. 101, 1068610696 (1994).
  47. Krier, G., Jepsen, O., Burkhardt, A. & Andersen, O. K. The TB-LMTO-ASA Program (Max-Planck-Institute for Solid State Research, 1995).
  48. Togo, A., Oba, F. & Tanaka, I. First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures. Phys. Rev. B 78, 134106 (2008).
  49. Akahama, Y. & Kawamura, H. High-pressure Raman spectroscopy of diamond anvils to 250 GPa: method for pressure determination in the multimegabar pressure range. J. Appl. Phys. 96, 37483751 (2004).
  50. McMahon, J. M., Morales, M. A., Pierleoni, C. & Ceperley, D. M. The properties of hydrogen and helium under extreme conditions. Rev. Mod. Phys. 84, 16071653 (2012).
  51. Akahama, Y. & Kawamura, H. Pressure calibration of diamond anvil Raman gauge to 310 GPa. J. Appl. Phys. 100, 043516 (2006).
  52. Loubeyre, P. et al. Equation of state and phase diagram of solid 4He from single-crystal X-ray diffraction over a large PT domain. Phys. Rev. Lett. 71, 22722275 (1993).
  53. Shishkin, M. & Kresse, G. Self-consistent GW calculations for semiconductors and insulators. Phys. Rev. B 75, 235102 (2007).

Download references

Author information


  1. School of Physics and MOE Key Laboratory of Weak-Light Nonlinear Photonics, Nankai University, Tianjin 300071, China

    • Xiao Dong,
    • Xiang-Feng Zhou &
    • Hui-Tian Wang
  2. Center for High Pressure Science and Technology Advanced Research, Beijing 100193, China

    • Xiao Dong
  3. Department of Geosciences, Stony Brook University, Stony Brook, New York 11794-2100, USA

    • Xiao Dong,
    • Artem R. Oganov,
    • Guang-Rui Qian,
    • Qiang Zhu &
    • Xiang-Feng Zhou
  4. Skolkovo Institute of Science and Technology, 3 Nobel Street, Moscow 143026, Russia

    • Artem R. Oganov
  5. Moscow Institute of Physics and Technology, 9 Institutskiy Lane, Dolgoprudny city, Moscow Region 141700, Russia

    • Artem R. Oganov &
    • Gabriele Saleh
  6. International Centre for Materials Discovery, Northwestern Polytechnical University, Xi'an 710072, China

    • Artem R. Oganov
  7. Geophysical Laboratory, Carnegie Institution of Washington, 5251 Broad Branch Road, Washington DC 20015, USA

    • Alexander F. Goncharov,
    • Elissaios Stavrou &
    • Sergey Lobanov
  8. Key Laboratory of Materials Physics and Center for Energy Matter in Extreme Environments, Institute of Solid State Physics, Chinese Academy of Sciences, 350 Shushanghu Road, Hefei, Anhui 230031, China

    • Alexander F. Goncharov
  9. Lawrence Livermore National Laboratory, Physical and Life Sciences Directorate, PO Box 808 L-350, Livermore, California 94550, USA

    • Elissaios Stavrou
  10. Sobolev Institute of Geology and Mineralogy, Siberian Branch Russian Academy of Sciences, 3 Pr. Ac. Koptyga, Novosibirsk 630090, Russia

    • Sergey Lobanov
  11. Istituto di Scienze e Tecnologie Molecolari del CNR (CNR-ISTM) e Dipartimento di Chimica, Universita’ di Milano, via Golgi 19, Milan 20133, Italy

    • Carlo Gatti
  12. Chair of Solid-State and Quantum Chemistry, RWTH Aachen University, Aachen D-52056, Germany

    • Volker L. Deringer &
    • Richard Dronskowski
  13. Center for Advanced Radiation Sources, University of Chicago, Chicago, Illinois 60637, USA

    • Vitali B. Prakapenka
  14. Photon Science DESY, Hamburg D-22607, Germany

    • Zuzana Konôpková
  15. Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322, USA

    • Ivan A. Popov &
    • Alexander I. Boldyrev
  16. Chemistry Department, Faculty of Science, RUDN University, 6 Miklukho-Maklaya Street, Moscow 117198, Russia

    • Ivan A. Popov
  17. Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

    • Hui-Tian Wang


X.D. and A.R.O. designed the research. X.D., G.S. and I.A.P. performed and analysed the calculations. V.L.D. and R.D. carried out COHP analyses. A.G. designed experiments. S.L. and A.G. loaded the sample. A.F.G., E.S., S.L., V.B.P. and Z.K. performed the experiment. E.S. and A.F.G. analysed the experimental data. G.-R.Q., Q.Z., X.-F.Z. and A.I.B. assisted with calculations. All authors contributed to interpretation and discussion of the data. X.D., A.R.O., A.F.G., G.S., I.A.P., A.I.B. and H.-T.W. wrote the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary information (791 KB)

    Supplementary information

Additional data