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.
Helium is the second (after hydrogen) most abundant element in the universe and it is present in significant quantities in normal stars and in gas giant planets such as Jupiter and Saturn1. Helium and neon are the most inert elements in the periodic table. This is easy to understand as the ionization potential of the He atom (24.59 eV)2 is the highest of all the elements and its electron affinity is zero3. In recent decades, many scientists have tried to find stable compounds of helium. The most successful example is the HeH+ radical4 (and, in general, HenH+ radicals, n = 1–6), which is stable only in its charged form, is extremely aggressive and protonates any base. All neutral molecules that have been found in theory or experiment, such as HHeF (ref. 5), (HeO)(CsF) (ref. 6) and LiHe (ref. 7), are metastable and very high in energy. For instance, HHeF has a computed energy more than 2 eV per atom higher than a mixture of HF molecules and He atoms. The only known stable solid compounds involving helium are van der Waals compounds such as NeHe2 (ref. 8) and He@H2O (ref. 9). For inclusion compounds, the enthalpy of formation is close to zero and removal of He atoms has little effect on the host's electronic structure.
Pressure greatly affects the chemistry of elements. For example, heavy noble gases become more reactive and form compounds with both electronegative and electropositive elements (for example, xenon oxides10,11 and Mg–NG (NG = Xe, Kr, Ar))12. Metallic sodium, when subjected to a pressure of 200 GPa, becomes an insulator due to strong core–core orbital overlap, leading to interstitial valence electron localization13. Furthermore, unexpected compounds such as Na3Cl, Na2Cl, Na3Cl2, NaCl3 and NaCl7 (ref. 14) become stable under pressure. We therefore performed a large-scale evolutionary search for possible stable compounds of helium with a variety of elements (H, O, F, Na, K, Mg, Li, Rb, Cs and so on). We found that only Na readily forms a stable compound with He at pressures accessible to static experiments. In the following, we focus on the Na–He system.
Results and discussion
Stability and structures
Searches for stable compounds were performed using a variable-composition evolutionary structure prediction algorithm15, as implemented in the USPEX code16. In such calculations, a phase is deemed stable if its enthalpy of formation from either elements or any other possible compounds is negative. Variable-composition structure searches were performed for the Na–He system at pressures of 0, 150, 200, 400, 700 and 1,000 GPa, allowing up to 36 atoms per primitive cell. We found a new compound, Na2He (Figs 1 and 2), which has lower enthalpy than the mixture of elemental Na and He, or any other mixture, at pressures above 160 GPa (Fig. 1). The reaction is predicted to be exothermic at pressures above 160 GPa, with reaction enthalpy as large as −0.51 eV at 500 GPa. Phonon calculations clearly indicate dynamical stability of Na2He above 100 GPa (Supplementary Fig. 1). This means that, once formed, this phase can be quenched down to 100 GPa, but at and below 50 GPa it is dynamically unstable and therefore unquenchable to ambient conditions. Quasiharmonic free energy calculations suggest that temperature has little effect on the Gibbs free energy of formation of Na2He: for example, it increases from −0.41 eV at 0 K to −0.39 eV at 800 K at 300 GPa (Supplementary Fig. 2).
Na2He becomes stable at a pressure near the cI16–tI19 transition of elemental Na (we also observed this in experiments, see section ‘Experiments’). The transition in Na has an underlying electronic stabilization mechanism related to the development of a pseudogap or gap at the Fermi energy (tI19 is a very poor metal and hP4, the phase appearing with a further increase in pressure, is an insulator13). This hints at a possible electronic stabilization of Na2He, which has a surprisingly wide bandgap in the entire pressure range of its stability. Insulating Na2He is predicted to form at a lower pressure than insulating hP4-Na (160 versus 273 GPa). The transition pressure for hP4–Na is significantly overestimated (the experimental value is 195 GPa; ref. 13). Density functional theory (DFT) is known to underestimate the stability fields of systems with localized electronic states, and it is expected that Na2He will similarly become stable at pressure below the theoretical estimate of 160 GPa.
Na2He has only one ground-state structure (Fig. 2) in the whole pressure range explored here (that is, from 160 to 1,000 GPa). There are several equivalent ways to describe it. (1) Considering only the positions of the atoms, this is a fluorite-type structure, a three-dimensional checkerboard with alternating He-filled and empty cubes formed by the Na atoms. However, the fluorite structure is not dense, and in all known compounds becomes unstable even at moderate pressures17. (2) Just like hP4–Na (ref. 13), Na2He is an electride, that is, an ionic crystal with a strong Madelung field and an interstitially localized electron (actually, an electron pair in both hP4–Na and Na2He) playing the role of the anion. If one also considers the positions of localized electron pairs (2e−), this is a topologically very dense Heusler alloy structure (AlCu2Mn-type, related to the Fe3Al-type), where He atoms form a cubic close packing, in which all tetrahedral voids are filled by the Na atoms and 2e− fill all octahedral voids. Every He atom (and every 2e−) is coordinated by eight Na atoms. Note that the 2e− form a cubic close packing of their own, and in hP4–Na, they form a nearly perfect hexagonal close packing13. (3) This structure can also be viewed as an ordered body-centred cubic (bcc) superstructure formed by Na, He and 2e−.
In the present experiments, Na was loaded into a He medium in a laser-heated diamond anvil cell (DAC) and compressed up to 155 GPa (Supplementary Table 1). The sample was monitored using synchrotron X-ray diffraction (XRD), Raman spectroscopy and visual observations. The latter verified (Supplementary Fig. 3) that there was He in the DAC high-pressure cavity, as there were transparent colourless areas around the Na sample, which remained up to the highest pressure reached. Below ∼110 GPa, only single-crystal reflections of elemental Na were observed in XRD and their positions agreed with previously reported structural data and the equation of state (EOS)18,19. Above 113 GPa, we detected the appearance of new single-crystal reflections, which became stronger after laser heating to T > 1,500 K. On further compression, unreacted Na (which remains dominant) in the quenched sample showed the transition sequence cI16–oP8–tI19 characteristic of Na at P > 113 GPa (ref. 18). At P > 140 GPa, the transformation to the tI19 phase was complete. Prolonged heating at 140 GPa yielded quasi-continuous diffraction lines (Fig. 3a,b), revealing substantial production of a new phase. Our laser heating experiments confirmed that compressed Na has a low melting temperature, slightly above 300 K near 120 GPa (refs 18, 20). Heating close to the melting temperature of He (∼1,500 K)21 yields more reaction product and the yield increases during further heating.
New reflections were assigned to the predicted fluorite-type Na2He (Fig. 3a,b). They can be indexed in a cubic structure based on their positions and relative intensities (Supplementary Table 2), with lattice parameter in good agreement with theory (Fig. 3c). Experiments show that Na2He has a much higher melting point than pure Na, perhaps above 1,500 K at 140 GPa (Fig. 3a,b), whereas pure sodium melts slightly above 550 K (refs 20, 22), indicating very different energy landscapes and bonding types in Na and Na2He. Experiments confirmed the stability of Na2He, as it is denser than the mixture of Na and He (Fig. 3c) and crystallizes from a sodium–helium melt. Our experiments traced this phase on decomposition down to 113 GPa and its volume–pressure dependence is in good agreement with theoretical predictions (Fig. 3c). The increased yield of the new phase after laser heating (Fig. 3a,b) indicates that a low yield of Na2He at near room temperature is due to kinetic hindrance for the Na (fluid)–He (solid) reaction. Raman experiments on samples quenched to 300 K (Supplementary Fig. 4) showed the presence of a new broad weak peak at 470 cm−1 in addition to peaks that can be assigned to tI19-Na (ref. 20).
Having experimentally confirmed the stability of this compound, we wished to understand its origin. By analogy with other noble gases, one could expect helium to rather form stable compounds with the most electronegative atoms, or perhaps with molecular entities such as H2 (for example, Xe forms stable fluorides under ambient conditions, stable oxides under pressure11 and compounds with H; ref. 23). However, due to its extremely high ionization potential, the highest among all elements, helium does not react with oxygen or fluorine even at the extremely high pressure of 800 GPa. Xenon was predicted to react with electropositive elements (for example, with Mg; ref. 12) under pressure, but in contrast to Xe, He has zero electron affinity and is much less reactive. So what is the chemical nature of Na2He?
It can be easily demonstrated that Na2He is not an inclusion compound. The formation of inclusion compounds involves little electronic redistribution, and host–guest interaction has only a moderate effect on physical properties. Na2He is very different. Its formation is strongly exothermic and its Na sublattice has a simple cubic structure with one valence electron per unit cell and must be metallic. However, upon insertion of He a wide bandgap opens up (Fig. 4). Electronic redistribution due to the insertion of He into the simple cubic sodium sublattice (Fig. 4) is also very large, again proving that this is not an inclusion compound. We observe a contraction of charge density towards all nuclei, but the main effect is its removal from the region occupied by helium and strong buildup in the empty Na8 cubes. Strong non-nuclear charge density maxima allow us to call this compound an electride24,25.
Na2He and hP4-Na differ fundamentally from the known low-pressure electrides26, where interstitially localized electrons are unpaired and spin-polarized. Spin pairing increases the density, making electron-paired electrides a novel type of compound, which are stable under pressure. Valence and conduction bands are expected to broaden under pressure, leading to gap closure and pressure-induced metallization (Wilson model). However, both hP4-Na and Na2He display the opposite behaviour: they are insulating throughout their stability fields, with bandgaps increasing under pressure (Fig. 4b). With direct bandgaps exceeding 1.8 eV at pressures above ∼200 GPa, both Na2He and hP4-Na are expected to be optically transparent, and for hP4-Na, this prediction has been confirmed experimentally13. In our experiments, optical transparency of Na2He could not be checked because of the presence of unreacted Na shielding the transmitted light. Theoretically, Na2He has an even wider gap than hP4-Na at pressures below 230 GPa. Interstitial localization of valence electrons can be viewed as a result of overlap of the core and valence orbitals of neighbouring atoms, forcing valence electrons into the voids of the structure. At 300 GPa, the Na–Na distance is 1.98 Å, shorter than twice the core radius27 (2.04 Å) of the Na atom. Compression leads to further localization of the interstitial electron pair, band narrowing and opening of the bandgap28. Quantum mechanics predicts that interstitial electron pairs, once localized in space, will tend to adopt a spherical shape to minimize their kinetic energy, and our calculations indeed show nearly spherical electron localizations (Supplementary Fig. 5), characterized by volumes and radii, as normal atoms.
We can take the electride description one step further, considering Na2He to be a special kind of ionic crystal, stable because it satisfies Pauling's rules29 for ionic structures. Pauling's first rule is satisfied here: the ratios of the radii (defined as the shortest distance to the Bader boundary30,31), rHe/rNa ≈ 0.83 and r2e/rNa ≈ 0.75, are compatible with eightfold coordination (which requires ratios >0.732). A favourable atomic size ratio rHe/rNa, alone, is not sufficient to stabilize this compound. We find that although the rNe/rK ratio under pressure is closer to the ideal 0.732 for eightfold coordination (Supplementary Figs 6 and 7 and Supplementary Table 3), all K–Ne compounds are massively unstable. Taking into account the positions and charges of ‘2e−’, Na2He also satisfies Pauling's second rule (local electrostatic balance), while hP4-Na does not satisfy it, explaining why Na so readily reacts with He to form Na2He at high pressure.
The Bader charges30 (Supplementary Table 5) of Na atoms in both hP4-Na and Na2He are close to +0.6, He atoms in Na2He have a small negative charge (∼−0.15e), while charges of ‘2e−’ are close to −1.1. For comparison, charge transfer in the inclusion compound He@H2O (ref. 9), predicted at ultrahigh pressures, is just 0.03e. Further insight can be obtained by considering the change in the properties of Bader atoms upon the formation of Na2He from the elements (Table 1). Below 300 GPa, all stabilization is due to volumetric gain (PV term in enthalpy), whereas above 300 GPa, energetic stabilization also comes into play. Table 1 shows large changes in the atomic energies as a result of electronic redistribution at 300 GPa. Although He atoms expand and lower their energy, all the other atomic basins shrink and their energy increases. The balance of different factors is quite complex, the greatest stabilizing factors being the decrease in the energy of the He atoms by 11.515 eV and shrinking of 2e− (PV decrease of 0.966 eV).
We performed a simple computational experiment, taking a large face-centred cubic (fcc) supercell of He and replacing one He atom with Na, as in refs 24 and 25. We found that at pressures of ∼80 GPa, occupied Na–3s (HOMO) and empty He–2s (LUMO) energies become equal, enabling orbital mixing (Supplementary Fig. 11) and some charge transfer from Na–3s to He–2s.
Further insight is provided by advanced methods such as solid-state adaptive natural density partitioning (SSAdNDP)32,33 and periodic natural bond orbital (NBO) methods34,35 (Supplementary Table 6) and integrated crystal orbital Hamilton populations (ICOHP)36,37 (Supplementary Fig. 10). SSAdNDP and NBO show small, but puzzling, charge transfer from He–1s to Na–3p, and more expected transfers from He–1s to He–2s and from Na–3s to Na–3p orbitals with increasing pressure. ICOHP shows that Na–Na and especially Na–2e− (but not Na–He and He–2e−) are the only important interactions and they are both bonding direct covalent interactions. This conclusion is consistent with the SSAdNDP and NBO analyses, where all electron density is assigned to the atoms, and electron pairs occupying empty Na8 cubes emerge as eight-centre two-electron (8c–2e) bonds. These bonds are formed by sp3-hybridized atomic orbitals of sodium as derived from the NBO method34,35. If one considers only the Na sublattice, on average there is just one electron located in every Na8 cube. On insertion of He into half of all Na8 cubes to form Na2He, He atoms push the electron density out of the filled Na8He cube and into the neighbouring empty Na8 cube, enhancing the formation of 8c–2e bonds. Even at 0 GPa, He pushes out ∼0.4 |e| from its cube, which helps to form the 8c–2e− bond with an occupation number (ON) of 1.40 |e| inside the neighbouring empty cube. There are still about 0.6 |e|, which can be found in the Na8He cube. With increasing pressure, He continues to push out the remaining electron density into the empty Na8 cube, increasing the ON of the 8c–2e bond to 1.80 |e| at 100 GPa, 1.88 |e| at 300 GPa and finally to 1.89 |e| at 500 GPa (Supplementary Table 6). This eight-centre two-electron bonding is essential for the stability of Na2He. A complementary view of this is that Na2He is an ionic salt (electride), stable thanks to long-range electrostatic interactions and a crystal structure that is in perfect harmony with the electronic redistribution.
Na is a light alkali metal and is less reactive than the heavier K, Rb and Cs at ambient pressure. Yet, our calculations show the absence of thermodynamically stable K–He, Rb–He and Cs–He compounds at pressures below 1,000 GPa. For Li, we do find that Li5He2 becomes stable at 780 GPa. The difference between light (Li and Na) and heavy (K, Rb and Cs) alkali metals has been discussed by Winzenick and colleagues38: only heavy alkalis under pressure undergo an s→d electronic transition, making them ‘incipient transition metals’. For example, the electronic configuration of K changes from [Ar]4s1 to [Ar]3d1 and the 3d electron will be rather localized and able to penetrate the core, explaining the reduced reactivity and absence of stable K–He compounds. Under pressure, Na paradoxically has lower electronegativity and higher reactivity than K. Indeed, we find that in A–He and A–Ne (A=Na, K) systems under pressure, Na compounds have much lower enthalpies of formation (for example, Supplementary Fig. 6). The high reactivity of compressed Na is due to the interstitial electron pair and is consistent with what is known about electrides—that they have extremely low work functions and can be used as powerful reducing agents39. It is very interesting that, according to our calculations (and consistent with the properties of known low-pressure electrides), the insulating electride phase of Na is more reactive than metallic Na. Li is only a weak electride, whereas heavier alkali metals (K, Rb and Cs) are not electrides and are less reactive under pressure.
With this in mind, we hypothesized that Na2He, with a bare interstitial electron pair, might be stabilized by a strong acceptor of an electron pair—for example, oxygen40. Our structure searches showed that Na2O, indeed, has the same structure as hP4-Na, and Na2HeO is isostructural with Na2He. In both cases, O2− (that is, oxygen with the absorbed electron pair) occupies the position of ‘2e−’ and both can be considered as salts. Importantly, Na2HeO is thermodynamically stable in the Na–He–O system in the pressure range 15–106 GPa.
In conclusion, a systematic search for stable compounds of helium has resulted in the prediction and experimental verification of a cubic-phase Na2He, stable from 113 GPa up to at least 1,000 GPa. This phase is an electride, that is, a crystal made of positively charged ionic cores and with strongly localized valence electrons playing the role of anions. The insertion of He atoms pushes away the electron gas, leading to localization of valence electrons and the formation of eight-centre two-electron bonds and opening of a wide bandgap, just as for a salt-like compound. The predicted two compounds, Na2He and Na2HeO, change the hitherto bare field of helium chemistry, provide new twists to the chemistry of noble gases, and will have an impact on our understanding of chemical bonding and of the chemical processes that occur inside giant planets.
The evolutionary algorithm USPEX16, used here for predicting new stable structures, searches for the lowest-enthalpy structures at a given pressure, and is capable of predicting stable compounds and structures knowing just the chemical elements involved. A number of applications11,13,14,16,41 illustrate its power. Structure relaxations were performed using DFT within the Perdew–Burke–Ernzerhof (PBE) functional42 in the framework of the all-electron projector augmented wave (PAW) method43, as implemented in the VASP code44. For Na atoms we used PAW potentials with 1.2 a.u. core radius and 2s22p63s electrons treated as valence. For He the core radius was 1.1 a.u. and 1s2 electrons were treated as valence. We used a plane-wave kinetic energy cutoff of 1,000 eV and the Brillouin zone was sampled with a resolution of 2π × 0.06 Å−1, which showed excellent convergence of the energy differences, stress tensors and structural parameters. The first generation of structures was created randomly. All structures were relaxed at constant pressure and 0 K and the enthalpy was used as fitness. The energetically worst structures (40%) were discarded and a new generation was created, 30% randomly and 70% from the lowest-enthalpy structures through heredity, lattice mutation and transmutation.
To obtain atomic properties (Bader charges, atomic volumes and atomic energies), perform critical point analysis, compute Mulliken charges and deformation density maps, we performed all-electron calculations using the CRYSTAL14 code45. Triple-zeta quality Gaussian basis sets were used for all atoms, including also basis functions centred on non-nuclear charge density maxima positions, which are the centres of interstitial electron localizations (details of the basis set and grid used to sample direct and reciprocal space are reported in section ‘Supplementary Methods’). The topological properties of charge density were obtained using the TOPOND code46 incorporated into CRYSTAL14. Bader volumes and charges were also obtained using VASP and code from ref. 31, and the results are essentially identical to those obtained using CRYSTAL14. Crystal orbital Hamilton population (COHP) analysis36 was performed using periodic localized orbitals as implemented in the TB-LMTO-ASA framework47. We also explored the effects of temperature on stability using the quasiharmonic approximation, for which phonon calculations were performed for all relevant structures using the PHONOPY code48; for each structure, phonons were computed at 20 different volumes to predict the Gibbs free energy.
We loaded thin Na (3–5 µm) plates (30 × 30 µm2 dimensions) in a DAC cavity (30–40 µm diameter) made in indented to 20 µm thickness rhenium gasket in a glove box and then filled the rest of the cavity with He gas compressed to 1,600 bar. Diamond anvils with 70–100 µm central tips bevelled to a 300 µm outside culet diameter were used. Synchrotron X-ray diffraction was monitored on increasing the pressure. The pressure was determined by measuring the position of the stressed first-order Raman diamond edge49. Laser heating was performed above 120 GPa. X-ray diffraction patterns and radiometric temperature measurements were used to characterize the sample state in situ. Laser heating remained very local during this procedure, as our radiometric measurements and finite element calculations show. We did not expect any reaction with the gasket material (which remains close to room temperature during heating) or with the diamond anvils, and this was verified by subsequent X-ray diffraction and Raman mapping of the sample cavity including areas near the gasket edge. Raman measurements were performed using the 488, 532 and 660 nm lines of a solid-state laser. The laser probing spot dimension was 4 µm. Raman spectra were analysed with a spectral resolution of 4 cm−1 using a single-stage grating spectrograph equipped with a charge-coupled device (CCD) array detector. X-ray diffraction was measured in a double-sided laser heating system at the undulator XRD beamline at GeoSoilEnviroCARS, APS, Chicago, and the Extreme Conditions Beamline P02.2 at DESY (Germany), which have online laser heating capabilities. Temperature was determined spectroradiometrically. The X-ray probing beam size was ∼2–5 µm in both beamlines.
The data that support the findings of this study are available from the authors on request.
This work was supported by the China Scholarship Council (grant no. 201206200030), NSAF (grant no. U1530402), National Science Foundation (grant no. EAR-1114313), DARPA (grant no. W31P4Q1210008), Russian Science Foundation (grant no. 16-13-10459), National 973 Program of China (grant no. 2012CB921900) and Foreign Talents Introduction and Academic Exchange Program (grant no. B08040). X.F.Z. acknowledges funding from the National Science Foundation of China (grant no. 11674176). Calculations were performed at the Tianhe II supercomputer in Guangzhou and the supercomputer of the Center for Functional Nanomaterials, Brookhaven National Laboratory, which is supported by the US Department of Energy, Office of Basic Energy Sciences, under contract no. DE-AC02-98CH10086. GeoSoilEnviroCARS is supported by the National Science Foundation – Earth Sciences (EAR-1128799) and Department of Energy – Geosciences (DE-FG02-94ER14466). Use of the Advanced Photon Source was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract no. DE-AC02-06CH11357. PETRA III at DESY is a member of the Helmholtz Association (HGF). The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007- 2013) under grant agreement no. 312284. The work of E.S. was performed under the auspices of the US Department of Energy by Lawrence Livermore National Security under contract no. DE-AC52-07NA27344. A.F.G. acknowledges support from the National Natural Science Foundation of China (grant no. 21473211), the Chinese Academy of Sciences (grant no. YZ201524) and the Chinese Academy of Sciences visiting professorship for senior international scientists (grant no. 2011T2J20) and Recruitment Program of Foreign Experts. S.L. was partly supported by state assignment project no. 0330-2016-0006. A.I.B. acknowledges the support of the National Science Foundation (CHE-1361413 to A.I.B.). I.A.P. acknowledges the support of the Ministry of Education and Science of the Russian Federation (agreement number 02.a03.21.0008).
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Nature Communications (2018)