Formation of ammonia–helium compounds at high pressure

Uranus and Neptune are generally assumed to have helium only in their gaseous atmospheres. Here, we report the possibility of helium being fixed in the upper mantles of these planets in the form of NH3–He compounds. Structure predictions reveal two energetically stable NH3–He compounds with stoichiometries (NH3)2He and NH3He at high pressures. At low temperatures, (NH3)2He is ionic with NH3 molecules partially dissociating into (NH2)− and (NH4)+ ions. Simulations show that (NH3)2He transforms into intermediate phase at 100 GPa and 1000 K with H atoms slightly vibrate around N atoms, and then to a superionic phase at ~2000 K with H and He exhibiting liquid behavior within the fixed N sublattice. Finally, (NH3)2He becomes a fluid phase at temperatures of 3000 K. The stability of (NH3)2He at high pressure and temperature could contribute to update models of the interiors of Uranus and Neptune.

K nowledge of the interior compositions of planets is crucial to understanding the processes of their formation and evolution. Various methods have been used to investigate the Earth's interior, while studies of the composition and structure of the solar system's ice giants, Uranus and Neptune, are limited by using only global observable properties such as gravitational and magnetic moments 1 . Uranus and Neptune are generally assumed to have a three-layer structure: a rocky core, an ice mantle (contains an upper mantle and a lower mantle), and a gas atmosphere [1][2][3][4][5][6] . Although many studies have focused on the interiors of Uranus and Neptune, their internal compositions remain to be fully understood [7][8][9][10][11][12] . A widely accepted model for each of these planets is that the upper mantle comprises a mixture of ionized H 2 O, NH 3 , and CH 4 5,8,11 , whereas the lower mantle consists of metallic H 2 O, NH 3 5,6 Much effort has been devoted to determine the ratio of the components in the interior of the ice planets 8,10,11 , however, no consensus were reached.
To understand realistic compositions of Uranus and Neptune, researchers have focused on high-pressure and high-temperature phases of NH 3 and H 2 O, and mixtures of the two [13][14][15] . Cavazzoni et al 16 . performed molecular dynamic simulations to estimate the phase diagram of water and ammonia at pressures and temperatures in the range of 30-300 GPa and 300-7000 K. They found that water and ammonia exhibited a superionic phase (at about 100 GPa, 1500 K) between the ionic solid phase and ionic fluid phase. However, for the component CH 4 , the results of equation of state have shown that it would dissociate into hydrocarbons at the extreme conditions 17 . A computational search undertaken by Pickard and Needs in 2008 found that ammonia transformed into an ionic phase consisting of (NH 2 ) − and (NH 4 ) + ions at pressures above 90 GPa 13 ; the transformation was subsequently confirmed by experiment 14,15 . By combining empirical and theoretical results, Ninet et al 18 . found that a novel superionic conductive phase of ammonia becomes stable at about 70 GPa and 8500 K. Using Raman spectroscopy and synchrotron X-ray diffraction, Laniel et al 19 . found two unusual ionic N-H stoichiometries, (N 2 ) 6 (H 2 ) 7 and N 2 (H 2 ) 2 , which are stable at about 50-GPa. While for water, it has a rich phase diagram, with at least 17 solid phases identified experimentally [20][21][22] , and seven other high-pressure phases predicted by theoretical studies 23 33 . These findings contribute to our understanding of the interiors of the giant ice planets.
The above results have led to the assumption that the elements (i.e., C, H, and N) in the ice giants' gaseous atmospheres except He appear in their solid mantles. Helium is generally considered likely to remain only in the atmosphere and not form solid compounds in the mantle, because it is the most chemically inert element due to its stable closed-shell electronic configuration. In fact, Nettelmann et al 11 . have proposed a three-layer structure model, in which the considering of small amount of He/H in the outer core of the planets reproducing well the gravitational moments of the ice giants. Recent studies have indicated that high pressure can induce He to form compounds such as HeN 4 39 . These results inspired us to explore whether some of the abundant elemental He from the planets' atmospheres could be trapped inside the mantles of Uranus and Neptune. Therefore, we carried out calculations to search for stable compounds in NH 3 -He systems at high pressure and high temperature. Our results show that He can react with NH 3 to form (NH 3 ) 2 He under extreme conditions, to a certain extent corresponding to the upper mantles of Uranus and Neptune, thereby providing information essential to the understanding of the interior models of these planets.

Results
Stable NH 3 -He compounds at high pressure. The formation enthalpies of the energetically most-stable structures of (NH 3 ) x He y (x = 1~3, y = 1~3) as compared to mixtures of NH 3 and He at selected pressures are summarized in Fig. 1. The phases lying on the convex hull are thermodynamically stable against decomposition into other compositions. The figure also shows the effects of zero-point vibrational energy (ZPE). The positive formation enthalpies show that, as expected, no thermodynamically stable compositions were found at ambient pressure. However, static-lattice enthalpy calculations revealed three stable compositions at high pressures: (NH 3 ) 2 He at 10 and 300 GPa, NH 3 He at 50, 100, and 150 GPa, and NH 3 He 2 at 300 GPa ( Supplementary  Fig. 1). The inclusion of ZPE alters significantly the stability of (NH 3 ) 2 He and NH 3 He 2 , i.e., (NH 3 ) 2 He becomes energetically stable also at 150 and 300 GPa, while NH 3 He 2 turns to be unstable at all pressures.
Figs. 2 and 3, respectively present detailed stable pressure ranges for the three obtained compositions and their corresponding crystal structures. Optimized lattice parameters for all the structures at selected pressures are listed in Supplementary  Table 1. The results indicate that (NH 3 ) 2 He with space group I4, labeled here as I4-(NH 3 ) 2 He, becomes energetically stable with respect to NH 3 and He at pressures as low as 9 GPa (Fig. 2). Tetragonal I4-(NH 3 ) 2 He consists of isolated NH 3 molecules and He atoms. Figure 3a depicts the NH 3 layers of this structure in the a-b planes, with He atoms located in the pockets formed by neighboring NH 3 molecules. Interestingly, the I4 structure displays unique channels formed by NH 3 molecules that are arranged parallel to the c-axis, and linear He chains localize within the interstices formed by four neighboring channels (Fig. 3b). To our knowledge, this is the first report of such a channel-bearing NH 3 structure.
(NH 3 ) 2 He remains energetically stable up to 40 GPa, above which it decomposes into a mixture of NH 3 and He. However, (NH 3 ) 2 He re-emerges as energetically stable phase at 110 GPa with the formation of an orthorhombic Fmm2 structure. A similar combination-decomposition-recombination pattern has previously been reported for CaLi 2 44 . Partial dissociation of NH 3 molecules into (NH 2 ) − and (NH 4 ) + ions is found to accompany the formation of Fmm2-(NH 3 ) 2 He. Bader analysis demonstrates the strongly ionic nature of the species, with Bader charges of −0.57 e − and 0.53 e − for (NH 2 ) − and (NH 4 ) + , respectively, similar to those observed in the ionic phase of pure NH 3 13 . The Fmm2 phase is also layered, consisting of layers formed by NH 3 , (NH 2 ) − , and (NH 4 ) + units in the a-c planes. The spacing between neighboring layers is 2.07 Å. Viewing the structure along the a-axis reveals unique channels formed by NH 3 , (NH 2 ) − , and (NH 4 ) + units, with He atoms located in the interstices. NH 3 He composition becomes energetically stable at 35 GPa, as shown in Fig. 2, adopting an orthorhombic Pmma structure. The Pmma phase is the most stable configuration over a large pressure range up to 180 GPa for NH 3 He, above which it transforms into the P2 1 2 1 2 1 structure. The P2 1 2 1 2 1 -NH 3 He phase will remain stable up to 300 GPa, which is the maximum pressure considered in this study. Both the Pmma and the P2 1 2 1 2 1 structures of NH 3 He are composed of isolated NH 3 molecules and He atoms, and there is no evidence of dissociation of NH 3 in the whole pressure range studied here. The calculated phonon dispersions confirm the dynamical stability of all these structures in their energetically stable pressure ranges (Supplementary Fig. 3).
Electronic properties. To examine the interactions among N, H, and He atoms in the two compounds, we calculate electronic properties including the electronic localization function (ELF) and Bader charges. The ELF is a quantum chemistry tool to visualize covalent bonds; values close to 1 corresponding to strong covalent bonding. The ELF results rule out covalent bonds between N-H units (NH 3 , (NH 2 ) − , (NH 4 ) + ) and He atoms, given the absence of any ELF local maxima between them (Supplementary Fig. 5). Interestingly, Bader analysis indicates a slight charge transfer from N-H units to He atoms. Table 1 lists the Bader charge of one He atom in I4-(NH 3 ) 2 He as~-0.02 e − at 10 GPa, which increases to -0.03 e − when the Fmm2 structure is adopted at 120 GPa. Similar to that in (NH 3 ) 2 He, each He atom in NH 3 He and NH 3 He 2 gains nearly 0.03 e − from the NH 3 molecules. The Bader charge of a He atom in the three NH 3 -He compounds is similar to the charges predicted for H 2 O-He, MgF 2 He, MgOHe, and FeO 2 He (between −0.02 e − and -0.07 e − ) [36][37][38]40 . The current results indicate the three compounds have an ionic nature and that He atoms could serve as a Coulomb shield in stabilizing them at high pressure. Electronic band structures show that all three compounds are insulators ( Supplementary Fig. 4). At the PBE-GGA level, the band gap of (NH 3 ) 2 He is calculated to be 6.0 eV at 10 GPa, which increases to 7.5 eV at 180 GPa. For NH 3 He, the band gaps is calculated to be 7.2 eV at 35 GPa.
Superionic phases of (NH 3 ) 2 He. The stable pressure and temperature regions of Fmm2-(NH 3 ) 2 He cover the geotherms in the upper mantle of Neptune and Uranus. We, therefore, performed ab initio molecular dynamics simulations at the pressure of 100 GPa, 200 GPa, and 300 GPa, respectively, to examine the formation of    . This result reveals that at this conditions the superionic Fmm2-(NH 3 ) 2 He phase transformed into a fluid phase. Here, we found the diffusion of H atoms occurs prior to that of He atom, which is opposite to that found for He 2 (H 2 O) 39 , where He atoms diffuse firstly. Generally, lighter atoms are easier to diffuse. The abnormal diffusive behavior in He 2 (H 2 O) was explained by that the H atoms has higher diffusion barrier than He atoms because of the strong covalent H-O bonds 39 . In fact, He atoms in He 2 (H 2 O) share large space that allows the free diffusion, as shown in Supplementary Fig. 6. As compared to He 2 (H 2 O), although form weak interaction with N-H units, He atoms are trapped in cages formed by NH 3 , (NH 2 ) − and (NH 4 ) + units, this makes helium atoms are more difficult to diffuse.
While for P = 200 GPa and T = 300 K, Fmm2-(NH 3 ) 2 He keeps its solid property. With the temperature increasing to 1000 K and up to 4000 K, Fmm2-(NH 3 ) 2 He becomes to a superionic phase and then turns in to a fluid when the temperature is above 4200 K, as shown in Supplementary Fig. 7. Under pressure of 300 GPa, the trend is similar to that under 200 GPa, but the critical point of the superionic phase to fluid is at the temperature of 4600 K, as shown in Supplementary Fig. 8. Figure 5 presents the pressure-temperature (P-T) phase diagram for the mixture of NH 3 and He, showing the (NH 3 ) 2 He and NH 3 He phases. Temperature has a significant effect on the system: I4-(NH 3 ) 2 He and NH 3 He decompose at high temperature ( Fig. 5 and Supplementary Fig. 2). Their maximum temperatures of stability vary, being >700 K for I4-(NH 3 ) 2 He (which decomposes fully to NH 3 and He), >1000 K for NH 3 He (for full decomposition to NH 3 and He at P < 100 GPa and decomposition into Fmm2-(NH 3 ) 2 He and He at P > 100 GPa). In contrast, Fmm2-(NH 3 ) 2 He has a large stability field and thermodynamically stable in pressure range of 80-300 GPa and at any temperature in the tested range (0-5000 K). Figure 5 also presents estimated geotherms for the interiors of Uranus and Neptune. We also pointed the phase states of Fmm2-(NH 3 ) 2 He in the Fig. 5. Our calculation show that the Fmm2-(NH 3 ) 2 He phase presents superionic and fluid properties at the condition which is close to the geotherms in the upper mantle of Neptune and Uranus. This suggests that He could be trapped as superionic (NH 3 ) 2 He inside the upper mantles of these planets with the mixture of superionic and fluid forms during their formation.
Previous studies have assumed the presence of NH 3 , CH 4 , H 2 O, and H 2 inside the giant ice planets. Our predicted stability of superionic (NH 3 ) 2 He as well as the recent reported superionic H 2 OHe 2 39 under the P-T conditions corresponding to the ice giants' upper mantles indicate that helium could be remained inside the planets during their formation. Coincidently, the stability of NH 3 -He and H 2 O-He compounds provide an evidence to support the new three-layer model suggested by Nettelmann 11 , in which helium was considered as a small component in outer core of the planets. Therefore, the current results are essential to the understanding of the interior models of these planets. Moreover, CH 4 and H 2 are another two main components in upper mantle of these planets, therefore, there is a high possibility that helium could react with CH 4 or H 2 at high pressures to form new compounds, which deserves further investigation. The I4 structure of (NH 3 ) 2 He at 10 GPa along the a-axis and c-axis, respectively. c, d The Fmm2 structure of (NH 3 ) 2 He at 180 GPa in the direction of b-axis and a-axis, respectively. e The Pnma structure of NH 3 He at 30 GPa, and f the P2 1 2 1 2 1 structure of NH 3 He at 180 GPa. The light blue, pink, and cream-colored atoms represent N, H, and He, respectively. Blue, light blue, and purple spheres in c, d are used to distinguish the N atoms in ðNH 2 Þ À , NH 3 , and ðNH 4 Þ þ , respectively. Bader charges of the I4 phase of (NH3)2He at 10 GPa, the Fmm2 phase of (NH3)2He at 120 GPa, the Pnma phase of NH3He at 40 GPa, and the P212121 phase of NH3He at 180 GPa. A negative (positive) sign indicates an electron gain (loss) for the particular atom or molecule.
In our submission process, we were aware of the work by Liu et al. 46 predicting plastic and superionic helium-ammonia compounds at extreme condition. They predicted three stable stoichiometries and eight new stable phases of He-NH 3 compounds under pressures up to 500 GPa and found that the predicted He-NH 3 compounds exhibit superionic behavior at high pressure and high temperature. These similar results further provide knowledge for our understanding of the composition of the planet's interior.
In summary, a combination of first-principles calculations and crystal structure predictions was carried out to search for stable compounds in the NH 3 -He systems under high-P-T conditions. Calculations at 0 K revealed two compounds ((NH 3 ) 2 He and NH 3 He) that are energetically stable relative to the equivalent mixture of solid NH 3 and He at high pressures. Specially, (NH 3 ) 2 He remains energetically stable under the extreme conditions corresponding to the upper mantles of Uranus and Neptune. The current results provide evidence that He could be trapped inside these planets as NH 3 -He compounds with the mixture of superionic and fluid properties, in contrast to the current view that He occurs only in their atmospheres. Molecule dynamic simulations results show that the Fmm2-(NH 3 ) 2 He phase will transform into a superionic solid and then to a fluid with the increasing temperature.

Methods
Structural predictions. Structure predictions for NH 3 -He compounds were performed using a particle-swarm optimization algorithm implemented in CALYPSO code 47,48 . This method is unbiased, not using any known structural information, and has successfully been used to predict various systems under high pressure [49][50][51][52][53][54][55][56][57] . We performed structural searches on (NH 3 ) x He y (x, y = 1, 2, 3) at 0-300 GPa with maximum simulation cells up to four formula units. Each generation of structures was evolved by selecting the 60% lowest-enthalpy structures in the last step and randomly producing the remaining 40%. The structure searches were considered converged when~1000 successive structures were generated without finding a new lowest-enthalpy structure.
Ab initio calculations. Density functional theory calculations were performed using VASP code 58 combined with the generalized gradient approximation (GGA) 59 for the exchange-correlation potential in the form of the Perdew-Burke--Ernzerhof 60 (PBE) functional. The electronic wave functions were expanded in a plane wave basis set with a cutoff energy of 1000 eV. The electronic interaction was described by means of projector augmented wave 61 pseudopotentials with valence electrons of 1s 1 , 2s 2 2p 3 and 1s 2 for H, N, and He atoms, respectively. Monkhorst-Pack k-point 62 meshes with a grid density of 0.03 Å −1 were chosen to achieve a total energy convergence of better than 1 meV per atom. The phonon dispersion curves were computed by direct supercell calculation 63 , as implemented in the PHONOPY program 64 .
Molecular dynamics. The molecular dynamics simulations were also carried out to explore the superionic property of (NH 3 ) 2 He compound at high pressures and high temperatures. The simulation supercells contain 32 NH 3 molecules and 16 helium atoms and the Brillouin zone was sampled by Γ point. Each simulation consists of 10,000 time steps with a time step of 0.5 fs.

Data availability
The authors declare that the main data supporting the findings of this study are contained within the paper and its associated Supplementary Information. All other relevant data are available from the corresponding author upon reasonable request.