Diverse Chemistry of Stable Hydronitrogens, and Implications for Planetary and Materials Sciences

Nitrogen hydrides, e.g., ammonia (NH3), hydrazine (N2H4) and hydrazoic acid (HN3), are compounds of great fundamental and applied importance. Their high-pressure behavior is important because of their abundance in giant planets and because of the hopes of discovering high-energy-density materials. Here, we have performed a systematic investigation on the structural stability of N-H system in a pressure range up to 800 GPa through evolutionary structure prediction. Surprisingly, we found that high pressure stabilizes a series of previously unreported compounds with peculiar structural and electronic properties, such as the N4H, N3H, N2H and NH phases composed of nitrogen backbones, the N9H4 phase containing two-dimensional metallic nitrogen planes and novel N8H, NH2, N3H7, NH4 and NH5 molecular phases. Another surprise is that NH3 becomes thermodynamically unstable above ~460 GPa. We found that high-pressure chemistry of hydronitrogens is much more diverse than hydrocarbon chemistry at normal conditions, leading to expectations that N-H-O and N-H-O-S systems under pressure are likely to possess richer chemistry than the known organic chemistry. This, in turn, opens a possibility of nitrogen-based life at high pressure. The predicted phase diagram of the N-H system also provides a reference for synthesis of high-energy-density materials.

a complete phase diagram for the N-H system is necessary for developing synthetic strategies, but such a phase diagram has not been determined. As a result, the high-pressure behavior, structures and stability of N-H phases are of great interest to both planetary and condensed-matter physics.
Extensive theoretical [15][16][17][18] and experimental 19 studies revealed exotic compounds appearing under compression, and exhibiting unique structures and properties different from usual compounds -see previous investigations of Na-Cl 19 [20][21][22] and the autoionization 7 found in NH 3 , new hydronitrogen compounds are expected to be found.

Results
Stoichiometries and structures. Using the evolutionary algorithm USPEX [23][24][25][26] , we have carried out structure and stoichiometry predictions in order to find all stable compounds (and their stability fields) in the N-H system (See Methods). Our calculations confirm that ammonia is the only stable hydronitrogen from ambient pressure to 36 GPa. Above 36 GPa, remarkably, a series of previously unknown compounds become stable, as shown in the pressure-composition phase diagram of the N-H system in Fig. 1. The detailed convex hulls at 60, 100, 200, 500, and 800 GPa are presented in Fig. 2. It needs to be emphasized that by calculating phonon dispersions, all the newly found compounds in this work are found to be dynamically stable in their corresponding stability field on the phase diagram (Fig. 1). Since zero-point energy can be a factor to affect the relative stability of structures, we have done zero-point energy calculations for N 2 H, NH, N 3 H 7 , NH 4 and NH 7 , and found out that the phase diagram shown in Fig. 1 does not change significantly. Therefore, in this work, the phase diagram of N-H is drawn without considering zero-point energy. We would like to leave more accurate phase diagram investigation of N-H at finite temperatures and with considering zero-point energy for further work.
We can classify these thermodynamically stable hydronitrogens compounds that we found into three types (See Table 1). (i) Infinite-chain polymeric hydronitrogens, including N 4 H, N 3 H, N 2 H and NH, with polymeric  chains featuring all-nitrogen backbones. (ii) Two-dimensional (2D) metallic N 9 H 4 phase consisting of 2D nitrogen planes and NH + 4 cations, interestingly, the 2D-nitrogen planes have not been reported in any other nitrogenous compounds before. (iii) Molecular compounds including N 8 H, NH 2 ,N 3 H 7 , NH 4 , NH 5 , and of course NH 3 . Here, molecular (or molecular ionic) compounds are bonded by hydrogen bonds.
One-dimensional polymeric hydronitrogens. We have found that, except N 9 H 4 and N 8 H, nitrogen-rich hydronitrogens (N x H, x ≥ 1) are more prone to adopt polymeric structures with N-backbones, The N 4 H, N 3 H and N 2 H compounds are predicted to be stable at 51-80 GPa, 42-75 GPa and 60-260 GPa, respectively. The ground state of N 4 H has a Cmc2 1 structure, containing four zigzag nitrogen chains (N-chains) in the unit cell, with pairs of nearest N-chains linked by hydrogen bonds, see Fig. 3 in the unit cell, see Fig. 3(c). At 200 GPa, the lengths of single N-N bonds in this polymer are 1.27 and 1.28 Å, and the double N= N bond is slightly shorter (1.24 Å). The smallness of the difference hints at a possible bond resonance along the chain. The doubly-bonded nitrogen atoms form weak asymmetric hydrogen bonds with nearby chains. Before the symmetrization of hydrogen bonds occurring at ∼ 280 GPa, P2 1 /c -N 2 H undergoes a spontaneous decomposition at ∼ 260 GPa. All these polymeric structures are metallic as a result of bond resonance and electronic delocalization along the nitrogen backbone.
With the equal ratio of nitrogen and hydrogen, the NH compound is predicted to be stable in a huge pressure range, from 36 GPa to at least 800 GPa. The P2 1 /c structure is more stable than the one predicted in the work of Hu & Zhang 27 . This phase consists of two tetrazene N 4 H 4 molecules in the unit cell. At 55 GPa, P2 1 /c -NH undergoes a phase transition to an ionic structure with P1 symmetry. As shown in Fig. 3 Fig. 3(e). Similar square chains have been reported in group VI elements under pressure, e.g. sulfur-II phase 28 and the I4 1 /amd phase of oxygen at pressure around 2 TPa 29 . The Fdd2-NH is predicted to be a wide-gap semiconductor (4.8 eV at 400 GPa). In contrast to the strongly localized electrons found in the I4 1 /amd-oxygen structure with isolated chains, Fdd2-NH has asymmetric hydrogen bonds between the square chains. Fdd2 transforms to an Fddd structure upon hydrogen bond symmetrization at 460 GPa. For 2D-polymeric hydronitrogen. Distinct from the polymeric chain structures, we also discovered an exotic stable nitrogen-rich compound N 9 H 4 . Its structure has Ccc2 symmetry, and is composed of negatively-charged 2D nitrogen planes and NH 4 + cations. Ccc2-N 9 H 4 was predicted to be thermodynamically stable in a narrow pressure range 50-60 GPa. As shown in Fig. 3(f), the 2D nitrogen plane is a loose structure due to the hexagonal star-shaped holes decorated by 18 additional nitrogen atoms. Parallel stacking of the nitrogen planes creates infinite channels in the perpendicular direction, and NH 4 + cations are located along these channels. The electrons in the plane are delocalized, as a result this compound is metallic with a flat band crossing the Fermi level. (See more details about properties of N 9 H 4 in Supplementary Information). Molecular hydronitrogens. N 8 H is found to be stable around 50 GPa, and adopts a very unusual molecular structure with four pentazole (N 5 H) and six nitrogen (N 2 ) molecules in the unit cell. (See more details about N 8 H structure in Supplementary Information).
Hydrogen-rich hydronitrogens, instead of polymeric structures, have hydrogen-bonded molecular structures. The NH 4 phases, containing a higher hydrogen ratio than NH 3 , are found to be thermodynamically stable above ∼ 50 GPa, and remain stable at least up to 800 GPa. At pressures above 50 GPa, NH 4 first adopts a host-guest structure of Pc symmetry with the structural formula (NH 3 ) 2 ·H 2 . Other host-guest structures, adopting P2 1 , C2/c and I4/m symmetries, have very close enthalpies to this structure below 80 GPa (See more details about these NH 4 structures in Supplementary Information). Accurate fixed-composition crystal structure predictions for NH 4 show that above 52 GPa, C2/c structure is located in the global minimum of the energy landscape for NH 4 , and other structures with close enthalpies are structurally similar to the C2/c structure. In all host-guest structures, H 2 molecules are captured in hydrogen-bonded frameworks formed by NH 3 molecules. In the pressure range 85-142 GPa, the ionic P1-NH 4 phase is more stable than host-guest molecular structures. In the unit cell of this low-symmetry ionic phase, as shown in Fig. 4(a), every eighths ammonia molecule reacts with an H 2 molecule to form the NH 4 + cation and H − anion. The distance of H − anion and the nearest hydrogen of the NH + 4 cation is 1.13 Å at 100 GPa. Above 142 GPa, the ionic phase undergoes a reentrant transition to the same C2/c host-guest structure again, thus returning to structures consisting of neutral NH 3 and H 2 molecules. Hydrogen-bond symmetrization was not observed in all stable NH 4 phases up to 800 GPa. With the 1:1 ratio of H 2 and NH 3 , several NH 5 phases are also found to be thermodynamically stable or nearly stable around 55-100 GPa. The ionic C2/c phase (See Fig. 4(b)) has the lowest enthalpy at pressures below 162 GPa. In the unit cell of C2/c-NH 5 , there are two [H 3 N···H···NH 3 ] + units and two H − anions. At pressure above ~162 GPa, C2/c-NH 5 phase transforms into metastable ionic P2 and Ama2 structures, then adopts a P2 1 /c structure containing alternating layers of NH 3 and H 2 molecules above ∼ 363 GPa. (See more details about NH 5 high pressure phases in Supplementary Information).
At about 140 GPa, a previously unreported remarkable compound with the composition N 3 H 7 is also found to be thermodynamically stable. For N 3 H 7 , we have predicted several thermodynamically stable phases with the structural sequence P1 → C2 → P-3m1 → P2 1 /m-I → P2 1 /m-II upon increasing pressure (See Fig. 4(c) for the first three structures). At 140-200 GPa, P1-N 3 H 7 adopts a stable molecular structure, consisting of one ammonia (NH 3 ) and one hydrazine (N 2 H 4 ) molecules in the unit cell. At 200 GPa, P1 undergoes a spontaneous molecular-to-ionic transition, resulting in a layered C2 structure. In this process, ammonia and hydrazine molecules react to form the NH 2 − (amide) anions and N 2 H + (hydrazinium) cations, respectively. The N 2 H + ions are in a parallel arrangement and connected by symmetric H-bonds. At 300-380 GPa, complicated ionic N 3 H 7 structure of P-3m1 symmetry becomes stable. As shown in Fig. 4 With pressure increasing, our calculation confirmed that NH 3 , above 36 GPa, undergoes phase transformations from hydrogen-bonded molecular P2 1 2 1 2 1 structure to layered ionic Pma2 and Pca2 1 phases, and then returns to Pnma structures consisting of neutral NH 3 molecules at very high pressure 7,9 . However, NH 3 , the only thermodynamically stable hydronitrogen compound at ambient conditions, is surprisingly predicted to decompose into N 3 H 7 and NH 4 at ~460 GPa at zero temperature. For NH 2 , the dense molecular hydrazine phase was also predicted to be stable and have a C2/c symmetry at ~200-780 GPa, which is consistent with Zhang's work 30 . The C2/c structure of NH 2 consists of hydrazine molecules, forming both symmetric and asymmetric hydrogen bonds with each other.

Discussion
Our theoretical calculations indicate that the N-H system exhibits rich chemistry under pressure. The infinite long-chain polymeric structures are widely found in nitrogen-rich hydronitrogen compounds, and are thermodynamically stable above 42 GPa. They could potentially serve as good high-energy-density and fuel materials due to the substantial energy difference between the single/double and triple nitrogen-nitrogen bonds. The nitrogen backbone evolves with increasing hydrogen concentration. With the "antiseeds" technique (See Methods), we found that metastable nitrogen phases containing zigzag N-chains have competitive enthalpies (~0.03 eV/atom higher at 60 GPa) to the molecular states and the singly bonded cg-N 31 structure at 40-70 GPa, and they are more energetically favorable than arm-chair-shaped and other N-chains (See Fig. S5 in Supplementary Information). A low hydrogen content stabilizes these chains and does not change much of the packing pattern of the chains and the electronic properties of the resonant N-N bonds. The lowest-enthalpy structures of metastable N 9 H and stable N 8 H phases contain infinite zigzag N-backbones. (See more details about these two compounds in Supplementary Information) With higher hydrogen content, the zigzag N-backbone become unstable in N 3 H, N 2 H and NH phases.
These long-chain polymeric hydronitrogen compounds would be an interesting alternative to commonly used high-energy-density materials. Compared to pure polymeric nitrogen (cg-N phase), layered P2 1 /c N 3 H is stable at pressures above ~42 GPa, i.e. at pressures lower than the stability pressure of cg-N (> 56 GPa). Hydrazoic acid 32 (N 3 H) may be an even better precursor for synthesizing long-chain polymers. With hydrazoic acid, the layered P2 1 /c N 3 H can be formed at as low as 6.0 GPa (See Table 2). The VC-NEB 33 calculation indicates that the phase transformation from hydrazoic acid to P2 1 /c N 3 H has an energy barrier of ~0.25 eV/atom at 10 GPa, (See   Table 2). Isoelectronic to oxygen, (NH) units generally serve as analogs of group VI elements in these polymeric chain structures. Besides the square-spiral chain in high-pressure phases found in NH, the monoclinic N 2 H phase can be considered as an analogue material of sulfur nitride (SN) n 34 or (ON) n 35,36 polymers. The proposed nitrogen oxides (ONNO) n chain oligomer also has comparatively strong N= N bonds. The monoclinic N 2 H phase is a metallic polymer as the Fermi level is crossed by anti-bonding π* bands (See Fig. S4 in Supplementary  Information), which is similar to the first known metallic polymer (SN) n 37 as a superconductor with T c = 0.26 K 38 . All our 1D long-chain hydronitrogen compounds containing delocalized nitrogen bonds are metallic. Our calculations reveal that N 4 H (at 55 GPa) and N 2 H (at 60 GPa) are superconductors with T c = 2.6 and 7.8 K (with the value of μ* = 0.13), respectively. In contrast, N 9 H 4 phase is not a superconductor.
Multiple stable stoichiometries exist in hydrogen-rich hydronitrogens at pressure. These hydronitrogens form molecular crystals at low pressure, and then tend to undergo auto-ionization under moderate compression, except NH 2 (See Table 1). The structures of these compounds show various characteristics and are quite different from each other. N 3 H 7 , NH 4 (and NH 5 ) can be considered as binary NH 3 + N 2 H 4 and NH 3 + xH 2 compounds, respectively. Therefore, in general, high-pressure hydrogen-rich hydronitrogens tend to contain molecules and molecular ions. It is predicted that hydrogen-rich hydronitrogens remains stable to extremely high pressures, NH 3 and NH 2 become unstable and decompose (into NH 4 and N 3 H 7 , or into NH and N 3 H 7 ) only at 480 and 780 GPa, respectively; and NH 4 and N 3 H 7 are thermodynamically stable at least up to 800 GPa. In contrast, methane (CH 4 ) was predicted to dissociate into ethane (C 2 H 6 ), butane (C 4 H 10 ), and finally, diamond plus hydrogen at 287 GPa 2 . NH 4 and NH 5 undergo a molecular⇒ ionic⇒ molecular phase sequence under pressure, which is very similar to NH 3 7 . The auto-ionization process also occurs in N 3 H 7 , which remains in the ionic phase at least up to 800 GPa. In contrast, C-H compounds have non-polar non-ionic structures, and the high energy cost of proton transfer in H 2 O 7,39 prevents auto-ionization until extremely high pressure (~1.4 TPa) 39 . Our calculation revealed that the energy cost of proton transfer from H 2 to NH 3 molecule and from NH 3 to N 2 H 4 molecule is ~0.7 eV and ~1.0 eV, respectively, while it costs ~0.9 eV 40 to form NH − 2 and NH + 4 ions in NH 3 . Therefore, NH 3 + xH 2 compounds would undergo auto-ionization at a lower pressure (NH 4 at ~85 GPa and NH 5 at ~42z GPa) than pure NH 3 (at ~90 GPa). Due to high cost of proton transfer, auto-ionization phenomenon was not observed in any stable H 2 O-H 2 compounds 1 . Calculations show that auto-ionization happens at ~200 GPa in N 3 H 7 , higher in NH 3 (90 GPa) 7 , due to the higher proton transfer energy cost, and survives up to at least 800 GPa. The pV term in the free energy plays an important role in deterring the phase transition sequence at high pressure. Under pressure, stable N 3 H 7 and NH 3 -xH 2 host-guest phases are more packing-efficient than the volume of NH 3 + N 2 H 4 and NH 3 + H 2 mixtures, respectively. The auto-ionization transition in N 3 H 7 leads to denser structures and enhances stability of N 3 H 7 under compression.

Conclusions
We have extensively explored the nature of hydronitrogen compounds up to ultrahigh pressures. It turns out that unusual compounds, such as N 8 H, N 4 H, N 3 H, N 9 H 4 ,N 2 H, NH, NH 2 ,N 3 H 7 , NH 4 and NH 5 are stable under pressure. These compounds possess intriguing crystal structures and remarkably novel, exotic properties. Three main features can be concluded, 1) the (NH) unit behaves similarly to its isoelectronic analogs, oxygen (also the sulfur) atoms, 2) molecular hydronitrogens are mainly composed of H 2 , NH 3 ,N 2 H 4 molecules and corresponding ions, 3) auto-ionization is common in N-H molecular phases due to the low energy cost of the proton transfer between the H 2 , NH 3 ,N 2 H 4 molecules.
Our investigation opens ways for designing synthesis of novel high-energy-density polymeric hydronitrogens. It is clear that starting with metastable precursors (such as N 2 H 4 , N 3 H) should lower polymerization pressure (compared to the lowest pressure of thermal dynamic polymeration, 42 GPa). We experimented with different mixtures of N 2 H 4 , N 3 H and N 2 give bulk N 3 H or NH compositions. We found that using N 2 in the precursor mixture does not give good results. Instead, pure N 2 H 4 and N 3 H, or their mixtures can polymerize already at near-ambient conditions. For planetary interiors (where H/N > 1), we expect the presence of N-contianing molecular ions at all pressures above ~55 GPa in NH 5 . This means a much thicker layer with ionic conductivity than previously thought, which will affect models of planetary magnetic fields (which are generated by convection of electrically conducting layers). High-pressure chemistry of hydronitrogens uncovered here has greater diversity than hydrocarbons.
We remind that at normal conditions, the only thermodynamically stable compound of carbon and hydrogen is methane (CH 4 ), all the other hydrocarbons being metastable and kinetically protected by high energy barriers. Here we have uncovered unique structural diversity among THERMODYNAMICALLY STABLE hydronitrogens. N-H bonds are directional covalent bonds (just like C-H), which should also lead to high energy barriers and ubiquitous metastability. If one includes metastable hydronitrogens, and adds other elements (such as O, S, smaller amounts of C), the diversity will most likely exceed the diversity of organic chemistry. This invites the question whether nitrogen-based (rather than carbon-based) life is possible in the interiors of gas giant planets. Briefly, we see the following conditions as necessary for emergence of life: (1) great structural and chemical diversity based on a small number of chemical elements (C-H-O or N-H-O), (2) abundance of metastable compounds with long lifetimes, (3) chemical reactions for energy production, (4) reversible reaction for storing/ releasing energy (similar to the function of ATP in carbon-based life), (5) a molecule that can be used as information matrix (analogous in its function to DNA). For nitrogen-rich compounds, condition (1) is clearly satisfied. Condition (2) is also likely satisfied at not very high temperatures. Energy source and storage can be related to metastable compounds -e.g. oxidation of hydronitrogens for energy production, and polymerization/depolymerization of hydronitrogens for energy storage. As for condition (5), it is too early to say which N-based molecules could be suitable -the main conditions seem to be 1D-or 2D polymeric nature and aperiodicity. Nitrogen-based life could be possible, but the likelihood of this is highly limited due to high temperatures in these planets' interiors, which could make lifetimes of metastable compounds too short. Given the abundance of N, H, O, C in giant planets, and high pressures in their interiors, we expect great diversity of molecular species there.

Methods
Crystal structure prediction. Crystal structure prediction was performed using the variable-composition evolutionary algorithm USPEX 15,[23][24][25][26] . A number of studies illustrate the power of the USPEX method 16,17,19 . Calculations for the N-H system were performed at various pressures in the wide range of 0-800 GPa.
Given the dramatically changed behavior of nitrogen under pressure and a wide pressure range of our investigation, we performed a number of different types of predictions with USPEX. We ran variable-composition predictions for N-H, N-NH and NH-H systems with up to 32 atoms per unit cell. Given molecular nature of all stable and nearly stable compounds in hydrogen-rich hydronitrogens, we also did structure prediction for the packing of well-defined NH 3 and H 2 molecules (rather than N and H atoms), by applying the specially designed constrained global optimization algorithm 26 , considering structures with up to 24 molecules (i.e. up to 96 atoms) per primitive unit cell. These calculations were run together in a global coevolutionary search with exchanging good (stable and some metastable) structures between different runs. This coevolutionary method is very efficient Scientific RepoRts | 6:25947 | DOI: 10.1038/srep25947 and has been implemented on top of the USPEX code. When performing prediction for metastable nitrogen structures containing zigzag N-chains, we applied the antiseeds technique 41 , which was adopted to search for all low-enthalpy structures based on zigzag N-chains.
DFT calculations. The underlying ab initio structural relaxations and electronic structure calculations in UPSEX were carried out using the all electron projector augmented wave (PAW) 42 method as implemented in the VASP code 43 . The plane-wave cutoff energy of 800 eV and dense Gamma-centered k-point meshes with a resolution better than 2π × 0.05 Åwere adopted, and ensured high-quality results. After identifing the most stable compositions and several candidate structures, we relaxed them at numerous pressures in the range of 0-800 GPa with harder PAW potentials, in which the core radius equals 0.42 and 0.58 Å for hydrogen and nitrogen, respectively. An extremely high cutoff energy of 1400 eV was used for these relaxations and calculations of enthalpies of reactions and phase diagram. In addition, phonon dispersions throughout the Brillouin zone were derived using the finite-displacement approach as implemented in the Phonopy code 44 . Superconducting T c was calculated in QUANTUM ESPRESSO 45 , with ultrasoft potentials 46 using 40 Ry plane-wave cutoff energy.