Novel lithium-nitrogen compounds at ambient and high pressures

Using ab initio evolutionary simulations, we predict the existence of five novel stable Li-N compounds at pressures from 0 to 100 GPa (Li13N, Li5N, Li3N2, LiN2, and LiN5). Structures of these compounds contain isolated N atoms, N2 dimers, polyacetylene-like N chains and N5 rings, respectively. The structure of Li13N consists of Li atoms and Li12N icosahedra (with N atom in the center of the Li12 icosahedron) – such icosahedra are not described by Wade-Jemmis electron counting rules and are unique. Electronic structure of Li-N compounds is found to dramatically depend on composition and pressure, making this system ideal for studying metal-insulator transitions. For example, the sequence of lowest-enthalpy structures of LiN3 shows peculiar electronic structure changes with increasing pressure: metal-insulator-metal-insulator. This work also resolves the previous controversies of theory and experiment on Li2N2.

Nitrogen can form many anionic species, e.g. [N 2 ] − , [N 2 ] 3− and [N 5 ] − , which have just been obtained in molecular complexes [16][17][18][19] . We wonder if solid-state compounds with these anions in Li-N system could be synthesized under high pressure. Evolutionary algorithm USPEX has been widely used to predict new ground state structures in various systems without any experimental information, such as B-H, Xe-O, and Na-Cl 20- 22 . The predicted counterintuitive compounds NaCl 3 and Na 3 Cl in the Na-Cl system have been confirmed by experiment 22 . In this work, we have performed extensive structure searches on the Li-N system using variable-composition evolutionary algorithm USPEX, and indeed found many new stable compounds with very diverse and unusual crystal structures.

Results and Discussion
We first studied the phase stability in the Li-N system by calculating the enthalpy of formation (Δ H) of Li-N compounds in the pressure range from 0 to 100 GPa. Stability of compounds is explored by the thermodynamic convex hull construction. If the enthalpy of decomposition of a compound into any other compounds is positive, then the compound is stable, which is depicted on the convex hull. The convex hulls are shown in Fig. 1 at selected pressures: 0, 20, 50, and 100 GPa. The various known phases of solid Li, N 2 , Li 3 N, LiN 3 , and Li 2 N 2 are reproduced readily in our evolutionary structure searches. Interestingly, five previously unreported compositions of Li-N system: Li 13 N, Li 5 N, Li 3 N 2 , LiN 2 , and LiN 5 are found to be on the convex hull under ambient or high pressure in our calculations. The calculated phonon spectra confirmed that all predicted structures are dynamically stable. In total, we have found three new N-rich compounds and two new Li-rich compounds.
Simultaneously with our work (in fact, with submission date after our paper appeared on arxiv.org) Peng et al. 23 investigated the Li-N system and found two new stable compounds, LiN 2 and LiN 5 . However, the phase diagram of the Li-N system published by Peng et al. 23 missed a number of stable compounds (Li 13 N, Li 5 N, Li 3 N 2 ). The enthalpies of reported phases in ref. 23 are recalculated and compared with our results. Detailed comparisons are shown in Figures S2 and S3 of the Supporting Information. Hence this paper presents a more complete and reliable picture, correcting omissions and presenting more stable crystal structures than those presented before.
We find that: (i) At ambient conditions (0 GPa), besides Li 3 N and Li 2 N 2 , LiN 2 with space group P6 3 /mmc is surprisingly stable. These three compositions are always stable in the pressure range from 0 to 100 GPa. (ii) However, the long-known LiN 3 is metastable below 49 GPa, which is in agreement with the known fact that it decomposes into N 2 and Li under external influences (heat, irradiation, etc) at 0 GPa. (iii) At 20 GPa, LiN 5 becomes stable, meanwhile Li 13 N, Li 3 N 2 and LiN 3 lie very close to (or nearly on) the convex hull. At 50 GPa, Li 13 N, Li 3 N 2 and LiN 3 are all stable, and Li 5 N lies very close to the convex hull. At 100 GPa, Li 5 N is stable, however, Li 13 N and Li 3 N 2 are becoming metastable although they both lie nearly on the convex hull.
The pressure-composition phase diagram of the Li-N system is depicted in Fig. 2. For pure Li, with increasing pressure, the bcc phase (Im3m) transforms into fcc (Fm3m), cI16 (I43d), Aba2-40, and Pbca phases in sequence, which is in accordance with previous experimental and theoretical data [24][25][26] . For pure N, the known Pa3, P2 1 /c, P4 1 2 1 2, and I2 1 3 structures are reproduced in our searches and agree well with other theoretical predictions 27,28 . For Li 3 N there is a peculiar situation: the experimentally known at ambient conditions P6/mmm structure is predicted to be stable only at pressures above 0.2 GPa -at lower pressures, at the GGA level of theory, the Pm3m structure is more stable (at 0 GPa, by 22 meV/formula unit). This small upward shift of phase transition pressures is typical of the GGA, but one wonders whether Pm3m structure could be stabilized by impurities, temperature etc. The subsequent phases of Li 3 N in our calculations are all in agreement with the previous works 5- 7 .
LiN 3 is a thermodynamically stable compound (on the convex hull) only above 49 GPa, but it is well known also at ambient conditions as a metastable material. We found P62m to have the lowest enthalpy in the pressure range 0-0.9 GPa, followed by C2/m and P6/m phases on increasing pressure. C2/m is the phase known experimentally at ambient conditions.
For LiN (actually Li 2 N 2 ), the obtained structure at 0 GPa is Pmmm, which is consistent with the previous theoretical result 14 . At 8.2 GPa, Pmmm phase of LiN transforms into the Immm structure, indicating that the experimental result obtained at around 9 GPa is also perfectly correct 15 . At 8.9 GPa, the Immm structure will lose its stability and the Pnma phase becomes stable in the pressure range from 8.9 to 66.4 GPa. Then the Cmcm phase is stable up to 100 GPa.
Phase transformations of five new compositions of Li-N system are as follows: (i) For Li 13 N, the Immm structure is predicted to be stable from 43 to 76 GPa, following which the C2/m structure is stable up to 83 GPa. In fact, Immm and C2/m phases have nearly identical enthalpies (within 0.2 meV/atom), suggesting that Li 13 N can exist as a mixture of Immm and C2/m phases in the whole range of stability of this compound. (ii) Li 5 N has a single stable phase P6/mmm from 80 to at least 100 GPa. (iii) From 30 to 89 GPa, Li 3 N 2 has two stable phases P4/mbm and C2/c. The pressure-induced structural transition from P4/mbm to C2/c occurs at about 39 GPa. (iv) Besides the P6 3 /mmc structure, LiN 2 has another phase P1, stable above 56 GPa, (v) For LiN 5 , the P2 1 /c structure becomes stable at 15 GPa and then transforms into the C2/c phase at the pressure of 65 GPa. The C2/c structure is stable at least up to 100 GPa.
The representative structures of above-mentioned Li-N compounds under ambient conditions and high pressure are presented in Fig. 3. We first analyze the structures of Li 3 N and LiN 3 , and remind that the lengths of nitrogen-nitrogen bonds are 1.10 Å for the triple N-N bond, 1.25 Å for the double N = N bond, and 1.45 Å for the single N-N bond. (i) For Li 3 N, the calculated lattice parameters of P6/mmm, P6 3 /mmc and Fm3m are in agreement with experimental data within 0.5%. The Pm3m structure is very simple, an anti-ReO 3 -type structure made of corner-sharing NLi 6 octahedra (Fig. 3a). Interestingly, across the phase transitions, the number of Li atoms surrounding each N atom increases from 6 for Pm3m to 8 for P6/mmm, 11 for P6 3 /mmc and 14 for Fm3m. (ii) for LiN 3 at ambient conditions, C2/m structure consists of Li + cations and linear azide anions [N 3 ] − 10 . As illustrated in Fig. 3b, unlike the C2/m structure, P62m phase does have [N 3 ] − anions, but instead its unit cell contains two Li atoms and three N 2 groups with the N-N distance of 1.151 Å at 0 GPa, smaller than that in the azide-ion [N 3 ] − (1.184 Å), but larger than that in the gas-phase N 2 molecule (1.10 Å) and indicating a bond order between 2 and 3.
The Pmmm structure of Li 2 N 2 consists of face-sharing Li 8 parallelepipeds (Fig. 3c). The N 2 groups sit in the center of parallelepipeds, which can be viewed that there are six Li atoms connecting to each N atom of N 2 molecule and each of four Li atoms connects to both N atoms. The N-N bond length is 1.263 Å at 0 GPa, slightly larger than that of Na 2 N 2 (1.24 Å) 14 and indicating a double N = N bond and ideal charge of the N 2 group equal to − 2, which matches perfectly the formula Li 2 N 2 . Our calculated lattice constants of Immm structure (Fig. 3d) are in good agreement with experimental results 15 . The predicted N-N bond length is 1.271 Å, slightly smaller than the experiment. Figure 3e presents the Pnma structure of Li 2 N 2 at 10 GPa. Its unit cell contains four N 2 2− groups and eight Li + ions. The N-N bond length is 1.269 Å. The P6/mmm phase of Li 5 N has a layered structure, made of alternating layers of stoichiometry Li 4 N (here, N atoms are sandwiched between two Li-graphene sheets) and Li, see Fig. 3g. Such unusual layered structures with alternation of "metallic" and "non-metallic" layers have been previously reported by some of us for the Na-Cl system (e.g., Na 3 Cl, also confirmed experimentally 22 ) and for the K-Cl system 30 . Bader analysis shows that Li 5 N at 90 GPa has charge configuration [Li 4 N] -0.68 Li +0.68 , indicating that most of the valence electrons of Li layer transfer to the Li 4 N sandwich layer 31 . Interestingly, the Bader charge of Li atom in upper Li-graphene sheet of Li 4 N sandwich layer is nearly neutral (+ 0.1 e) and the charge of Li atom in bottom Li-graphene sheet is + 0.74 e.
As observed in Fig. 3h1, the P4/mbm structure of Li 3 N 2 consists of a three-dimensional network of Li atoms, which has open channels along z direction. This structure is very similar to the structure of the new compound Mg 3 O 2 predicted by some of us recently 32 , except that in Li 3 N 2 there is pairing of N atoms with the N-N distance of 1.353 Å at 30 GPa, indicating bond order between 1 and 2. Just like in P4/mbm-Mg 3 O 2 , we can clearly see columns of face-sharing body-centered cubes of metal atoms. The electron localization function (ELF) of Li 3 N 2 (Fig. 3h2) shows strong charge transfer from Li to N. However, unlike Mg 3 O 2 which is an electride, there is no strong interstitial electron location in Li 3 N 2 . Bader analysis also confirms the above result. The charges of P4/mbm-Li 3 N 2 are + 0.794 e for one Li atom, + 0.809 e for the other two Li atoms, and − 1.146e and − 1.266 e for two N atoms, respectively. The C2/c structure has a more complex three-dimensional network of lithium atoms with N 2 groups also sitting in its channels (Fig. 3i), with the N-N distance of 1.391 Å at 40 GPa.
The P6 3 /mmc structure of LiN 2 can be described as a NiAs-type structure, where anionic positions are occupied by the N 2 groups (Fig. 3j). At zero pressure, the N-N distance is 1.173 Å, indicating a bond order between 2 and 3. The P1 phase contains an infinite polyacetylene-like nitrogen chain (Fig. 3k), similar to the metastable phase of LiN 3 10 . The N-N distances are 1.316, 1.320 and 1.333 Å at 60 GPa, suggesting bond order between 1 and 2. We can clearly see how pressure destroys molecular groups, favoring extended structures.
As observed in Fig. 3l, the P2 1 /c structure of LiN 5 consists of isolated Li atoms and N 5 rings, which up to now were only detected in molecular complexes 19 . At 50 GPa, the N-N distances are 1.286, 1.291, 1.299, 1.303 and 1.305 Å, respectively. The higher-pressure C2/c phase also consists of isolated Li atoms and N 5 rings (Fig. 3m). Unlike in P2 1 /c, the N 5 ring here is a nearly isosceles pentagon, with N-N distances of 1.277, 1.277, 1.301, 1.301, and 1.281 Å, respectively, at 80 GPa.
To obtain deeper insight into these new Li-N compounds, we calculated their band structures and density of states (DOS) at selected pressures. We found that all stable phases of Li 13 N, Li 5 N and Li 3 N 2 are metallic. The Pm3m phase of Li 3 N is a semiconductor with the DFT band gap of 0.84 eV. All three stable phases of Li 2 N 2 are also metallic, in agreement with experiment 15 . Interestingly, LiN 2 has a metal-insulator transition: P6 3 /mmc is metallic at low pressure, but semiconducting in the high-pressure P1 phase, with the band gap of 0.13 eV at 60 GPa. Since the newly predicted P62m phase of LiN 3 is also metallic, combining with previously known phases of LiN 3 , we find that the sequence of transitions of LiN 3 under pressure is extremely unusual: from metallic to insulating to metallic to insulating. The P2 1 /c and C2/c phases of LiN 5 are wide-gap insulators: e.g., the DFT band gap of the C2/c phase at 80 GPa is 2.19 eV.
Some electronic structures are shown in Fig. 4. As is seen from Fig. 4(a-c), the PDOSs of two different phases of Li 3 N (or Li 2 N 2 or LiN 3 ) at 0 GPa are obviously different. The newly found phases Pm3m -Li 3 N, Pmmm-Li 2 N 2 and P62m-LiN 3 have one character in common: the states near the Fermi level come mostly from Li-s and N-p orbitals. Figure 4(d-e) show the band structures of P1-LiN 2 and P6 3 /mmc-LiN 2 at different pressures, respectively. The band structures at different pressures for the same phase are similar. When pressure increases, the band structure is more dispersive and the bandwidths also increase: both the conduction and valence bands broaden, and conduction band tends to shift upwards in energy. These changes can lead to both metallization and demetallization: for example, P1-LiN 2 is metallic at 0 GPa, whereas it becomes semiconductor with the gap of 0.13 eV at 60 GPa.

Conclusions
A number of new Li-N compounds have been predicted using ab initio evolutionary structure search. Other than the well-known compositions Li 3 N, Li 2 N 2 and LiN 3 , we found five novel compositions which should be experimentally synthesizable under pressure, including Li 13 N, Li 5 N, Li 3 N 2 , LiN 2 , and LiN 5 . Notably, the N-N bonding patterns evolve from isolated N ions to N 2 dumbbells, to linear N 3 groups, infinite nitrogen chains, N 5 rings with increasing N content. Interestingly, for the experimentally known compounds Li 3 N and LiN 3 at ambient conditions we find new lowest-energy structures (Pm3m and P62m, respectively): these are stable (at the GGA level of theory) in very narrow pressure ranges near 0 GPa. While this is most likely an artefact of the GGA (known to slightly overstabilize open structures and shift phase transition pressures upwards), these phases may be stabilized by doping, temperature, etc. We also resolve previous discrepancy on stable phases of Li 2 N 2 . In conclusion, this paper presents a more complete and reliable picture, correcting omissions and presenting more stable crystal structures than those presented before. Our work provides the basis for the future experimental investigations of the Li-N system.

Methods
To search for stable compounds, the Li-N system was first explored using the variable-composition evolutionary technique, as implemented in the USPEX code [33][34][35] . Evolutionary crystal structure predictions were performed in the pressure range from 0 to 100 GPa. Initial structures included up to 16 atoms in the unit cell. The first generation of structures was produced randomly. The child structures were obtained applying heredity, transmutation, softmutation, and random symmetric generator, with probabilities of 40, 20, 20 and 20%, respectively. Then we performed detailed fixed-composition evolutionary calculations to explore the most promising compositions.
All structure relaxations and electronic structure calculations were done using the Vienna Ab Initio Simulation Package (VASP) in the framework of density functional theory 36 . The Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) was employed to treat the exchange-correlation energy 37 , and the all-electron projector augmented wave (PAW) potentials were used to describe the core-valence interactions 38 . The cut-off energy of 650 eV and Monkhorst-Pack k-point meshes for sampling the Brillouin zone with resolution 2π × 0.04 Å −1 ensured that all the enthalpy calculations were well converged to better than 1 meV/atom. To ensure that the structures of predicted compounds in Li-N system are dynamically stable, phonon calculations were carried out using the Phonopy code 39 . Our tests showed that the effect of van der Waals interactions 40,41 on stability of lithium nitrides is negligible, which is consistent with other works 23 .