We have performed first-principles evolutionary searches for stable Ti-N compounds and have found, in addition to the well-known rock-salt TiN, new ground states Ti3N2, Ti4N3, Ti6N5 at atmospheric pressure, and Ti2N and TiN2 at higher pressures. The latter nitrogen-rich structure contains encapsulated N2 dumbbells with a N-N distance of 1.348 Å at 60 GPa. TiN2 is predicted to be mechanically stable and quenchable. Our calculations on the mechanical properties (bulk modulus, shear modulus, Young's modulus, Poisson's ratio, and hardness) are in excellent agreement with the available experimental data. Further analyses of the electronic density of states, crystal orbital Hamilton population and the electron localization function reveal that the hardness is enhanced by strengthening directional covalent bonds and disappearance of Ti-Ti metallic bonding.

Stable structures and stoichiometries of binary Mg−N compounds are explored at pressures from ambient up to 300 GPa using ab initio evolutionary simulations. In addition to Mg 3 N 2 , we identified five nitrogen-rich compositions (MgN 4 , MgN 3 , MgN 2 , Mg 2 N 3 , and Mg 5 N 7 ) and three magnesium-rich ones (Mg 5 N 3 , Mg 4 N 3 and Mg 5 N 4 ), which have stability fields on the phase diagram. These compounds have peculiar structural features, such as N 2 dumbbells, bent N 3 units, planar SO 3 -like N(N) 3 units, N 6 six-membered rings, 1D polythiazyl S 2 N 2 -like nitrogen chains, and 2D polymeric nitrogen nets. The dimensionality of the nitrogen network decreases as magnesium content increases; magnesium atoms act as a scissor by transferring valence electrons to the antibonding states of nitrogen sublattice. In this context, pressure acts as a bonding glue in the nitrogen sublattice, enabling the emergence of polynitrogen molecule-like species and nets. In general, Zintl−Klemm concept and molecular orbital analysis proved useful for rationalizing the structural, bonding and electronic properties encountered in the covalent nitrogen-based units. Interestingly, covalent six-membered N 6 4− rings containing P−1 (I) MgN 3 phase is recoverable at atmospheric pressure. Moreover, ab initio molecular dynamics analysis reveals the polymeric covalent nitrogen network, poly-N 4 2− , encountered in the high-pressure Cmmm MgN 4 phase can be preserved at ambient conditions. Thus, quenchable MgN 4 , stable at pressures above 13 GPa, shows that high energy-density materials based on polymeric nitrogen can be achievable at reduced pressures. The highpressure phase P−1 (I) MgN 3 with covalent N 6 rings is the most promising HEDM candidate with an energy density of 2.87 kJ• g −1 , followed by P−1 MgN 4 (2.08 kJ•g −1 ).

Molybdenum dinitride (MoN 2 ) was recently synthesized at a moderate pressure of 3.5 GPa, and a layered MoS 2 -type structure has been proposed. However, our firstprinciples calculations of thermodynamic, mechanical and dynamical properties suggest that this layered R3m structure is unstable. Therefore, stable structures of MoN 2 at pressures from atmospheric pressure to 100 GPa have been further examined by utilizing a widely adopted evolutionary methodology USPEX for crystal structure prediction. We find that the ground state of the MoN 2 system is a pernitride structure with space group P6 3 /mmc which transforms to a P4/mbm phase above 82 GPa. Chemical bonding analysis shows that one could assign MoN 2 as Mo 4+ (N 2 4− ); i.e., Mo is formally a d 2 metal, in agreement with the experimental results of Wang et al. The presence of covalent N 2 dumbbells and strong bonding between Mo 4+ and N 2 4− is the source of the superior mechanical properties of these predicted ultra-incompressible MoN 2 pernitrides.

Using a variable-composition ab initio evolutionary algorithm, we investigate stability of various Zr–N compounds.