Fig. 1. Enthalpy difference of BeN₄ relative to the P4/nmm structure under high pressure. P1-BeN₄ and P2₁/c- BeN₄ are previously known high-pressure structures from Ref. 29. The phase transition pressures are indicated by the arrows.

Fig. 2. Crystal structure of the stable P4/nmm-BeN₄ at ambient pressure: (a) side view along c axis; (b) a axis. The green spheres are Be atoms and the gray spheres N atoms.

Fig. 3. Phonon dispersions and phonon density of states (PHDOS) of P4/nmm-BeN₄ at ambient pressure.

Fig. 4. Molecular dynamics simulations and radial distribution function of P4/nmm-BeN₄. (a) and (b) Equilibrium structures at 10 ps and fluctuations of the total potential energies during the AIMD simulation at temperatures of 300 and 500 K, respectively. (c) RDF for N–N separations.

Fig. 5. Electronic properties of P4/nmm-BeN₄ at ambient pressure. (a) Band structure. (b) PDOS of Be and N atoms. (c) COHP between N and N atoms.

Fig. 6. SSAdNDP-derived chemical bonding pattern of P4/nmm-BeN₄ at ambient pressure: (a) 4 × 2c-2e Be–N σ bonds, ON = 1.65|e|, iso-value = 0.15; (b) 4 × 2c-2e N–N σ bonds, ON = 1.65|e|, iso-value = 0.2; (c) 2 × 2c-2e N–N π bonds, ON = 1.65|e|, iso-value = 0.1; (d) 1 × 4c-2e N–N large π bond, ON = 1.70|e|, iso-value = 0.03.

Fig. 7. Enthalpy of formation of P4/nmm-BeN₄ relative to Be₃N₂ and N₂.