First principle (FP) calculations were performed to systematically study the structural properties of ZrN, LaN and ThN with GGA correction. The ground state properties, wave velocities and Debye temperature of B1, P6 3 /mmc, Pnma and B2 phase in ZrN, LaN and ThN were investigated and agree well with other theoretical and experimental results. More importantly, some novel phases are predicted in these materials, i.e. with the increasing pressure the phase transition sequence in ZrN and ThN is found to be B1 → P6 3 /mmc → B2 phase, while in LaN, the sequence of B1 → Pnma → B2 is observed. Furthermore, our calculated elastic properties also confirm the prediction of phase transition under high pressure. These phase transitions arise from the optical phonon softening of B1 at around X, M and G points of Brillouin zone and P6 3 /mmc (or Pnma) structure at around G, and H-K points.

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