Prediction of novel tetravalent metal pentazolate salts with anharmonic effect

In recent decades, pentazolate salts have gained considerable attention as high energy density materials (HEDMs). Using the machine-learning accelerated structure searching method, we predicted four pentazolate salts stabilized with tetravalent metals (Ti-N and Zr-N). Specifically, the ground state MN $$ (M = Ti, Zr) adopts the space-group P4/mcc under ambient conditions, transforming into the I-4 phase at higher pressure. Moreover, the I-4-MN $$ becomes energetically stable at moderate pressure (46.8 GPa for TiN $$ , 38.7 GPa for ZrN $$ ). Anharmonic phonon spectrum calculations demonstrate the dynamic stabilities of these MN $$ phases. Among them, the P4/mcc phase can be quenched to 0 GPa. Further ab-initio molecular dynamic simulations suggest that the N $$ rings within these MN $$ systems can still maintain integrity at finite temperatures. Calculations of the projected crystal orbital Hamilton population and reduced density gradient revealed their covalent and noncovalent interactions, respectively. The aromaticity of the N $$ ring was investigated by molecular orbital theory. Finally, we predicted that these MN $$ compounds have very high energy densities and exhibit good detonation velocities and pressures, compared to the HMX explosive. These calculations enrich the family of pentazolate compounds and may also guide future experiments.