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In this article, the crystal structure of solid hydrazine under pressure has been extensively investigated using ab initio evolutionary simulation methods. Calculations indicate that hydrazine remains both insulating and stable up to at least 300 GPa at low temperatures. A structure with P21 symmetry is found for the first time through theoretical prediction in the pressure range 0-99 GPa and it is consistent with previous experimental results. Two novel structures are also proposed, in the space groups Cc and C2/c, postulated to be stable in the range 99-235 GPa and above 235 GPa, respectively. Below 3.5 GPa, C2 symmetry is found originally, but it becomes unstable after adding the van der Waals interactions. The P21[rightwards arrow]Cc transition is first order, with a volume discontinuity of 2.4%, while the Cc[rightwards arrow]C2/c transition is second order with a continuous volume change. Pressure-induced hydrogen-bond symmetrization occurs at 235 GPa during the Cc[rightwards arrow]C2/c transition. The underlying mechanism of hydrogen-bond symmetrization has also been investigated by analysis of electron localization functions and vibrational Raman/IR spectra.

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