We developed a full quantum time-dependent wave-packet evolution method to simulate the multibody breakups of polyatomic molecular ions. The interaction picture theory was used to propagate the wave packet, where the effects of strong and long-range interactions are considered by basis functions and the weak and short-range interactions are included in the perturbation term. In this method, the Coulomb interactions, polycentric interactions, vibration-rotation coupling of molecular fragments, and the rotation-rotation coupling between molecular fragment and parent molecule are considered accurately. Using this method, we simulate the two-body breakups of ${\mathrm{H}}_{2}{\mathrm{Ar}}^{2+}$ and ${\mathrm{N}}_{2}{\mathrm{Ar}}^{2+}$. The simulated results show that the ultrafast rotation of the molecular fragment generally exists in the breakup of the polyatomic molecular ion. For ${\mathrm{H}}_{2}{\mathrm{Ar}}^{2+}, {\mathrm{H}}_{2}^{+}$ can rotate from an initial broad distribution around ${35}^{\ensuremath{\circ}}$ and ${145}^{\ensuremath{\circ}}$ to a narrow distribution around ${75}^{\ensuremath{\circ}}$ and ${105}^{\ensuremath{\circ}}$ within 30 fs. For ${\mathrm{N}}_{2}{\mathrm{Ar}}^{2+}$, the initial sine-shaped angular distribution ($j$ = 0) shrinks to a narrow range (${90}^{\ensuremath{\circ}}\ifmmode\pm\else\textpm\fi{}{20}^{\ensuremath{\circ}}$) within 120 fs and then spreads to an approximately random distribution within 300 fs. Such ultrafast rotations are dominated by the polycentric interaction between fragments and impacted by the vibration-rotation and rotation-rotation couplings.
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