We present a general variational approach for computing the laser-induced rovibrational dynamics of molecules, taking into account the hyperfine effects of the nuclear quadrupole coupling. The method combines the general variational approach TROVE (Theoretical Ro-Vibrational Energies), which provides accurate rovibrational hyperfine energies and wavefunctions for arbitrary molecules, with the variational method RichMol, designed for generalized simulations of the rovibrational dynamics in the presence of external electric fields. We investigate the effect of the nuclear quadrupole coupling on the short-pulse laser alignment of a prototypical molecule CFClBrI, which contains nuclei with large quadrupole constants. The influence of the nuclear quadrupole interactions on the postpulse molecular dynamics is negligible at early times, for the first several revivals; however, at longer time scales, the effect is entirely detrimental and strongly depends on the laser intensity. This effect can be explained by dephasing in the laser-excited rotational wavepacket due to irregular spacings between the hyperfine-split nuclear spin states across different rotational hyperfine bands.
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