  We present a theoretical study of the time-dependent laser alignment of
molecules taking into account the hyperfine coupling due to nuclear-quadrupole
interactions. The coupling of nuclear spins to the overall angular momentum of
molecules significantly influences their rotational dynamics. Here, we
systematically analyze the impact of the nuclear-quadrupole coupling on the
rotational dynamics of the linear $\text{I}_2$ and the asymmetric-top
diiodobenzene molecule induced by external laser fields. We explore different
regimes of pulse shapes and laser-pulse intensities and detail under which
conditions the quadrupole coupling cannot be neglected in the description of
the laser alignment of molecules.
