We have carried out non-equilibrium molecular dynamics simulations of a model diatomic molecular liquid subjected to an oscillatory shear perturbation. In two series of simulations we examine the effects of applying the perturbation to the centres of mass of the molecules and to the constituent atoms. The responses in the microscopic stress and the molecular orientation are observed. The differences in the results of applying the two types of perturbation are seen to vanish at low frequencies, as expected, and they do not affect the extrapolation to zero frequency, which adopts a square-root cusp form as seen in atomic systems. However, the differences between ‘atomic’ and ‘molecular’ experiments are quite clear in the moderate- and high-frequency regions. A simple projection operator description, with a single non-analytic stress memory function, is shown to be insufficient to explain the relative magnitudes of the cusps in the stress and orientation responses.