In response to recent helium atom scattering (HAS) and neutron scattering results, Monte Carlo simulations and perturbation theory calculations have been performed for D-2 on MgO(0 0 1). Monte Carlo simulations predict that D-2 molecules form a series of interesting structures, p(2 x 2) -> p(4 x 2) -> p(6 x 2), with coverages Theta = 0.5, 0.75, 0.83 respectively, and followed by a formation of a top layer of p(6 x 2) unit cell symmetry. The three types of mono-layers are stable up to 13 K, whereas the top layer still exists up to 10 K. This is in partial agreement with the neutron scattering and HAS results that report c(2 x 2), c(4 x 2) and c(6 x 2); they agree in terms of coverage and stability, but disagree in terms of symmetry. A quantum mechanical examination of the D-2 molecules' rotational motion shows the molecular axes are azimuthally delocalized and hence the simulated structures are c-type rather than p-type. These calculations also indicate that ortho-D-2 and helicoptering para-D-2 prefer cationic sites, while cartwheeling para-D-2 prefers anionic sites. (C) 2009 Elsevier B.V. All rights reserved.