Monte Carlo (MC) simulations of D₂ molecules on the MgO(001) surface are reported and show that a series of interesting structures form with increasing coverage, viz. p(2 × 2) → p(4 × 2) → p(6 × 2), with coverages Θ = 0.5, 0.75, and 0.83 respectively, and are stable up to 13 K. The p(2 × 2) structures contain two D₂ molecules per unit cell, with each molecule lying parallel to the plane of the surface (θ = 90°) directly above every other Mg²⁺ site. The molecules adopt a “T” configuration with respect to their nearest neighbors. The p(4 × 2) and p(6 × 2) structures, have two kinds of adsorption sites: a parallel site, as in the case of p(2 × 2), and a tilted site, where the D₂ molecules sit between cationic and anionic sites with the molecular axis directed towards the anionic site, with θ ≈ 60°. These structures are consistent with recent neutron scattering results in terms of coverage and stability, but disagree in terms of symmetry; the neutron scattering work found “c” type structures whereas the MC simulations (without quantum considerations) yield a “p” type structures. To reconcile the results of the simulations and experiments, the quantum mechanical rotational motion of the adsorbed D₂ molecules was studied using perturbation theory. These calculations show that the adsorbed D₂ molecules are azimuthally delocalized and hence the structures are indeed “c” type rather than “p” type. [DOI: 10.1380/ejssnt.2009.207]