Classical Monte Carlo (MC) simulations of D 2 molecules physisorbed on LiF(001) surfaces are reported and show a series of interesting commensurate structure forms, viz., p(2×2) → p(8×2) → p(4×2), with coverages Θ=0.5, 0.625, and 0.75, respectively, and are stable up to 8K. These structures are consistent with recent helium atom scattering (HAS) results (the p(4×2) is not observed) in terms of coverage and stability, but disagree in terms of symmetry. The p(2×2) structure contains two D 2 molecules per unit cell, with each molecule lying parallel to the plane of the surface directly above every other cationic site. For the p(4×2) structure, there are two kinds of adsorption sites: a parallel site, as in the case of p(2×2), and a tilted site, where the D 2 molecules sit between cationic and anionic sites with the molecular axis directed toward the anionic site, with a tilt angle of θ∼63°. Perturbation theory calculations show that the adsorbed D 2 molecules are azimuthally delocalized and hence the structures are indeed c-type. Our calculations also indicate that o-D 2 and helicoptering p-D 2 species prefer cationic sites, compared to cartwheeling p-D 2 species.