Classical Monte Carlo (MC) simulations of D-2 molecules physisorbed on LiF(0 0 1) Surfaces are reported and show a series of interesting commensurate structure forms, viz., p(2 x 2) -> p(8 x 2) -> p(4 x 2), with coverages Theta = 0.5, 0.625, and 0.75, respectively, and are stable LIP to 8 K. These structures are consistent with recent helium atom scattering (HAS) results (the p(4 x 2) is not observed) in terms of coverage and stability, but disagree in terms of symmetry. The p(2 x 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 x 2) structure, there are two kinds of adsorption sites: a parallel site, as in the case of p(2 x 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 theta similar to 63 degrees. 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 cart-heeling p-D-2 species. (c) 2009 Elsevier Inc. All rights reserved.