The structure and orientational ordering of N 2 molecules adsorbed on the Cu(110) surface is investigated in a combined experimental and theoretical study. Using He atom diffraction we find that monolayer N 2 forms a high-order commensurate phase with an oblique unit cell. Minimum energy calculations based on realistic potentials show that the unit cell contains seven N 2 molecules arranged in a novel type of pinwheel structure unexpected for linear molecules adsorbed on a smooth surface. Molecular dynamics simulations corroborate this structure and its remarkable thermal stability. [S0031-9007(97)02476-9] PACS numbers: 68.35.Bs, 34.20.Gj, 79.20.Rf In contrast to adsorbed atoms, nonspherical molecules carry additional degrees of freedom related to their relative orientation on the surface. As a result, the corresponding phase diagram can be quite complex. Besides the positional ordering, various orientationally ordered superstructures may exist as well as new classes of order-order and order-disorder phase transitions. The simplest type of adsorbates to study orientational ordering are diatomic homonuclear molecules, such as H 2 or N 2 . In fact, one of the best studied systems is molecular nitrogen adsorbed on the graphite (0001) basal plane [1].Mean-field theory [2,3] has been used to study the ordering of point quadrupoles on a two-dimensional hexagonal lattice under the influence of a homogeneous crystal field (substrate holding potential V c ). A generic phase diagram is obtained in which four distinct orientationally ordered phases can occur depending on temperature and the relative strength of the holding potential and the quadrupole coupling constant G. (i) In the "two-in" herringbone phase, the molecules are lying flat with two possible in-plane orientations. (ii) In the "two-out" phase the molecules also form a two-sublattice herringbone structure, but the molecular axes are tilted by a finite angle with respect to the surface plane. (iii) At smaller jV c ͞Gj a four-sublattice "pinwheel" structure is obtained, in which one pin molecule standing upright is surrounded by six molecules forming the wheel. However, each of the six wheel molecules belongs to two neighboring pinwheels such that the unit cell contains only four molecules. (iv) Finally, for large positive V c (repulsive potential) a ferrorotational "ferro" phase with a single tilted molecule per unit cell is obtained.The large number of experiments on N 2 and CO adsorbed on graphite has, indeed, revealed the occurrence of all three realistic structures (i)-(iii) [1]. Early LEED studies of N 2 on graphite [4,5] have provided the first clear evidence for a commensurate ͑2 p 3 3p 3 ͒R30 ± and a uniaxially compressed in-plane herringbone structure. At higher coverages an almost uniformly compressed triangular incommensurate phase was observed and the superstructure was assigned to a two-out herringbone lattice [6]. Subsequent neutron diffraction experiments corroborated these results [7]. However, a reinvestigation of the diffraction pattern at m...