Search for Stable Orientational Orders in Rigid-Lattice Models of fcc Orthohydrogen

An iterative method is applied to the search for stable and metastable orders in rigid-lattice models of fcc ortho-${\mathrm{H}}_2$ with various amounts of quadrupole-quadrupole coupling: unshielded coupling between all molecules, shielded coupling beyond first-neighbor molecules, and coupling between first neighbors or first and second neighbors only. The model with nearest-neighbor couplings gives results that are decidedly different from the others in that the order with space group $\mathrm{Pa}3\mathrm{}$ becomes less stable than one with space group $\frac{P{4}_2}{\mathrm{mnm}}$ as $T$ rises, and in the very small difference in the free energies of the stable order and three metastable orders. The $\frac{P{4}_2}{\mathrm{mnm}}$ order is probably without physical significance, since it is destabilized when the model contains any physically reasonable amount of coupling between farther neighbors. The existence of complicated metastable phases with relatively low free energy persists in all models, and suggests that theoretical methods for the study of ortho-${\mathrm{H}}_2$ may be inadequate if they place too great a dependence on the assumption of $\mathrm{Pa}3\mathrm{}$ order, particularly in the treatment of the model with only first-neighbor coupling, or of the order-disorder transition in any model.