The hindered rotation of orbitally—singlet diatomic molecules in ionic crystals at sites of symmetry has been studied using the Hindered Rotor model. The static crystalline field due to the crystal is expanded in terms of spherical harmonics and symmetrized to transform like the totally symmetric representation of the group. The rotational wave functions are also expanded in terms of spherical harmonics up to about t = 2 and symmetrized to transform like any one of the ten irreducible representations of the ^ group. The eigenvalues are calculated in terms of the molecular moment of inertia for various values of the parameters characterizing the hindering potential.