The Rotational Motion of Molecules in Crystals

It is shown by the discussion of the wave equation for a diatomic molecule in a crystal that the motion of the molecule in its dependence on the polar angles $\theta$ and $\phi$ may approach either one of two limiting cases, oscillation and rotation. If the intermolecular forces are large and the moment of inertia of the molecule is large (as in ${\mathrm{I}}_2$, for example), the eigenfunctions and energy levels approach those corresponding to oscillation about certain equilibrium orientations; if they are small (as in ${\mathrm{H}}_2$), the eigenfunctions and energy levels may approximate those for the free molecule, even in the lowest quantum state.