Group theory for matrix isolated molecules in static crystal fields

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Abstract
The group theory is solved for molecules of any symmetry matrix isolated at a site in a crystal field of any symmetry. As the potential barrier to rotation of the molecule relative to the host crystal is raised, certain symmetry operations become decreasingly ``feasible'' in the sense of Longuet‐Higgins. Using correlation methods the symmetry species of the rotational states are determined from the free rotation limit to any of the librational limits. Examples of linear, symmetric, and spherical rotors are given. From the symmetry of states and the dipole and polarizability tensors, selection rules are applied to predict spectra in the infrared and Raman effect.