Rovibrational states of a tetrahedral molecule in a hexagonal close-packed crystal

The vibration-rotation states of a tetrahedral molecule in a field of $D_{\text{3h}}$ symmetry are studied by an extended group theory. Symmetry adapted rotational wave functions for the ground and the triply degenerate excited vibrational states are constructed. The crystal field potential is derived explicitly for a tetrahedral molecule in a hexagonal close-packed crystal. As an example, the rovibrational energy states of methane in solid parahydrogen are computed. Optical selection rules are also derived from the theory.