Rotation-translation levels of a tetrahedral molecule in an octahedral cell

The theory of King and Hornig dealing with the rotation of a tetrahedron in an octahedral cell is extended to include the translational motion of the molecular center of mass (c.m.) with respect to the center of the cell (c.c.). Use is made of a representation diagonalizing the total angular momentum, composed of the angular momenta associated with the rotation of the molecule about its c.m. and that of the molecular c.m. relative to the c.c. Moreover, the particular symmetry of the system has been fully exploited. Closedform expressions for the second-order energy corrections are given and used to interpret experimental data on the spectra of matrix-isolated methane.