The G 36 permutation-inversion group theoretical tunneling-rotational formalism originally developed for the methanol dimer has been modified (for the subgroup G 18 ) and extended (to the larger group G 54 ) for application to dimethyl methylphosphonate, CH 3 -P(= =O)-(OCH 3 ) 2 , which has three large-amplitude methyl top internal rotation motions and one large-amplitude methoxy interchange motion. Energy levels of this chiral molecule are conveniently labeled by symmetry species corresponding to a mixed set of irreducible and reducible representations of G 18 denoted by A 1 , A 2 , E, E 1sep , E 2sep , and G sep . The separably degenerate species (with subscript sep) consist of pairs of irreducible representations of G 18 whose energies are degenerate for Hamiltonians invariant to time reversal. All characters of these separably degenerate representations are real. Comparison of the group-theoretically derived splitting patterns with Fourier transform microwave and ab initio results from the preceding paper permit drawing a semiquantitative energy level diagram showing how a given
components when the large-amplitude motions are turned on in the following order: (i) low-barrier methyl top internal rotation, (ii) medium-barrier methyl top internal rotation, (iii) top-top interaction, and (iv) methoxy interchange motion. (Internal rotation of the high-barrier methyl top is ignored.) Spectral splitting patterns observed for K a = 1-1 transitions are also quite regular, being either the same as, or mirror images of, the K a = 0-0 patterns. Theoretical work on K a > 0 splitting patterns is in progress.