Application of Permutation–Inversion Group Theory to the Interpretation of the Microwave Absorption Spectrum of Dimethyl Methylphosphonate

Abstract

The G36 permutation–inversion group theoretical tunneling–rotational formalism originally developed for the methanol dimer has been modified (for the subgroup G18) and extended (to the larger group G54) for application to dimethyl methylphosphonate, CH3P(O)(OCH3)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 G18 denoted by A1, A2, E, E1sep, E2sep, and Gsep. The separably degenerate species (with subscript sep) consist of pairs of irreducible representations of G18 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 Ka=0 level splits into A1⊕A2⊕2E⊕E1sep⊕E2sep⊕2Gsep 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 Ka=1–1 transitions are also quite regular, being either the same as, or mirror images of, the Ka=0–0 patterns. Theoretical work on Ka>0 splitting patterns is in progress.