Internal motions in a complex consisting of a rare gas atom and a C2v molecule: theoretical formulations and their applications to Fourier transform microwave spectra of Ne-dimethyl ether and Ar-dimethyl ether

The internal motion of the rare gas atom, i.e., the relative motion of the two constituents, in a complex shown in the title was discussed by paying special attention to its effect on the rotational motion of the complex in order to extract as much precise information on this motion as possible from the observed rotational spectra. We have set up two theoretical formulations. One is based on a coordinate axis system attached to the C2v molecule, but its origin is floating with the motion of the rare gas atom, while keeping the orientation parallel to the original C2v molecule-fixed coordinate system. The second approach starts with counting the number of equivalent potential minima, which are well separated from the others by high potential barriers, and then collects all permutation-inversion operations, which transform the system from one minimum to another, to set up a group appropriate for the complex. By using the symmetry properties thus derived, a phenomenological Hamiltonian is set up to fit the observed spectra. The two formulations result in alike rotational energy matrices, and we have applied them to analyze the internal motions in the two complexes of present concern: neon-dimethyl ether (Ne-DME) and argon-dimethyl ether (Ar-DME). Some of the transitions observed by the present study exhibited additional splittings, which were interpreted as due to an internal rotation of the methyl groups in DME and were analyzed by the second formulation. For Ar-DME the splittings appeared only in high-K transitions, yielding the V3 potential barrier to be 778(1) cm(-1), whereas those observed for Ne-DME were ascribed to the effects of the CH3 internal rotation on the inversion splitting.