An ab initio determination of the bending–torsion–torsion spectrum of dimethyl ether, CH3OCH3 and CD3OCD3

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Abstract
We have calculated the potential energy hypersurface of dimethyl ether with respect to the COC bending coordinate α and the torsional angles of the two methyl groups, θ1 and θ2. Two sets of ab initio calculations were carried out. The first was made at the level MP2/6‐31G(d,p) in which the structural coordinates were fully relaxed except for the grid points on the hypersurface. More extensive calculation were carried out with MP4 corrections for electron correlation with the same molecular structure. The torsional bending Hamiltonian matrix was symmetrized by the operations of the G36 nonrigid group and was solved variationally. The effect of explicitly considering the bending mode in the three‐dimensional treatment was determined by a comparison to the two‐dimensional model in which the flexibility of the frame was absorbed into the calculation by the fully relaxed method. It was found that the three‐dimensional calculation gave a much better account of the sin(3θ1)sin(θ2) intermode coupling than the two‐dimensional treatment.