Nov. 2011: decoding of K_a and K_c quantum numbers has been corrected with respect to the initial entry from May 2010. Erham does not provide these quanta. The version number has been retained.
Dimethyl ether is an asymmetric top molecule with two equivalent methyl groups, which undergo large amplitude motions along the CO-bond. This internal rotation causes a splitting of each rotational level into four substates. The AA, EE, EA, and AE substates are represented by the v designations of 0, 1, 3, and 5, respectively. The work
(1) C. P. Endres, B. J. Drouin, J. C. Pearson, H. S. P. Müller, F. Lewen, S. Schlemmer, and T. F. Giesen, 2009, Astron. Astrophys. 504 635
gives a detailed overview of the experimental data and its analysis. Transitions up to almost 2.1 THz have been measured. As reported in this reference, previous data published by
(2) F. J. Lovas, H. Lutz, and H. Dreizler, 1979, J. Phys. Chem. Ref. Data 8, 1051,
(3) W. Neustock, A. Guarnieri, J. Demaison, and G. Wlodarczak, 1990, Z. Naturforsch. 45a, 702, and
(4) P. Groner, S. Albert, E. Herbst, and F. C. De Lucia, 1998, Astrophys. J., 500, 1059
has been included in the analysis. The lines are fit to an effective Hamiltonian for two symmetric internal rotors proposed by P. Groner (see
(5) P. Groner, 1997, J. Chem. Phys., 107, 4483)
and the fitting routine erham has been used. The experimental lines have been reproduced within experimental uncertainty. While AA and AE states have only b-type transitions, EE and EA states have also c-type transitions. The spin statistical weights are 6, 16, 4, 2 for the ee and oo rotational states, and 10, 16, 4, 6 for the oe and eo states, as reported by
(6) R. Myers and E.B. Wilson, Jr., 1960, J.Chem.Phys. 33, 186.
Predictions with uncertainties larger than 0.5 MHz should be viewed with some caution. This should not be a problem for astronomical observation.
A separate treatment of spin modifications at low temperatures is not required as dimethyl ether is only abundand in hot cores at temperatures of about 100 K.
The dipole moment has been taken from
(7) U. Blukis, R. J. Myers, and P. H. Kasai, 1963, J. Chem. Phys. 38, 2753.
The partition function takes excited states into account. While contributions of the torsionally excited states v₁₁ = 1 and v₁₅ = 1 were calculated based on a detailed analysis, contributions from the COC bending state (v₇ = 1) and from v₁₁ + v₁₅ = 2 were estimated based on the ground state analysis.