The far‐infrared spectra of trimethylene sulfide and cyclobutanone have been investigated. The positions of the trimethylene sulfide bands observed are well fitted by the potential function derived from the microwave studies of Harris et al. However, some of the band shapes cannot be explained in detail although the anomalies are probably due to Coriolis terms in the Hamiltonian. The positions of the lower frequency bands of cyclobutanone can be fit approximately by a quartic—quadratic potential with a small barrier. Although this potential function fits the rotational constants measured by Sharpen et al., it does not predict the positions of the higher frequency bands correctly. Furthermore the band shapes cannot be explained on the basis of the simple potential function, and it is suggested that the low‐frequency out‐of‐plane vibration of cyclobutanone is perturbed by a higher frequency vibration.

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15.
This formula may easily be derived from the formulas in Ref. 12. This reference also lists the formulas that relate the tau’s to the energy of a rotating molecule.
16.
The low‐lying trimethylene sulfide frequencies were also obtained by A. D. Walsh and P. A. Warsop from a study of the electronic spectra of trimethylene sulfide. They fit their observation with a potential function with a Gaussian barrier, but this potential function does not fit the lower vibrational levels as well as the quartic‐quadratic potential function of Harris et al.6a (private communication to W. D. Gwinn).
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18.
For example, the υ = 4 and the probably perturbed υ = 8 levels differ in energy by about 400 cm−1. The value of the matrix element 〈4|Q2|8〉 is about 0.2. The value of this matrix element would, of course, be zero if the vibration were harmonic. L. Sharpen and V. W. Laurie have just found that the rotational constants of the υ = 8 state of cyclobutanone differ significantly from the values predicted by the extrapolation from previous states. The states υ = 9 and υ = 10 have the expected rotational constants. This is additional evidence for a perturbation of at least the υ = 8 state.
19.
This equation differs slightly from the equation given in Ref. 3 because a slightly different reduced mass was used.
20.
The half‐half‐width of an individual line is 1.17w.
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That is Ax = ΣyBx−yCy, where A, B, and C are vectors.
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1966
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