Table A.2.
Rotational constants and internal rotation parameters in the ρ-axes-frame.
| Axes and anglesa | Parametersb | Our fit from refs.d | MP2/aug-cc-pVTZ | Our work | Units |
|---|---|---|---|---|---|
 |
ARAM | 38641.(160) | 38149.2 | 38587.00(11) | MHz |
| BRAM | 4768.2(63) | 4803.4 | 4773.813(29) | MHz | |
| CRAM | 4135.854(16) | 4137.9 | 4139.199(46) | MHz | |
| Dab | −2980.(38) | −3157.1 | −3015.26(39) | MHz | |
| V3 | 404.333(63) | 424.7 | 429.38 (11) | cm−1 | |
| ρ | [0.19640] | 0.191 | 0.194354(13) | − | |
| F | [186.680] | 187.9 | 192.511(39) | GHz | |
| s | 28.859(45) | 30.1 | 29.718(14) | − | |
| δ | 39.39 | 38.7 | 39.71 | ∘ | |
| θRAM | 4.99 | 5.3 | 5.06 | ∘ | |
| Iα (F)c | 3.26 | [3.2] | 3.14 | uÅ2 | |
| Iα (ρ)c | 3.18 | [3.2] | 3.17 | uÅ2 |
Notes.
Axis frames in methyl ketene under the Ir representation: in black the principal axis frame and in red the rho-axis. In blue, it is indicated the internal rotation axis.
ARAM, BRAM, CRAM are the rotational constants in the rho-axis-frame. V3 is the height of the torsional barrier. ρ is the norm of the ρ vector described in Sect. 4 and represented in green in the figure. F is the internal rotational constant defined by F = h2/2rIα where 
and λg the direction cosines mentioned in Sect. 4. s is the reduced barrier parameter which is calculated as s = 4V3/9F. δ is the angle between the internal rotation and the aPAM axis, which is thus related to the direction cosines as cos(δ)=λa. θRAM is the angle of frame rotation and can be calculated based on the ρ projections: θ = arctan(ρx/ρy). Finally, Iα is the reduced mass of the methyl top.
Iα is, in case of the ab initio parameters, fixed to 3.2 which is its average value for a methyl top in the calculation from the ab initio structure. In the other cases it is calculated from the RAM rotational constants and either the ρ or F values as follows (Ilyushin 2011): 
and 
.
Values obtained employing our RAM36 fit of the transitions from Bak et al. (1962) and the methyl ketene experimental structure from Bak et al. (1966).
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