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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



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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