1. Analysis of the rotation-torsion spectrum of CH 2 DOH within the e 0, e 1, and o 1 torsional levels L. H. Coudert, a John C. Pearson, b Shanshan Yu, b L. Margulès, c R. A. Motyenko, c and S. Klee d a LISA, CNRS/Universités Paris Est et Paris Diderot, Créteil, France b Jet Propulsion Laboratory, Pasadena, California, USA c PhLAM, CNRS/Université de Lille I, Villeneuve d’Ascq, France d Physikalisch-Chemisches Institut, Gießen, Germany

2. CH 2 DOH is molecule of astrophysical relevance First detected in Orion. 1 Used to study methanol deuteration in Orion by measuring the [CH 2 DOH]/[CH 3 OD] abundance ratio. 2 Internal rotation of an asymmetric top methyl group. 1. Jack, Walmsley, Mauersberger, Anderson, Herbst, and De Lucia, A&A 271 (1993) 276 2. Peng, Despois, Brouillet, Parise, and Baudry, A&A 543 (2012) A152

3. Overview Model Torsion-rotation Hamiltonian Torsional energy levels & functions Distortion terms Analysis results Line intensity calculation

4. The model z x y Fixed Frame Axis Method α angle of internal rotation α Hecht and Dennison, J. Chem. Phys. 26 (1957) 31 Quade and Lin, J. Chem. Phys. 38 (1963) 540

5. Exact Torsion-Rotation Hamiltonian 1. Lauvergnat, Coudert, Klee, and Smirnov, J. Mol. Spec. 256 (2009) 204 2. El Hilali, Coudert, Konov, and Klee, J. Chem. Phys. 135 (2011) 194309 No analytical expression for μ(α)

6. Torsional energy level diagram Lauvergnat, Coudert, Klee, and Smirnov, J. Mol. Spec. 256 (2009) 204 o3e2oo3e2o o1e1eo1e1e

7. J = 0 torsional functions Lauvergnat, Coudert, Klee, and Smirnov, J. Mol. Spec. 256 (2009) 204 0 cm  11 cm  16 cm  289 cm  211 cm  206 cm 

8. Distortion effects Torsion-Rotation operators are added to the exact Hamiltonian 3-fold symmetry no longer required CH 3 & CH 2 DCH 2 D

9. Analysis results

10. Data set & analysis results 8637 transitions with J  30 and K a  11 including: 7813 microwave and THz transitions from Ref. (1) 243 microwave and THz transitions measured at JPL 481 FIR transitions measured in Giessen 100 low resolution torsional subband centers The unitless standard deviation of the fit is 2.9 RMS of the Microwave and THz data: 0.458 MHz RMS of the FIR data:   cm  RMS of the torsional subband centers: 0.1 cm  Number of fitted parameter: 96 1. Pearson, Yu, and Drouin, J. Mol. Spec. 280 (2012) 119

11. Uncertainty is  MHz J  J  expansion yields B  cm  a-type  transitions with K  within e 0

12. Uncertainty is  MHz J  J  expansion yields B  cm  a-type  transitions with K  within e 1

13. Rotational constants change e 0 -type levels Centered around α  e 1 and o 1 -type levels Centered around α  Theoretical approach accounts for changes in the rotational constants

14. I. J  J  expansion with B, D, H, and L II. This work a-type  transitions with K  within o 1 K , o 1 interacts 1 with K , e 0 1. Pearson, Yu, and Drouin, J. Mol. Spec. 280 (2012) 119

15. a-type  transitions with K  within e 0 Uncertainty is  MHz

16. Torsional energy level diagram o3e2oo3e2o o1e1eo1e1e

17. Line intensity calculation z x y α μ x =  D 1 μ z =  D 1. Sastry, Lees, and van der Linde, J. Mol. Spec. 88 (1981) 228

18. The K , o 1  K , o 1 Q branch

19. The K , e 1  K , o 1 Q branch o 3 : 12 1,11  11 1,10 o 2 : 12 0,12  11 1,11 8 3,5 e 2  9 4,5 o 2