1. Molecular Spectroscopy Symposium 2007 18-22 June 2007 The v t =1 State of Methanol John C. Pearson, Carolyn Brauer, Brian J Drouin, & Herbert Pickett Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 Jonathan Fisher, Hongyu Shi, & Li-Hong Xu Centre for Laser, Atomic and Molecular Sciences (CLAMS), Department of Physical Sciences, University of New Brunswick, Saint John, N.B., Canada E2L 4L5 John C. Pearson, Carolyn Brauer, Brian J Drouin, & Herbert Pickett Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 Jonathan Fisher, Hongyu Shi, & Li-Hong Xu Centre for Laser, Atomic and Molecular Sciences (CLAMS), Department of Physical Sciences, University of New Brunswick, Saint John, N.B., Canada E2L 4L5

2. 2 Molecular Spectroscopy Symposium 2007 18-22 June 2007 Motivation Methanol is insufficiently known for astrophysics! –Was use to test Herschel HIFI instrument to 1.9 THz ~6000 spectra –Will ultimately extract calibration parameters need synthetic spectra

3. 3 Molecular Spectroscopy Symposium 2007 18-22 June 2007 Previous v t =1 Methanol Predictions from Anderson et al., Xu et al. are significantly off for some b-types not in analysis and high J & K transitions –Fit constrained by IR data if at all –Fits limited to J<20 data No published predictions >1 THz –Need to make assignments and de-bug line list for global fit V t =1 has the most problems of the lowest 4 states –Low K E-state level crossings –Interactions with v t =0 & 2 –Accidental degeneracy of K levels

4. 4 Molecular Spectroscopy Symposium 2007 18-22 June 2007 Data and Spectrometer Data Set –Complete spectrum 8-540 GHz, 582-702 GHz, 767-965 GHz, 1056-1200 GHz, 1575-1654 GHz –Some Pieces in the 540-582 GHz –Some Pieces between 1654-2530 GHz Most taken with direct multiplication spectrometer at JPL

5. 5 Molecular Spectroscopy Symposium 2007 18-22 June 2007 Data Set A states Vt=2 K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 K=10 K=11 K=12 K=13 K=14 Vt=1 24 P24 R1 Q10 46 44 R21 Q38 P60 R14 Q12 P34 42 R0 Q8 P35 R2 Q12 38 34 P44 R6 Q28 P42 32 R18 Q6 P0 32 P22 R4 Q44 20 P24 R24 Q40 22 R10 Q20 P8 22 P2 R0 Q0 24 P20 R2 Q22 24 1418 P0 R0 Q0 P0 R0 Q0 7 8 32 21 12 18 6 12 10 2 20 1 3 6 5 2 12 4 2 22 6 Vt=1 Vt=0 K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 K=10 K=11 K=12 K=13 K=14

6. 6 Molecular Spectroscopy Symposium 2007 18-22 June 2007 A-State Pathologies K=1 crosses v t =0 K=8 spectra assigned to J=41 –Large delta K no significant effect K=5 is strongly resonant with v t =0 K=9 cross at J=30 –K/torsional state assignment questionable above J=29 K=8 on top of K=1 of v t =2, nearly degenerate with K=9 of v t =1 –Few MHz of impact around J=28 K=9 crosses K=1 of v t =2 at J=27, nearly degenerate with K=8 of v t =1 –K=8 & 9 do not fit K=13 is strongly resonant with v t =0 K=15 and v t =2 K=11

7. 7 Molecular Spectroscopy Symposium 2007 18-22 June 2007 Vt=1 K=1 & vt=0 K=8 Vt=0 K=8 Vt=1 K=1 Levels Cross with little effect in the spectra

8. 8 Molecular Spectroscopy Symposium 2007 18-22 June 2007 Vt=1 K=5 and Vt=0 K=9 Vt=1 K=5 Vt=0 K=9 Vt=1 K=5? Levels cross at J=30 transitions between vt=1 K=4 and vt=0 K=9 levels found

9. 9 Molecular Spectroscopy Symposium 2007 18-22 June 2007 Vt=1 K=8 & 9 and Vt=2 K=1 Vt=1 K=8 Vt=1 K=9 Vt=2 K=1 Large Delta K interaction but some apparent effect on K=8 and 9 transitions problems at and above crossing

10. 10 Molecular Spectroscopy Symposium 2007 18-22 June 2007 Vt=1 K=13, Vt=0 K=15 and Vt=2 K=11 Mess vt=2 K=11 vt=0 K=15 vt=1 K=13 Mixed levels give rise to extra torsional transitions between states

11. 11 Molecular Spectroscopy Symposium 2007 18-22 June 2007 Data set E state vt=1 to vt=1 bR R0 R0 R2 R0 R8 R0 R8 R6 R2 R6 R2 R4 R1 R3 bQ Q6 Q0 Q0 Q0 Q29 Q0 Q0 Q27 Q29 Q0 Q19 Q33 Q24 Q11 aR 4 8 9 10 13 15 16 17 18 18 20 21 21 21 24 bP P6 P0 P0 P10 P15 P7 P2 P23 P28 P2 P24 P28 P27 P5 K -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 bR R19 R11 R12 R3 R2 R4 R9 R9 R1 R1 R7 R0 R0 R0 bQ Q45 Q3 Q26 Q26 Q5 Q2 Q13 Q33 Q1 Q0 Q30 Q0 Q0 Q0 aR 24 23 22 18 20 17 18 17 16 15 12 12 8 8 4 bP P26 P15 P22 P23 P17 P1 P20 P16 P2 P0 P14 P12 P0 P0 K 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Data set vt=1 to vt=1 |K|>12 still requires some more attention. Higher J lines are in data but have not been systematically assigned

12. 12 Molecular Spectroscopy Symposium 2007 18-22 June 2007 E-State data set vt=1 to vt=0 &2 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 13 1 7 7 5811 28 14 11311 2 2 Vt=2 Vt=1 Vt=0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 28 22 311 2 4 812 63 1 2 1 Vt=2 Vt=1 Vt=0

13. 13 Molecular Spectroscopy Symposium 2007 18-22 June 2007 E-State Pathologies Low K crossings –K=-1 & K=3 are strongly resonant at J=29  K=-4 vt=1 and K=9 vt=0 are also involved –K=-2 and K=4 are strongly resonant at J=34 Torsional interactions –K=-3 vt=1 and K=-8 vt=0 cross at J=21 –K=9 vt=1 and K=0 vt=2 cross at J=30  Vt=0 K=12 interacts at high J with K=9 vt=1 Remainder of states relatively well isolated so levels followed to J=34+ –|K|>12 requires more analysis data is currently tentative

14. 14 Molecular Spectroscopy Symposium 2007 18-22 June 2007 Vt=1 K=3 & -1 et al. K=-1 vt=0 K=3 vt=0 K=2 vt=1 K=-4 vt=0 K=-9 vt=0 K=9 vt=0 V t =1 K=3 & K=-1 are strongly resonant K=3 eventually interacts with v t =0 K=9 and v t =1 K=-4 at high J

15. 15 Molecular Spectroscopy Symposium 2007 18-22 June 2007 K=-2 and K=4 vt=1 K=-2 vt=1 K=4 vt=1 Vt=1 K=-2 and vt=1 K=4 are strongly resonant at J=33 and 34

16. 16 Molecular Spectroscopy Symposium 2007 18-22 June 2007 K=-3 vt=1 and K=-8 vt=0 Vt=0 K=-8 Vt=1 K=-3 Vt=1 K=-3 and vt=0 K=-8 interact weakly does not really affect spectra

17. 17 Molecular Spectroscopy Symposium 2007 18-22 June 2007 K=9 vt=1, K=12 vt=0 & K=0 vt=2 K=9 vt=1 K=12 vt=0 K=0 vt=2 Vt=1 K=9 interacts weakly with vt=2 K=0 and Strongly with vt=0 K=12 at high J

18. 18 Molecular Spectroscopy Symposium 2007 18-22 June 2007 Next Steps Completed power series fits |K|</=12 in E state –Assign transitions in well behaved K states to higher J, J~45 Complete power series fits of |K|>12 Complete power series fits of ground state E –Problems with low K interactions Assign additional torsional transitions at high J Fit with IAM Hamiltonian that will predict level crossings –Predict frequencies on the other side of crossings –Assign transitions & repeat fit & do quantum mechanics as necessary Measure dipole moment as function of K & vt Compare with HIFI spectrum Talk on Friday about initial step in IAM fitting of data set