1. Global Modelling of the First Three Torsional States of Methanol ( v t = 0, 1, 2, J max = 30): (CH 3 OH & CH 3 18 OH) Jonathan Fisher, Gregory Paciga, Li-Hong Xu, R.M. Lees Centre for Laser, Atomic and Molecular Sciences (CLAMS) Department of Physical Sciences University of New Brunswick, Saint John, N.B., Canada E2L 4L5 Jon T. Hougen Optical Technology Division, National Institute of Standards & Technology, Gaithersburg, MD, CA USA 20899-8441 John C. Pearson, Brian J. Drouin Jet Propulsion Laboratory, NASA, California Institute of Technology, Pasadena, CA USA 91109

2. Challenges to the Global Modeling More level crossings and perturbations as torsional v goes up Dense spectra with line overlap and line intensity variation Possible variation in measurement uncertainties – six bands were used involving different multipliers …. Coverage: 330 to 1830 GHz with some holes More than 15,000 peaks detected using the JPL software A big question is the uncertainty: < 750 GHz: ±50 kHz, 750 GHz 1.655 THz: ±200 kHz Motivation = New JPL THz Measurements

3.  K  J  K = -1, 0, +1 p, q, r  J = -1, 0, +1 P, Q, R J = 18  17 a-type ( q R) J = 17  16 p Q: t = 1, -2  -3 E r Q: t = 0, 5  4 E New JPL Methanol Spectrum (MHz) Intensity drop partly due to atm. water abs.

4. New Methanol Spectrum at 1.2 THz (Small A Splittings Have Been Seen) Frequency (GHz) Q-branch:  t = 0, K = 5  4  A  19 18 12 10 5= J -  + +  - 14 16

5. Fitting is done with Isabelle Kleiner’s internal rotation program, using a number of new terms added by undergraduate Jonathan Fisher, who also replaced some home-made routines from Brussels with LaPAC routines to gain speed. This program has been described at the OSU Symposium here previously. The next slide shows the torsional-K-rotation levels of CH 3 OH for 0  K  15 and 0  v t  3 (The J levels are missing.)

6. 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 0 1234 5 6789 10 11121314 15 Torsional-K-Rotational Energy Structure for CH 3 OH [cm -1 ] V 3 = 373.59 cm -1 A E1E1 E2E2 t = 0 t = 1 t = 2 t = 3 (1,10,A) (2,7,A) (0,12,E) & (1,9,E) (0,9,A) & (1,5,A) ( t, K, Γs) Level crossings Interactions with t = 3 (2, 2, A) (3, 2, A) (2, -3, E) (3, -3, E) (2, 8, E) (3, 8, E) K Values t lowest SAVibrations

7. Overview of present work Region # of Lines weighted σ All24319 1.58 MW v t = 0 3046 1.96 v t = 1 1839 2.66 v t = 2 712 3.27 FTIR v t = 0,1,218722 1.21 What are the weights???

8. This data set is very large = 24236 lines. We cannot look at every line in detail (i)to determine correct meas. unc. (weight) (ii) to decide to include or exclude from fit (24236  5 min = 1 year of 40-hour weeks) Therefore the “philosophy” will be to treat the line list and fit as a “living document” to be criticized by users and updated periodically.

9.  Global analysis carried for CH 3 OH and CH 3 18 OH covering first three torsional states up to J max = 30, a 50% increase in torsional and rotational coverage  For CH 3 OH: the current data set has been increased 4 times including many newly measured THz transitions from JPL  For CH 3 18 OH: this is the first global fit effort  Based on the model parameters, THz line lists up to 3 THz have been compiled for both species: line positions (Unc.), level energies, and transition strengths  The databases will support astronomical studies: Orion surveys, HIFI on the Herschel Space Observatory, SOFIA, and ALMA Acknowledgements: Financial support from NSERC and CSA

10. Residuals (MHz) # of loops # of loop residuals greater than 200kHz => significantly increased If  i ~ 50 – 100 kHz, for a four line loop, then  ~ 100 - 200 kHz Loop Sum Checks Typos

11. UnitlessNB dataUnitlessNB data STD.DEV.1.035866561.395618911 # of PARA56+8(fixed) 81 RMS.DEV.MW1.19690.138 MHz11061.670.184 MHz3987 t = 0-01.13700.0937281.270.140 MHz2590 t = 1-01.54160.419552.530.567 MHz43 t = 1-11.25960.1283232.090.218 MHz1048 t = 2-12.700.539 MHz37 t = 2-22.620.187 MHz269 Wt = 0.050 MHz1.09130.055 MHz8921.770.088 MHz1890 Wt = 0.070 MHz1.190.083 MHz391 Wt = 0.080 MHz2.430.195 MHz104 Wt = 0.100 MHz1.42450.142 MHz1501.530.153 MHz1116 Wt = 0.200 MHz1.95720.391 MHz551.880.377 MHz411 Wt = 1.000 MHz0.88220.882 MHz90.620.621 MHz75 RMS.DEV.IR0.99520.00020 cm -1 55501.200.00033 cm -1 14924 t = 0-00.92240.00018 cm -1 11931.120.00023 cm -1 1615 t = 1-00.99100.00020 cm -1 33201.310.00026 cm -1 5917 t = 1-11.08510.00022 cm -1 10370.820.00029 cm -1 1574 t = 2-00000.970.00059 cm -1 2342 t = 2-10001.690.00059 cm -1 2867 t = 2-20001.760.00088 cm -1 609 CH 3 OH – previous work present work in progress  t = 0 and 1 (J max =20) t = 0, 1 and 2 (J max =30) to be updated Current data set has increased 4x

12.  SPIRE:Spectral and Photometric Imaging REceiver  PACS:Photodetector Array Camera and Spectrometer  HIFI:Heterodyne Instrument for the Far-Infrared (THz) (very high resolution & sensitive heterodyne spectrometer) Herschel Space Observatory – 2008 (there will be three instruments on board) HIFI Coverage (in GHz) (via Cascaded Frequency Multiplication) Band 1 2 3 4 5 6 Freq.480-640640-800800-960960-1,1201,120-1,2501,410-1,910 Small hole 0.5 THz 2 THz  A new spectrometer has been built at JPL based on new THz sources utilizing a number of technologies developed for the HIFI on the HSO and ALMA.  Methanol was one of the 1 st testing molecules on this new instrument. For expt. detail, Drouin, Waiwald, and Pearson, Rev. Sci. Instrum, 76, 093113 (2005).

13. UnitlessNB data STD.DEV.1.07217565 # of PARA79 RMS.DEV.MW1.20520.061 MHz550 t = 0-01.310.066 MHz366 t = 1-10.980.050 MHz154 t = 2-20.830.042 MHz30 Wt = 0.050 MHz1.210.061 MHz540 Wt = 0.100 MHz0.810.081 MHz10 RMS.DEV.IR1.0650.00033 cm -1 17015 t = 0-01.0120.00026 cm -1 2495 t = 1-01.0560.00023 cm -1 6226 t = 1-10.9150.00032 cm -1 2170 t = 2-11.1090.00039 cm -1 4421 t = 2-21.2240.00054 cm -1 1703 CH 3 18 OH ( t = 0, 1, 2, J max =30) – submitted to JMS Similar global fits have been carried out for: t max J max CH 3 OH:230 CH 3 18 OH:230 13 CH 3 OH:120 CH 3 OD:120 CD 3 OH:120 CD 3 OD:120 Model results allow generation of atlases of observed and predicted transitions with line positions, level energies and transition strengths calculated with the modeling parameters.

14. CH 3 OH & 13 CH 3 OH (1THz) On-Line Freq. Unc. Int. E” QN, etc. Critical to astronomy and astrophysics New Terahertz Database of CH 3 OH & CH 3 18 OH: up to 3 THz

15. K values V3V3 Methanol Torsion and Hamiltonian E tor = F + V 3 /2 (P a n1, P b n2, P c n3 ) Rotation 12 =1 12 =0 Torsion P  2n, (P a P  ) n, (1- cos3n  ) Torsional energy (cm -1 ) EAEA Non-linear  weighted datasets  multi-parameters least squares fit:  aim for experimental accuracy (RMS=1) Large Amplitude Torsion Very Flexible many distorsion terms (80-100 parameters for t =0, 1, 2) 12 =2