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 John C. Pearson, Brian J. Drouin Jet Propulsion Laboratory, NASA, California Institute of Technology, Pasadena, CA USA 91109

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 THz: ±200 kHz Motivation = New JPL THz Measurements

 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.

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

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.)

Torsional-K-Rotational Energy Structure for CH 3 OH [cm -1 ] V 3 = 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

Overview of present work Region # of Lines weighted σ All MW v t = v t = v t = FTIR v t = 0,1, What are the weights???

This data set is very large = 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.

 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

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

UnitlessNB dataUnitlessNB data STD.DEV # of PARA56+8(fixed) 81 RMS.DEV.MW MHz MHz3987 t = MHz2590 t = MHz43 t = MHz1048 t = MHz37 t = MHz269 Wt = MHz MHz MHz1890 Wt = MHz MHz391 Wt = MHz MHz104 Wt = MHz MHz MHz1116 Wt = MHz MHz MHz411 Wt = MHz MHz MHz75 RMS.DEV.IR cm cm t = cm cm t = cm cm t = cm cm t = cm t = cm t = cm 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

 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 Freq ,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, (2005).

UnitlessNB data STD.DEV # of PARA79 RMS.DEV.MW MHz550 t = MHz366 t = MHz154 t = MHz30 Wt = MHz MHz540 Wt = MHz MHz10 RMS.DEV.IR cm t = cm t = cm t = cm t = cm t = cm 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: 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.

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

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 ( parameters for t =0, 1, 2) 12 =2