GLOBAL FIT ANALYSIS OF THE FOUR LOWEST VIBRATIONAL STATES OF ETHANE: THE 12  9 BAND L. Borvayeh and N. Moazzen-Ahmadi Department of Physics and Astronomy University of Calgary V.-H. HORNEMAN Department of Physical Sciences, University of Oulu, Finland

Ethane on Titan F.M. Flasar et al., Science 308 (2005).

Ethane on Saturn in emission F.M. Flasar et al., Science 307 (2005).

To retrieve reliable abundances from low resolution spectra:  Obtain a high-resolution laboratory spectrum of the band.  Obtain a good fit of the line positions (frequency model).  Measure intensities for selected lines.  Model the intensity.  Apply the frequency and intensity models to the whole band.

High Resolution spectrum of the 9 band at room temperature 9 9  4  4 9  2 4  2 4

High Resolution spectrum of the 9 band at T = 133 K 9 9  4  4

Resolution cm -1 Path Length 172 m Pressure 10 Torr Temperature 296 K The torsional bands N. Moazzen-Ahmadi et al., JMS (2001).

V 9 = 1 gs Two-band model Torsion-mediated Coriolis interaction Level crossing at K = 18 in the P branch N. Moazzen-Ahmadi et al., JCP (1999).

Three-band model D. Bermejo, et al., JCP (1992); N. Moazzen-Ahmadi, JMS (2002). Strong torsion-mediated Fermi interaction

The hot band  4 + Torsion

Difference between calculated (three-band model) and observed frequencies in the P branch J.R. Cooper and N. Moazzen-Ahmadi, JMS (2006).

The hot band  4 Interaction with v 12 =1

The hot band  4 12  9 band 12  9 band

PQ5PQ5 Wavenumber / cm -1 H2OH2O Resolution = cm -1, 15 Torr, 172 m

12  9 and 6  9 bands 12  9 and 6  9 bands Wavenumber / cm -1 RQ2RQ2 H2OH2O H2OH2O

The hot band  4 Four-band model

Comparison of simulated and experimental spectra using List3 line parameters

Ethane on Titan GEISA LIST3 List3 with abundance adjusted

Ethane on Titan GEISA LIST3 List3 with abundance adjusted

Ethane on Titan at high resolution

Effect of ethane on acetylene band

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  + 2  Torsional splitting in  4 due to internal rotation

Effect of skeletal bond vibration on the bath states Strong torsion-mediated Fermi interaction

Effect of skeletal bond vibration on the bath states Strong torsion-mediated Fermi interaction

Comparison of simulated and experimental spectra using List3 line parameters

The hot band  4

Summary Using results from a global analysis of data involving the four lowest vibrational states of ethane, we have generated a new set of line parameters which we have shown to provide much more accurate description of the experimental spectrum of ethane in the 12  m region. An isolated band analysis which often works in the case semi-rigid molecules is not appropriate in the case of ethane and ethane-like molecules. (1) The torsional mode is very low frequency and strongly anharmonic. (2) Torsion results in a high density of torsional bath states which mix strongly with the small amplitude vibrational fundamentals and dramatically alters the fine structure of the vibrational bands.

Torsional energy CH 3

Two-band model Change in the barrier height and shape, vibrational frequency,.....

Three-band model Change in the barrier height, vibrational frequency,.....

Torsional motion Near the bottom of the barrier Above the top of the barrier

C-C stretching fundamental A. Al-Kahtani et al., JCP (1993); D. Bermejo, et al., JCP (1992); N. Moazzen et al., JMS (2002).

The simplest molecule with internal rotation  Ethane is a benchmark molecule exhibiting internal rotation about a single bond.  The Hamiltonian describing the vibration-torsion- rotation for ethane is much simpler than that for a less symmetrical molecule.  As a result, much fewer interactions are allowed between the vibrational states.

To retrieve reliable abundances from low resolution spectra:  Obtain a high-resolution laboratory spectrum of the band.  Obtain a good fit of the line positions (frequency model).  Measure intensities for selected lines.  Model the intensity.  Apply the frequency and intensity models to the whole band.

 Torsional motion is strongly anharmonic.  It is also of much lower frequency than the remaining modes.  Torsion results in a high density of torsional bath states which mix strongly with the small amplitude vibrational fundamentals and dramatically alters the fine structure of the vibrational bands. Complications arising from large amplitude internal rotation Ground vibrational state Excited vibrational state Torsional sublevels

Complications arising from large amplitude internal rotation  An isolated band analysis which often works in the case semi-rigid molecules is doomed to failure in the case of ethane and ethane-like molecules.