Interaction of the hyperfine coupling and the internal rotation in methylformate M. TUDORIE, D. JEGOUSO, G. SEDES, T. R. HUET, Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM) UMR 8523 CNRS, Bât. P5, Université des Sciences et Technologies de Lille 1, 59655, Villeneuve d’Ascq Cedex, France L. H. COUDERT, LISA, CNRS/Universités Paris 12 et 7, 61 Avenue du Général de Gaulle, Créteil, France

b a  Molecules in interstellar media – identified in most of the cases thanks to preliminary laboratory studies Laboratory database for Herschel, Alma and Sofia 12 HCOO 12 CH 3 : Class 1molecule = weeds; “clean” the spectra of known molecules lines in order to detect new species Importance of isotopic species: they give information on the abundances-essential for the interstellar chemistry models MF 18 O : measurements up to 30 GHz (Curl, R.F. 1959, J. Chem. Phys., 30, 1529) New measurements of MF 18 O with FTMW spectrometer in Lille (2-20GHz) –hyperfine structure observed Test on the normal species MF Astrophysics and methylformate:

Performances of the Spectrometer 0.46 kHz Sampling 120 MHz  t = 8.33 ns Nmax.points = Example of transition of methylformate   t = ms either  = 0.46 kHz 3 12 – 3 03 (A) 15 kHz

Gas injection Detection Polarization Mirror displacement motor Gaussian envelop pump Resonant cavity and supersonic pulsed jet Spectral range : 1.7 – 20 GHz Sensibility : cm -1 Resolution : 10 kHz Precision : < 1 kHz Rot. Temp.:  1 K Pressures : Carrier gas: 1-3 bars Molecules: bar Scanning : 1GHz/12h Cavity Technical achievements of the new FTMW spectrometer d = 70 cm

Hyperfine structure is observed only for the A type lines. Methylformate: A and E lines in the 2 – 20 GHz spectral region A lines examples: E lines examples: « top » (CH 3 group) b a  r(1H-2H) = 1.77 Å r(2H-3H) = 1.78 Å r(1H-3H) = 1.78 Å

Representation of the nuclear spin function: The symmetry of nuclear spin functions and the associated total spin:  (  ns ) = 4A E a The HCOOCH 3 symmetry and the spin-spin interaction { (CH 3 ) The 8 nuclear spin functions given by the 3 H of CH 3 group {

 (  evRT )  = 0 A 1 A 2  =  1E  (  ns ) 4A 1 + 2E4A 1 (I=3/2) + 2E(I=1/2) 4A 1 + 2E 4A 2 (I=3/2) + 2E(I=1/2) 4A 1 + 2E 4E(I=3/2) + 2A 1 (I=1/2)+2A 2 (I=1/2)+2E(I=1/2)  (  tot ) g The HCOOCH 3 symmetry and the spin-spin interaction Pauli’s Principe: the permitted symmetries for the total wave function are A 1 or A 2 a Conclusion: - A associated to the total nuclear spin 3/2 Rotation-torsion levels: - E associated to the total nuclear spin 1/2

- A associated to the total nuclear spin 3/2 Rotation-torsion levels - E associated to the total nuclear spin 1/2 The spin-spin interaction is written as the scalar product of positions and nuclear spin tensors: a Conclusion: by considering 3 H atoms the spin-spin interaction is therefore zero for the E type lines and it appears only for the A type lines. The HCOOCH 3 symmetry and the spin-spin interaction K. Bahloul, PhD Thesis, Université Paris 7 – Denis Diderot 1997 (“Des Interactions Hyperfines et de la Conversion des Isomères de Spin Nucléaires de CH 3 F”)

Effective approach - PAM (Principal Axis Method)- SPFIT program b a  1 2 b a  1 2 3

Effective approach Purely geometrical parameter a The internal rotation has an influence on the hyperfine structure? The effective rotational constants are « contaminated » by the internal rotation. The internal rotation has an influence also on the centrifugal distortion for transitions with higher K - it manifests analogous to a fourth-order term introduced in the centrifugal distortion treatment.  A more appropriate model is needed! D.R. Herschbach, J. Chem. Phys. 31 (1959) D. Gerhard et al., J. Mol. Spectrosc. 220 (2003) J. E. Wollrab, Rotational Spectra and Molecular Structure, Academic Press, New York and London, 1967

L. COUDERT approach and IAM (Internal Axis Method) All the spin-spin interactions are considered: 1H, 2H, 3H, 4H The hyperfine Hamiltonian is written in a more suitable manner for symmetry considerations, and connected to the rotation-torsion wave function using first-order perturbation theory H sr = H sr (A 1 )·O sr (A 1 )+H sr (E a ) ·O sr (E a )+H sr (E b ) ·O sr (E b ) The spin-rotation interaction is considered without the non-diagonal terms A and E type lines are considered together Coudert and Lopez, J. Mol. Spectrosc. 239 (2006) 135 b a 

Preliminary results – L. COUDERT approach All the parameters values are fixed: The rotation parameters are fixed to the values resulting from the IAM fit of all the transitions from Ilyushin et al. JMS 2008 Spin-spin parameters –ab initio (J. Demaison) Spin-rotation parameters –ab initio (J. Demaison)

L. COUDERT approach: a fit will be done for the determination of spin- rotation tensors, which present a more important contribution for transitions having higher J and K a a Conclusion Effective fit (PAM): rotation fitted centrifugal distortion fitted + higher order spin-spin fitted for 3 H atoms of CH 3 top spin-rotation fixed to ab initio values Observed transition: 5 15 – 4 22 (A type) L. COUDERT approach: all parameters are fixed  Good agreement for the majority of transitions!

Acknowledgement GdR Specmo for financial support ANR All colleagues in the lab Thank you for your attention!