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, FranceL. H. COUDERT, LISA, CNRS/Universités Paris 12 et 7, 61 Avenue du Général de Gaulle, 94010 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

• 12HCOO12CH3: 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 18O : measurements up to 30 GHz (Curl, R.F. 1959, J. Chem. Phys., 30, 1529)

• New measurements of MF 18O 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 = 262144

Example of transition of methylformate

t = 2.18453 ms either = 0.46 kHz

312 – 303 (A)

15 kHz

Gas injection

DetectionPolarization Mirror

displacement motor

Gaussian envelop

pump

Resonant cavity and supersonic pulsed jet

Spectral range : 1.7 – 20 GHz

Sensibility : 10-11 cm-1

Resolution : 10 kHz

Precision : < 1 kHz

Rot. Temp.: 1 K

Pressures :Carrier gas: 1-3 barsMolecules: 10-2 bar

Scanning : 1GHz/12h

Cavity

Technical achievements of the new FTMW spectrometer

d =

70

cm

4551,90 4551,95

Frequency (MHz)

523 - 524 (A)

8577,45 8577,50 8577,55

Frequency (MHz)

624 - 625 (A)

10718,55 10718,60

Frequency (MHz)

624 - 533 (A)

4549,72 4549,76

Frequency (MHz)

523 - 524 (E)

8570,70 8570,75

Frequency (MHz)

624 - 625 (E)

10773,1 10773,2

Frequency (MHz)

624 - 533 (E)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 »(CH3 group)

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r(1H-2H) = 1.77 Å

r(2H-3H) = 1.78 Å

r(1H-3H) = 1.78 Å

Spin-spin parameter (kHz) 1H-2H 2H-3H 1H-3H Daa 21.68 -11.16 -11.16 Dbb 21.68 5.64 5.64 Dcc -43.36 5.52 5.52 Dab 0.00 22.32 22.32 Dac 0.00 -22.44 22.44 Dbc 0.00 15.48 -15.48

Representation of the nuclear spin function:

The symmetry of nuclear spin functions and the associated total spin:

,,

,,

(ns) = 4A1 + 2 E

The HCOOCH3 symmetry and the spin-spin interaction

{(CH3)

The 8 nuclear spin functions given by the 3 H of CH3 group

{A1A11-3/2

EA1A1 + E3-1/2

EA1A1 + E31/2

A1A113/2

I = 1/2I = 3/2SymmetryNb. Spin

functionsMI

A1A11-3/2

EA1A1 + E3-1/2

EA1A1 + E31/2

A1A113/2

I = 1/2I = 3/2SymmetryNb. Spin

functionsMI

(evRT)

= 0 A1

A2

= 1 E

(ns)

4A1 + 2E 4A1(I=3/2) + 2E(I=1/2)

4A1 + 2E 4A2(I=3/2) + 2E(I=1/2)

4A1 + 2E 4E(I=3/2) + 2A1(I=1/2)+2A2(I=1/2)+2E(I=1/2)

(tot) g

4

4

4

The HCOOCH3 symmetry and the spin-spin interaction

Pauli’s Principe: the permitted symmetries for the total wave function are A1 or A2

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 3/2Rotation-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: 22 IBH HHHH

ss

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.

02/12/1 2 IHH

2152/32/3 2 IHH

The HCOOCH3 symmetry and the spin-spin interaction

5

22

02 3

4 R

RRRgB jiijN

Hij

K. Bahloul, PhD Thesis, Université Paris 7 – Denis Diderot 1997 (“Des Interactions Hyperfines et de la Conversion des Isomères de Spin Nucléaires de CH3F”)

)21( ssdrA HHHH

srssdrA HHHHH )31,32,21(

Effective approach - PAM (Principal Axis Method)- SPFIT program

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2

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4589,84 4589,88

Frequency (MHz)

515 - 422 (A)

16047,9 16048,0

Frequency (MHz)

413 - 414 (A)

4589,84 4589,88

Frequency (MHz)

515 - 422 (A)

16047,85 16047,92 16047,99

Frequency (MHz)

413 - 414 (A)

Effective approach

22 IBH HHHHss

5

22

02 3

4 R

RRRgB jiijN

Hij

Purely geometrical parameter

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) 91-107

D. Gerhard et al., J. Mol. Spectrosc. 220 (2003) 234-241

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

Hsr = Hsr(A1)·Osr(A1)+Hsr(Ea) ·Osr(Ea)+Hsr(Eb) ·Osr(Eb)

• 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

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4

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)

Spin - rotation tensor (kHz) 1H 2H 3H 4H Caa -1.8 -1.8 1.0 -0.9 Cbb -0.4 -0.4 -0.7 0.3 Ccc 0.0 0.0 -0.6 -0.4

• 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 Ka

Conclusion

Effective fit (PAM): rotation fitted

centrifugal distortion fitted + higher order

spin-spin fitted for 3 H atoms of CH3 top

spin-rotation fixed to ab initio values

Observed transition: 515 – 422 (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!