1. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Rotational Raman Spectroscopy of Ethylene Using a Femtosecond Time-Resolved Pump-Probe Technique Arnaud ROUZEE, Vincent BOUDON, Olivier FAUCHER and Bruno LAVOREL Laboratoire de Physique de l’Université de Bourgogne – CNRS UMR 5027, 9 Av. A. Savary, BP 47870, F-21078 DIJON, FRANCE E-mail : Vincent.Boudon@u-bourgogne.fr Web : http://www.u-bourgogne.fr/LPUB/tSM.html

2. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Aim and scope Show how a femtosecond time-resolved experiment can provide valuable spectroscopic data Extract molecular parameters from such data Carefully account for experimental conditions (pulse shapes, etc) to allow intensity analysis We consider a simple asymmetric top: ethylene (C 2 H 4 ) whose rotational Raman spectrum is obtained from a RIPS experiment.

3. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Outlook I.The RIPS experiment II.Analyis: Fit of line positions III.Analysis: Fit of line intensities IV.Conclusion and perspectives

4. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 I. The RIPS experiment

5. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Experimental set-up

6. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Raman-Induced Polarization Spectroscopy (RIPS) J J+2 J-2 J e e’ PROBE ANALYSER PUMP Es E LO  /4  = Pump-Probe delay

7. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Raman-Induced Polarization Spectroscopy (RIPS): general idea 0  (Pump-Probe delay) Transient realignments Recurrences Pump pulse Pump:Raman transition « launches » a rotational wavepacket at  = 0. A very small molecular alignment is produced. Probe: Small depolarization at each rephasing of the wavepacket, due to anisotropy.

8. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Heterodyne signal Heterodyning the signal with a local oscillator: (This is obtained thanks to a birefringent plate on the probe path) Obtaining the heterodyne signal: (Through the difference between two experiments with opposite sign of local field) with: For Fourier transform limited Gaussian pulses: ~~ ~~~

9. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Time-domain spectrum J-type transients:  J = ±1, ±2,  K = 0,period 1/2(B+C) = 9.1 ps C-type transients:  J = 2,  K = 2,period 1/4C = 10.06 ps P = 250 mb T = 293 K

10. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Fourier transform of temporal trace: Wavenumber-domain spectrum Resolution ≈ 0.083 cm -1

11. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 II. Fit of line positions

12. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Model using the O(3)  D 2h group chain y = B x = A z = C III r representation Basis set: Tensorial Hamiltonian:

13. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Results of line position fit Watson’s A-reduction Order  (K g,n  g ) Value / cm -1 02(0 g,0A g )2.230812(48) 2(2 g,0A g )0.8063170174* 2(2 g,1A g ) 3.0568(26)  10 -2 24(0 g,0A g ) -2.265(14)  10 -5 4(2 g,0A g ) 7.456236198  10 -6 * 4(2 g,1A g ) 5.26(11)  10 -7 4(4 g,0A g ) -2.412(51)  10 -6 4(4 g,1A g ) -6.787767391  10 -7 * 4(4 g,2A g )0.0* Statistics: 170 data, Jmax = 33, RMS = 0.017 cm -1 * Fixed Residuals Undetermined parameters fixed from: T. L. Tan, S. Y. Yau, P. P. Ong, K. L. Goh and H. H. Teo, J. Mol. Spectrosc., 203, 310 (2000).

14. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Experiment vs. Simulation: overview

15. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 III. Fit of line intensities

16. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Intensity calculations Laboratory-fixed frame component of the polarizability Expression in terms of molecule-fixed frame components Stimulated Raman intensity ~ Multiplication by the pump and probe autocorrelation factor ~~~ ~ ~ ~

17. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Finding the convolution factor width Optimum:  = 185 cm -1 (112.5 fs)

18. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Results of intensity fit Order (Lg,ng)(Lg,ng) Value / Å 3 Type 0t 1 = (0 g,0A g )Undetermined Iso.,  K = 0 t 2 =(2 g,0A g )1.2610(75) Aniso.,  K = 0 t 3 =(2 g,1A g )0.272(41) Aniso.,  K = ±2 R = t 3 /t 2 = 0.211(33) Statistics:41 data,J max = 22,RMS = 7.2 % Residuals From the spontaneous Raman spectrum: R = 0.22(3) G. W. Hills and W. J. Jones, J. Chem. Soc. Faraday Trans. II, 71, 812 (1975).

19. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Experiment vs. Simulation (1)

20. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Experiment vs. Simulation (2)

21. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Experiment vs. Simulation (3)

22. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Rotational energy levels Calculated and observed energy levels Classically: J = 33

23. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 IV. Conclusion and perspectives

24. 60th Ohio State University Symposium on Molecular Spectroscopy June 20–24, 2005 Conclusion Perspectives The temporal trace of the RIPS experiment can be viewed as an interferogram Its Fourier transform is identical to a stimulated Raman spectrum multiplied by a Gaussian (pump and probe autocorrelation factor) Quick method to record wide-range high-resolution Raman spectra! Application to other molecules Study of the alignment of ethylene using intense laser pulses