1. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 1 MEASUREMENT OF ROTATIONAL STATE- TO-STATE RELAXATION COEFFICIENTS BY RAMAN-RAMAN DOUBLE RESONANCE. APPLICATION TO SELF-COLLISIONS IN ACETYLENE. J. L. DOMENECH, R. Z. MARTINEZ AND D. BERMEJO Molecular Physics Department Instituto de Estructura de la Materia (CSIC) Serrano 123, 28006 Madrid, Spain

2. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 2 MOTIVATION Rotational energy transfer rates are relevant in a number of important problems: energy balance in astrophysical environments, non LTE problems, plasma diagnostics, pressure broadening of spectral lines, etc. Intermolecular PES are often validated by checking their ability to reproduce the state to state collision cross sections derived from the PES and some calculation (CC, CS, classical trajectories…). Experimentally, the state-to-state rates have been derived from: sound propagation measurements, crossed molecular beam scattering experiments, time evolution of non-equilibrium populations (double resonance experiments, free jet mapping), line-mixing and broadening measurements... Raman spectroscopy has provided a wealth of information.

3. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 3 MOTIVATION Pressure broadening and line-mixing of Raman spectra of polarized Q- branches are largely dominated by rotationally inelastic collisions (the polarizability tensor is not affected by elastic reorientations) The relationship between pressure broadening coefficients and state- to-state rate coefficients can be very simple in isotropic Raman Q- branches (within some assumptions): In principle, by an inversion procedure, the k’s can be obtained from the widths as a function of J. However, the number of unknowns is generally higher than the experimental data available, and it is necessary to resort to fitting and scaling laws that relate the rate coefficients to a smaller number of parameters (EGL, IOS, ECS,…)

4. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 4 MOTIVATION A more direct approach to obtain the state-to-state rates is to monitor the time evolution of non-equilibrium populations with rotational state resolution. Time-resolved pump-probe techniques have been widely used to address this type of problems: –Pump: IR absorption, Stimulated Raman effect –Probe: LIF, REMPI, IR absorption Our group has long experience in the measurement of collisional effects on high resolution Raman and IR spectra. We have also developed a Raman-Raman double resonance technique to record high resolution spectra from vibrationally excited states Could we use our Stimulated Raman techniques to obtain rotational energy transfer rates?

5. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 5 “Inverse Raman Spectroscopy”, aka Stimulated Raman Spectroscopy It is a particular case of Coherent Raman Spectroscopy (CARS, SRS, RIKES, SRGS, ASTERISK, …) Four EM fields couple through  (3), that becomes resonant when the frequency difference between any two of them matches a Raman allowed transition.  1  2  3  4 RR RR  1  2 Inverse Raman

6. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 6 Double resonance Raman-Raman spectroscopy of vibrationally excited states Ground state J J J 594 nm 591 nm 529 nm 3 2 1 0 3 2 1 0 3 2 1 0 Pump Spectroscopy V=2 V=1 532 nm

7. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 7 Ph.ACOUSTIC CELL Ar + Laser chopper 100  s Ring Dye Laser Nd:YAG PULSED DYE AMPLIFIER 11 22 Resolution 0.0025 cm -1 PULSED DYE LASER

8. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 8

9. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 9 JMS 209(2001)259

10. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 10 Raman-Raman double resonance with time resolution Ground state J J J 591 nm 3 2 1 0 3 2 1 0 3 2 1 0 Bombeo Espectroscopía V=2 V=1 532 nm Spectroscopy Ground state J J J 3 2 1 0 3 2 0 3 2 1 V=2 V=1 Virtual state Virtual state 1 0 Pump tens of ns If we pump a single level of v=1, and record spectra of v=2←v=1 at controlled time delays, (i.e. number of collisions) we can monitor the time evolution of the rotational populations, and obtain the state-to-state coefficients.

11. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 11 If there are no other gain (pumping is over), or loss mechanisms (vibrational relaxation, fluorescence, diffusion out of the probe volume), the change of population of a given level is due to rotationally inelastic collisions, and can be expressed: In matrix form, for all levels, applying the sum rule The number of unknowns can be reduced by the the detailed balance condition:

12. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 12 Experimental approach For acetylene at 150 K, we can observe up to J=21. Considering only the odd levels, there are 55 unknowns. Our approach is to record the populations of all accessible levels as a function of the time delay between pump and probe stages, and pump as many J levels in v=1 as possible. The integrated master equation (our fitting function) is: Eigenvectors of K Eigenvalues of K

13. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 13 Experimental Setup Stimulated Brillouin Scattering Pulse compressor

14. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 14 Experimental results SRS signal Probe PDA Pump SBS Pump PDA

15. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 15 Experimental results 400 ns 400

16. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 16 Experimental results: normalization

17. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 17 Experimental results

18. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 18 Experimental results

19. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 19

20. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 20 Experimental results: the matrix Units:  s -1 Torr -1 ; s.d. ~10 %

21. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 21 Experimental: comparison with linewidths

22. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 22 Experimental results: some caveats The work is in progress. There are still more measurements to do, specially to improve the observations when pumping on J=19, J=21. The fit has 9 x 25 x 11 = 2475 experimental data points, to determine 55 k’s. However, no restriction or scaling/fitting law has been imposed on the elements of the K matrix, other than detailed balance, sum rule and forcing the constants in columns J=19, J=21 to be positive The procedure implicitly assumes a structureless collision partner. Therefore the k’s are averages over the rotational levels of the collider (mostly ground state molecules)

23. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 23 Summary and future work We have developed an experimental technique based on SRS pump and SRS probe, able to monitor the evolution of rotational populations in vibrationally excited levels. The work is in progress but these preliminary results show the possibility of extracting state-to-state rate constants without resorting to scaling or fitting laws for acetylene at 150 K. Future work: –Improve the S/N in J=19, 21. Higher pressures, improve pulse compression. –Explore the possibility of obtaining the complete evolution within a single shot of the spectroscopy PDA. –Extensive comparisons with calculations and new self-broadening measurements. –H 2, both in self collisions and as collision partner.

24. 64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 24