1. PUMP-PROBE MEASUREMENTS OF ROTATIONAL ENERGY TRANSFER RATES IN HBr + HBr COLLISIONS M. H. Kabir, I. O. Antonov, and M. C. Heaven Emory University Department of Chemistry Atlanta, GA 30322 63 rd Ohio State University International Symposium on Molecular Spectroscopy June 16 - 20, 2008

2. MOTIVATION  Detailed knowledge of collision-induced rotational energy transfer kinetics of HBr : quantum state populations for laser modeling.  HBr has been demonstrated to lase near 4  m region.  Provide test of fitting and scaling laws in modeling long range attractive potential in HBr-HBr. W. Rudolph et al. IEEE J. Quant. Elec. 40, 1471 (2004).  The development of high-power lasers using Fiber and Diodes are currently limited by material damage and heat dissipation.

3. PREVIOUS STUDY k =1.5x10 -11 cm 3 s -1 3. Leone et al. JCP 69, 5319 (1978): Isotopic resonant V-V transfer 1. Chen et al. CPL 17, 500 (1972): V-V transfer k =2.97 x10 -12 cm 3 s -1 k =1.78 x10 -14 cm 3 s -1 2. Chen et al. JCP, 55, 5551 (1971): V-T transfer

4. Pump-probe Double Resonance Scheme v” = 0, J” v’ =1, J’ X 1  + g 3  - (0 + ) v = 0, J Pump: Stimulated Raman Scattering Probe: (2+1) REMPI Ionization level Collision-induced population evolution Energy (cm -1 ) 75378 2559 0 pp ss HBr + + e - HBr(v’ =1, J’)+ HBr (v” =0)  HBr (v’ =1, J’+  J’)+ HBr (v” =0)  HBr(v” = 0, J+  J) + HBr (v” =0)

5. Experimental Setup Nd:YAG laser 532 nm HBr CARS Cell Delay Generator Dye laser Nd:YAG laser 355 nm Dye laserSHG Filter PMTPMT MCMC HV Pre-amp Oscilloscope Computer Delay line HBr REMPI cell Dichroic mirror ~274 nm, ~1 mJ 4 mJ 532 nm, 10 mJ ~ 615 nm + - C

6. CARS Spectrum of HBr: Q-branch (1-0) transition Isotopic abundance: H 79 Br (50.5%) and H 81 Br (49.5%) pp ss pp 2  p -  s =  CARS CARS energy scheme v=0 v=1

7. 2 + 1 REMPI Spectra & Line Strengths Q-branch of the g 3  - –X 1  + (0-0) transition Q-branch of the g 3  - –X 1  + (0-1) transition

8. Total Removal Rate Measurement

9. Total removal rate constants Hanson et al. : JMS 200, 138 (2000) Pressure broadening coefficient  [P(2)]:118.3 x10 -3 cm -1 /atm  [R(7)]: 87.9 x10 -3 cm -1 /atm Our expt.  (1,2): 64.7 x10 -3 cm -1 /atm  (8,7): 36.9 x10 -3 cm -1 /atm

10. 2+1 REMPI spectrum of the g 3  - –X 1  + 0-1 band What this Figure tells us ? 1. Relative peak intensity tells: propensity for  J = ±1 >  J = ±2 >  J=±3. Multiquantum transitions: higher order multipole interactions 2.Population in the  J = ±2 and  J=±3 levels: direct population transfer and multiple  J = +1 or –1 steps. Neglecting multiple inelastic collisions Single collision limit !! Experimental (raw): 29 rate constants

11. Fitting Laws Exponential Energy Gap law (EGL): Statistical Power Gap Law (SPGL): Modified Exponential Gap Law (MEG): Only consider energy dependence of rate constants

12. Scaling Laws Energy Corrected Sudden Power (ECS-P) law: Angular Momentum & Energy Corrected Sudden (AECS) law: Rate constants dependence on transferred angular momentum

13. State-t0-State Rate Constants k x 10 -10 cm 3 s -1

14. 3D PLOTS OF MATRICES OF RATE CONSTANTS a) MEGb) EG c) SPEG d) ECS-Pe) AECS

15. SIMULATION Master Equation approach: models the evolution of individual level populations Diffusional loss out of the probe laser volume at the focal point Loss process:

16. Kinetic Traces: Experiment & Simulation J i = 3, J f = 1- 6

17. Kinetic Traces: Experiment & Simulation J i = 5, J f = 2- 6

18. Spectral Traces: Experiment & Simulation

19. Comparison of State-to-State Rate Constants

20. Comparison of Rate Constants: Experiment & Fitting Laws

21. Contributions of  J Transitions in Population Removal First order (  J = ±1) transitions : dipole-dipole interactions Multiquantum transitions (  J = ±2,  J=±3 …... ): dipole-quadrupole interactions or quadrupole-quadrupole interactions.

22. Contributions of  J Transitions: Other’s report G.D. Hager et al. JCP 21, 9281(2002) D. Chandler et al. JCP 87, 5229(1987)

23. SUMMARY  Time-resolved pump-probe measurements were used to examine HBr + HBr RET within the HBr v =1 rotational manifold for the first time.  State-to-state rate constants matrix for HBr + HBr collisions generated using fitting and scaling laws.  Largest state-to-state rate constants were found for  J =  1 transitions.  Measured total rate coefficients were found pretty close to the self-collisional pressure broadening coefficients.  ECS-P law provided a physically reasonable intermolecular interaction length, l c = 4.0  0.1 Å (Lennard-Jones diameter for HBr is 3.35 Å) which is close to the value (4.1 Å) of equilibrium intermolecular distance of (HBr) 2.  Flow of energy in HBr+HBr collisions is dominated by both the anisotropy of the long range intermolecular potential and the internal rotational level structure.