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 rd Ohio State University International Symposium on Molecular Spectroscopy June , 2008

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.

PREVIOUS STUDY k =1.5x cm 3 s 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 x cm 3 s -1 k =1.78 x cm 3 s Chen et al. JCP, 55, 5551 (1971): V-T transfer

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 ) 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)

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

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

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

Total Removal Rate Measurement

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

2+1 REMPI spectrum of the g 3  - –X 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

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

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

State-t0-State Rate Constants k x cm 3 s -1

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

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:

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

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

Spectral Traces: Experiment & Simulation

Comparison of State-to-State Rate Constants

Comparison of Rate Constants: Experiment & Fitting Laws

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.

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

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.