64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 1 MEASUREMENT OF ROTATIONAL

64th OSU International Symposium on Molecular SpectroscopyJune 22-26, 2009

José Luis DoménechInstituto de Estructura de la Materia

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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



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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.

, ,(v ) (v ) ; with rate constant f iX J i M X J f M k



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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,…)

'

(v, v ', ') 12 2

upperlowerj i j i

j i j i

J i J i P k kc



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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?



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“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

1 2Inverse Raman



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Double resonance Raman-Raman spectroscopy of vibrationally excited states

Groundstate

J

J

J

594 nm

591 nm529 nm

3210

3210

3210

Pump Spectroscopy

V=2

V=1

532 nm



8



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Raman-Raman double resonance with time resolution

Groundstate

J

J

J

591 nm

3210

3210

3210

Bombeo Espectroscopía

V=2

V=1

532 nm

Spectroscopy

Groundstate

J

J

J

32

1

0

32

0

321

V=2

V=1

Virtualstate

Virtualstate

1

0Pump

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.



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• 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:

(2 1)exp

(2 1)i fi

f i i ff

E EJk k

J kT

f f i fi f

k k

f f i i i f fi f i f

dN k N Pdt k N Pdt



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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



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Experimental Setup

Stimulated Brillouin

ScatteringPulse compressor



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Experimental results

SRS signal

Probe PDA

Pump SBS

Pump PDA



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-5 0 5 10 15 20 25 30 35-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

time / ns

sign

al /

mV

C2H

2, Pump J=7, 150 K, 1 mbar

probe J=7

probe J=3

400 ns

400



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Experimental results: normalization



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18




19

5 10 15 20 25 30-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

time / ns

rela

tive

po

pu

latio

ns

Pump J=1, 150 K, 1 mbar

1

3

5

7

9

11

13

15

17

19

21



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Experimental results: the matrix

Ji

Jf

1 3 5 7 9 11 13 15 17 19 21

1 -55.26 10.83 4.97 3.20 2.68 1.64 0.83 0.45 0.10 0.10 0.10 3 22.58 -48.19 13.45 6.91 4.82 3.56 3.14 2.06 0.36 0.10 0.10 5 13.32 17.27 -47.94 14.90 7.49 6.08 4.71 3.83 3.58 0.99 0.10 7 8.74 9.03 15.17 -48.90 14.67 9.51 7.10 5.83 1.99 1.08 0.10 9 6.32 5.45 6.59 12.68 -46.38 12.82 8.00 6.74 4.37 3.06 0.10 11 2.93 3.04 4.05 6.22 9.69 -45.47 10.76 8.02 5.79 1.62 0.10 13 1.00 1.80 2.10 3.11 4.05 7.21 -43.57 11.21 7.10 0.10 0.10 15 0.32 0.70 1.02 1.53 2.04 3.22 6.71 -45.33 13.31 0.10 0.10 17 0.04 0.07 0.51 0.28 0.71 1.25 2.29 7.17 -52.74 24.30 20.27 19 0.02 0.01 0.07 0.07 0.24 0.17 0.02 0.03 11.80 -31.49 0.10 21 0.01 0.00 0.00 0.00 0.00 0.01 0.01 0.01 4.33 0.04 -21.17

Units: s-1Torr-1; s.d. ~10 %



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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)



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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.– H2, both in self collisions and as collision partner.

Documents

64th OSU International Symposium on Molecular Spectroscopy June 22-26, 2009 José Luis Doménech Instituto de Estructura de la Materia 1 MEASUREMENT OF ROTATIONAL