Collisional Energy Transfer of Highly Vibrationally Excited Molecules

Chapter 18

Downloaded by UNIV OF ARIZONA on January 11, 2013 | http://pubs.acs.org Publication Date: June 10, 1997 | doi: 10.1021/bk-1997-0678.ch018

Collisional Energy Transfer of Highly Vibrationally Excited Molecules: The Role of Long-Range Interaction and Intramolecular Vibronic Coupling Hai-Lung Dai Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104-6323 In the experimental study of collisional energy transfer of highly vibrationally excited molecules (1, 2), several techniques have been developed and applied to monitoring the energy content of either the highly excited energy donor or the energy receiving bath molecules. The highly excited molecules are often prepared with electronic excitation followed by internal conversion (3) or with multiple resonance techniques such as Stimulated Emission Pumping (4). The probe techniques include thermal lensing (5), photoacoustic (6), Doppler width measurement, diode laser transient absorption spectroscopy (2), optical absorption (7, 8) and ionization (9), laser induced fluorescence (4), sensitized chemical reaction (10) and IR emission (11). The IR emission from vibrationally excited molecules can in principle be used to reveal the rovibrational energy content of both the energy donating and receiving molecules. This can be best achieved if the IR emission is detected with sufficient frequency and time resolution so that the energy content of the emitting molecules during a collisional relaxation process can be continuously monitored. The average energy and energy distribution of the highly excited molecules can then be directly extracted from the time -resolved IR emission spectra. Time-Resolved F T I R Emission Spectroscopy We have recently developed a Time-Resolved Fourier Transform Emission Spectroscopy (TR-FTIRES) technique based on a step-scan FTIR spectrometer (72). This technique affords the ability for acquiring emission spectra in the IR and near-IR region with 50 ns (presently limited by detector response time and excitation laser pulse width) time-resolution for the study of collisional deactivation of highly vibrationally excited molecules. In TR-FTIRES, a Fourier transform spectrometer is coupled to a fast IR detector/transient digitizer system to temporally and spectrally resolve IR emission from a pulsed laser excited sample. The attributes of TR-FTIRES, in addition to the fast time resolution, are fine spectral resolution («0.1 cm" in principle), wide spectral range covering the mid- and near-IR regions, and high sensitivity due to the multiplex detection and throughput advantages of FT spectrometers. By using TR-FTIRES the complete time evolution of all IR active vibrational modes can be monitored at high spectral resolution in a single experiment (75). Using the TR-FTIRES technique we have examined the collisional energy transfer of N 0 (excited to as high as 22,000 cm" ) (75-75 and G. V. Hartland et al., / . 1

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© 1997 American Chemical Society In Highly Excited Molecules; Mullin, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1997.

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Chem. Phys. submitted), S 0 (32,000 cm ) (75, 76, and D. Qin et al.. / . Phys. Chem. submitted), C S (32,000 cm ) (75, 76), and pyrazine (40,000 cm ) (76) to a variety of collisional partners, ranging from inert gases to aromatic molecules. In the experiments, all the highly excited molecules are prepared through photoexcitation of an electronic transition followed by internal conversion, which proceeds with or without the assistance of collisions. The time resolved FTIR emission spectra following the (25 ns FWHM) laser pulse excitation of N 0 at 21,050 cm' is shown in Figure 1. Emission from all the IR active modes has been detected. All emission peaks are shifting towards blue with time (by as much as 300 cm" for the N 0 v peak), indicating that the emitting molecules are relaxing from the highly excited, anharmonic levels to the lower energy, more harmonic ones during collisional quenching. Through spectral simulation (see below), the profile of the energy distribution is extracted. Figure 2 shows that the distribution of the ensemble of excited molecules during collisional deactivation can be well described by a Gaussian function as stipulated by many workers in this field. The average energy, , as a function of time can be extracted, and the energy transferred per LennardJones collision, , of the excited molecules can then be determined. 2

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Analysis of the IR Emission Spectra Simulation of the emission spectra from the highly excited molecules was done by using the following assumptions/principles: 1) The energy of all the vibrational levels are calculated using the experimentally determined vibrational constants. The N O , vibrational constants, for example, have been determined by Jost and coworkers (77) from assigned vibrational levels up to about 10,000 cm" . 2) Emission intensity from levels containing IR active mode quantum numbers is calculated according to the experimentally measured absorption intensity with scaling to vibrational quantum number according to the harmonic oscillator model. 3) Isoenergetic levels are assumed to have the same population. This statistical model is justified because of the rapid intramolecular vibrational relaxation and the high vibrational level densities at high energies. Fast IVR ensures that nearby molecular eigen levels have similar vibrational characters. High density of the levels favors a rapid equilibration of population of nearby vibrational levels during collisional deactivation. 4) An arbitrary functional form is used for describing the excited molecules' energy distribution at any given time during the deactivation process. It is shown that this distribution can be best described by a Gaussian function (C. Pibel, E. Sirota, and H . L . Dai, to be published). A second Gausian function is used to describe the molecules at lower vibrational levels populated by V - V transfer or Franck-Condon pumping. An example of simulated spectrum of N 0 emission is shown in Figure 3. The average energy of the excited Gaussian population as a function of time, which is directly proportional to the number of collisions, is obtained. The derivative of this curve gives the average amount of energy removed per collision, , as a function of , which is shown for the case of N 0 quenching by C 0 in Figure 4, and N 0 and C S by a variety of colliders in Figure 5. 1

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Observations That Point to the Importance of Long Range and Intra-Molecular Vibronic Coupling

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Among the many interesting observations are the ones that seem to arise because of intramolecular vibronic couplings occuring at high energies of the excited molecule. These particular observations, in combination with some previous works on this subject (75), appear to point to a somewhat surprising revelation that the mechanism

In Highly Excited Molecules; Mullin, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1997.

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Wavenumbers Figure 1. Selected FT emission spectra, recorded with a -10 ns response time IR detector, from a sample of 1 Torr NO^ excited by a 475 nm, ~1 mJ laser pulse. The baseline of each spectrum is marked on the abscisca.



Figure 2. Energy distribution of excited N0 in collisional quenching with ambient NO^. The points are obtained without assuming any functional form. The solid line is a Gaussian function and the dashed line Lorentzian. 2



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Figure 4. Energy transfer probability from N 0 excited at to the v = l C 0 level. Solid line is calculated from the transition dipole model. Dashed line and the point are extracted from measurements by Flynn and coworkers (79). (Adapted from Ref. 14) 2

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(cm-i)

Figure 5. - curves of excited N 0 and C S quenched by collision partners noted in the figure. The origin of the lowest, optically detected electronic excited states are marked; A and Β states for N 0 and the R state for C S . (Reproduced with permission from Ref. 15. Copyright 1995, American Institute of Physics.) 2

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responsible for energy transfer of highly excited molecules, in contrast to those excited at lower energies, is dominated by long range, Coulombic interactions. These observations are: Transition Dipole Coupling. Whenever we could quantitatively (in relative magnitude) test the V - V transfer probability, we have found that the transition-dipole coupling model works well. In this model, the donor molecule would make a downward transition while the receiver molecule makes an upward transition in energy during the collision. The probability of energy transfer is then proportional to the square of the downward and upward transition dipoles multiplied together. The receiver molecule defines the energy of the transition. Its transition dipole can be obtained from the conventional absorption spectrum of the receiver molecule. The downward transition dipole of the highly excited donor molecule, on the other hand, can be extracted (in relative magnitude as a function of the donor energy) from the emission intensity at the energy defined by the receiver. This emission intensity is registered in the emission spectra recorded in our experiment. So from our experimental emission spectra we could calculate the relative magnitude of energy transfer probability to a particular receiver vibrational mode as a function of the donor excitation energy. One example of this test is shown in Figure 4. The solid line is the calculated probability of energy transfer per Lennard-Jones collision from highly excited N 0 to the v = l level of C 0 as a function of the N 0 energy. The calculation is done with the transition-dipole coupling model and the N 0 IR emission spectra. An excellent comparison is made against the experimental measurements from Flynn and coworkers (79) who used the diode laser absorption spectroscopy to measure the C 0 v = l population. The importance of the transition dipole mechanism has been pointed out by several investigators on this subject previously (see for example Refs. 19-21). For energy transfer out of the vibrational levels in the low energy region, the dorninant contribution of the transition dipole interaction has been alluded to for situations where the energy gap is small (27). For the highly excited molecules, the high density of states will relax the resonant conditions for V-V energy transfer (small energy gap), thus, it is consistent that the transition dipole coupling mechanism appears to work. 2

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Threshold in and Intramolecular Vibronic Coupling. For a few excited molecules such as N 0 and C S that have known strong vibronic coupling at high energies, appears to increase dramatically with as the energy exceeds a threshold energy, Figure 5 (75). The threshold for a specific excited molecule is always at the same value for all collision partners and correlates well with the beginning of vibronic coupling within the excited molecule. Similar threshold behavior has also been observed in V-T transfer studies by Barker and coworkers (22). This threshold behavior may also be understood through the transition dipole coupling model (75, and G. V. Hartland et al., / . Chem. Phys., submitted). In energy regions where strong vibronic coupling occurs, the highly excited vibrational levels of the electronic ground state are mixed in with the excited electronic states, i.e. the molecular eigenlevels at high vibrational energies contain excited electronic state characters. The downward transition from the highly excited donor molecule in this energy region may have its transition dipole enhanced due to the electronic character. The transition dipole may have electronic transition contribution in addition to the vibrational transition dipole. Consequently the energy transfer probability increases. The enhanced transition dipole in the post-threshold energy region is evidenced by the broad band emission peaks over wide wavelength range for both excited N 0 and C S (75). I For molecules that do not have strong vibronic coupling, such as pyrazine, the threshold behavior does not show up in the - relationship. In terms of the 2

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magnitude of matrix element, vibronic coupling in pyrazdne is a few orders of magnitude smaller than the triatomics. Here, energy transfer from pyrazine excited with 10,000 to 40,000 cm" does not show any threshold behaviour. The increase in with appears to be linear (76) despite the fact that there are several excited electronic states within this energy range. But even here the transition dipole coupling model appears to be at least semi-quantitatively correct In fact, in the pyrazine-pyrazine energy transfer the vibrational distribution of the energy receiving pyrazine molecules appears to be non-statistical which can be rationalized by the transition dipole coupling model (76).


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Mass Effect vs. Polarizability. Even though the SSH theory (23) gives a qualitatively accurate description of the observed V-T transfer probabilities for molecules excited at lower vibrational energies, in the post threshold energy region, it does not appear to be adquate for understanding the observed energy transfer behaviour. For N 0 excited below 10,000 cm* the lighter inert gas collider is more effective in relaxing the N 0 vibrational energy. Here the per collision is on the order of 1 cm* . For N 0 molecules excited at much higher energies, i.e. above 10,000 cm' , by inert gases increased to 10 c m . Also, it seems that in this post threshold regime the efficiency of the collisional partner is no longer solely correlated with its mass (G.V. Hartland et al., J. Chem. Phys., submitted and C. Pibel et al., to be punlished). Ar is about as effective as X e and both are much more effective than He for relaxing N 0 . Polarizability appears to play a role in collisional efficiency. It has been suggested in the above that the transition dipole involved in the energy transfer mechnism for a highly excited molecule is much stronger in the postthreshold energy region because of intramolecular vibronic coupling. Based on this, we speculate that for a colliding partner with large polarizability, the non-repulsive contribution to V-T transfer can no longer be ignored. The S S H model is based primarily on the repulsive part of the inter-molecular potential. Its effectiveness is anticipated for V-T transfer involving low energy vibrational levels where the energy gap is large. But for the highly excited vibrational levels with high level density where the energy gap in V-T transfer is small and where the transition dipole is stronger, contributions from long range Coulumbic interactions should be included in our consideration. 1

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Concluding Remarks The above observations, combined with observations made in other laboratories, have pointed to a seemingly non-intuitive mechanism for energy transfer out of a highly excited molecule: the large amount of energy transferred, either through V - V or V-T/R channels, to an ambient collider is through a long range, Coulombic type interaction. In this mechanism vibronic couplings at high energies will greatly accelerate the energy transfer, likely through an increase in the transition dipole of the excited molecule. With this possibility in mind, many questions now await to be answered.We would like to know in general how would the long range interaction channel compare quantitatively with the short range impact force induced energy transfer? Can the long range interaction mechanism involving vibronic coupling be able to provide a rationalization for the 'super collisions' where in one collisional encounter tens of thousands of wavenumber energy is transferred (24)1 We are planning experiments using the TRFTIRES on molecules with known vibronic coupling strength to further test our understanding on energy transfer from highly excited large molecules. On the theoretical front, in addition to classical trajectory calculations based on repulsive potentials (25), quantum or semi-classical calculations with realistic electrostatic coupling potentials involving the electronically excited states need to be performed for comparison.


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Acknowledgments: This work is supported by the Basic Energy Sciences of the U . S . Department of Energy through Grant No. DE-FG02-86ER134584 and a U . S . Department of Energy University Instrumentation Grant Support from the Department of Advanced Technology of the Brookhaven National Laboratory is also acknowledged. The author is grateful to Professor Gregory Hardand, Dr. Dong Qin, Professor Charles Pibel, and Mr. Egor Sirota for their contribution to this work. Literature Cited 1. I. Oref and D. C. Tardy., Chem. Rev., 1990, 90, 140. 2. R.E. Weston, Jr. and G. W. Flynn, Annu. Rev. Phys. Chem. 1992, 559. 3. a). R. Atkinson, and B.A. Thrush, Chem. Phys. Lett., 1969, 3, 684. b). H. Hippler, K. Luther, J. Troe, and R. Walsh, J. Chem. Phys., 1978, 68, 323. 4. X. Yang, J.M. Price, J.A. Mack, C.G. Morgan, C.A. Rogaski, D. Mcguire, Ε. H. Kim, and A. M. Wodtke, J. Phys. Chem.,1993, 97, 3944. 5. a). D.R. Siebert, and G.W. Flynn, J. Chem. Phys., 1974, 60, 1564. b). B.M. Toselli, T.L. Walunas, and J. R. Barker, J. Chem. Phys., 1990, 92, 4793. 6. a). A. Karbach and P. Hess, J. Chem. Phys., 1986, 84, 2945; b). K . M . Beck and R.J. Gordon, J. Chem. Phys., 1987, 87, 5681. 7. H. Hippler and J. Troe, in Bimolecular collisions, Boggort, J.E. and Ashford, M.N.R., Eds.; The Royal Society of Chemistry, London, 1989. 8. T.J. Bevilacqua and R.B. Weissman, J. Chem. Phys. 1993, 98, 6316. 9. H.G. Lohmannsroben and K. Luther, Chem. Phys. Lett. 1988, 144, 473. 10. S. Hassoon, I. Oref, and C. Steel, J. Chem. Phys. 1988, 89, 1743. 11. J. R. Barker and Β. M. Toselli, Int. Rev. Phys. Chem., 1993, 12, 305. 12. G. V. Hartland, W. Xie, and H.L. Dai, A. Simon, and M. J. Anderson, Rev. Sci. Instrum. 1992, 63, 3261. 13. G.V. Hartland, D. Qin, and H.L. Dai, J. Chem. Phys., 1994, 100, 7832. 14. G.V. Hartland, D. Qin, and H.L. Dai, J. Chem. Phys. 1994, 101, 8554. 15. G.V. Hartland, D. Qin, and H.L. Dai, J. Chem. Phys., 1995, 102, 8677. 16. D. Qin, Ph.D. Thesis, University of Pennsylvania 1996. 17. a) A. Delon and R. Jost, J. Chem. Phys. 1991, 95, 5686; b) A. Delon, R. Jost, and M. Lombardi, J. Chem. Phys. 1991, 95, 5701. 18. a) A.S. Mullin, C.A. Michaels, G.W. Flynn., and R.E. Weston, J. Chem. Phys. 1993, 175, 53. b)C.A.Michaels, A.S. Mullin., and G.W. Flynn., J. Chem. Phys., 1995, 102, 6682. 19. a) J.Z. Zhou, S.A. Hewitt, J.F. Hershberger, B.B. Brady, G.B. Spector, L. Chia, and G.W. Flynn, J. Chem. Phys. 1989, 91, 5392. b) J.Z. Zhou, S.A. Hewitt, J.F. Hershberger, and G.W. Flynn, J. Chem. Phys. 1990, 93, 8474. c) J.Z. Zhou and G.W. Flynn, J. Chem. Phys. 1990, 93, 6099. 20. J.C. Stephenson and C.B. Moore, J. Chem. Phys. 1972, 56, 1295. 21. a) R.D. Sharma and C.A. Brau, J. Chem. Phys. 1969, 50, 924; b) R.D. Sharma and C.A. Brau, Phys. Rev. Lett. 1967, 19, 1273. 22. B.M Toselli, T.L. Walunas, and J.R. Barker, J. Chem. Phys. 1990, 92, 4793. 23. a) R.N. Schwartz, Z.I. Slawsky and K. F. Herzfeld, J. Chem. Phys. 1952, 20, 1591; b) R.N. Schwartz and K.F. Herzfeld, J. Chem. Phys. 1954, 22, 767. 24. a) I.M. Margulis, S.S. Sapers, C. Steel, and I. Oref, J. Chem. Phys. 1989, 90, 923. b) A. Pashutzki and I. Oref, J. Phys. Chem. 1988, 92, 178. 25. See for example G. Lendvay, C. Schatz, and L.B. Harding, Faraday Disc. 1995, 102.


Collisional Energy Transfer of Highly Vibrationally Excited Molecules

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