1004
J. Phys. Chem. 1987, 91, 1004-1006
Collision-Free Lifetimes of Vibrational Levels in So p-Difluorobenzene: A View of IVR and an Application of SEP-SVLF Spectroscopy Scott H. Kable, John W. Thoman, Jr.,+ Steve Beames, and Alan E. W. Knight* School of Science, Griffith University, Brisbane, Queensland, 41 I I , Australia (Received: September 11, 1986; In Final Form: December 17, 1986) Collision-free lifetimes of selected vibrational levels in So p-difluorobenzene have been measured by stimulated emission pumping-single vibronic level fluorescence spectroscopy (SEP-SVLF). The So levels 31302 (1 577 cm-I), 52302(2027 cm-I), 5,302 (2884 cm-'), and 3,5*302(3276 cm-') display lifetimes T~ = 5 , 3.3, 2.3, and 1.7 ps, respectively. These lifetimes are much shorter than the radiative lifetime estimated from the infrared transition strength. They are interpreted as being indicative of the time scale for the slow component of intramolecular vibrational redistribution occurring among vibrational levels that are in the sparse-intermediate coupling regime. The decrease in lifetime with increasing vibrational energy may be indicative of increased vibration-rotation state mixing as one ascends the So manifold in pDFB.
Introduction Vibrational levels in the ground electronic state of small to medium sized polyatomics have been studied extensively by infrared emission spectroscopy. Applications cover a range of phenomena. Collision-induced vibrational energy transfer among low vibrational levels has attracted sustained interest for over a the dynamics of reactive processes have been revealed beautifully in the experiments of Leone and co-workers;6 tunable IR laser-induced fluorescence excitation spectroscopy has been exploited by McDonald and co-workers7~* to define many details of collision-free intramolecular vibrational redistribution (IVR). There are, however, limitations in the application of IR methods. Vibrational selection rules impose inherent restrictions on the excitation channels available through direct IR pumping. Selective probing via IR emission is often hampered by the poor spectral discrimination available with IR bandpass filters. These restrictions in studying collision-induced properties of vibrational levels in ground electronic states of polyatomics may be circumvented by using stimulated emission pumping (SEP) to populate an initial state9J0and laser-excited single vibronic level fluorescence (SVLF) to view selectively the time evolution of the initially prepared state."X1* In this Letter we describe an application of SEP-SVLF spectroscopy in determining the collision-free lifetimes of selected vibrational levels in the ground electronic state of p-difluorobenzene (pDFB). These levels would normally be inaccessible through direct pumping with infrared radiation since they involve multiple combinations and overtones. Their energies lie in the range 1500 to 3300 cm-I, where the vibrational density of states (estimated from direct counting) ranges from ==2to 200 per cm-I. These state densities are in the range where intramolecular vibrational redistribution may become significant and they begin to approach a regime for which state-specific dynamical studies may offer useful comment concerning the behavior of reactive regions of polyatomic manifolds.
Methodology State preparation in So pDFB (room temperature, bulb) is achieved by using SEP in a manner analogous to that described p r e v i o ~ s l y . ~The . ' ~ pump transition, 5;30:, is coincident with the 266-nm fourth harmonic of a pulsed Nd:YAG laser. The dump wavelength, from a dye laser driven by the same Nd:YAG laser, is selected to coincide with a fluorescence transition that originates from the 5I3O2 level and terminates in the So level of interest. Four So levels are investigated in this study, namely 3,302, 52302,5,302, and 3,s23o2,with vibrational energies 1577, 2027, 2884, and 3276 cm-I, respectively. Population of the selected So vibrational level is monitored via dispersed SVL fluorescence generated by a third 'Present address: Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139.
0022-3654/87/2091-l004$01.50/0
laser wavelength derived from a second Nd:YAG pumped dye laser. The time evolution of population is followed by scanning the delay between the preparation and probe lasers while collecting and computer averaging the SVL fluorescence signal. Apparent single exponential decays are observed in all cases and decay rates are extracted by using a linear least-squares fit to the data. Rates for total decay of the initially excited So level are obtained for a range of 15-20 pDFB pressures from ==20 to ~ 4 0 mTorr. 0 The low-pressure range serves to define the zero pressure intercept as best possible while the higher pressure range provides a check that the decay rates scale linearly with pressure and that the data are free from complications due to incomplete rotational relaxa t i ~ n . ' ~ ,Figure '~ 1 summarizes the decay measurements for the level 5,302 in the form of a plot of measured decay rate vs. pressure of pDFB. The decay rates display a linear dependence on pressure and deviations from a weighted least-squares fit to the data are within experimental error. The slope and intercept derived from the fit to the data in Figure 1 provide respectively estimates for k,, the total collision-induced vibrational relaxation rate constant and for ko, the rate constant for collision-free decay of the 5,302 level. Choosing weights equal to the inverse of the variance of The vibrational each data point, we obtain ko = 0.42 f 0.3 @ I . relaxation rates k , are discussed elsewhere in comparison with rates for relaxation by a range of foreign gases.14 The precision of the estimate for ko bears comment. Normally, one would rely on the standard error of the intercept as a gauge of the precision. We suspect however that, in general, estimates such as these for collision-free rates may be better constrained than that suggested by the standard error of the intercept. Figure 2 illustrates how the estimate for the intercept changes as one includes successively more of the data points displayed in Figure 1. The estimate is unacceptable when only a few decay rates are included in the least-squares fit. The estimate then stabilizes as successively more of the data points are included. In this stable (1) Weitz, E.; Flynn, G. W. Annu. Rev. Phys. Chem. 1974, 25, 275. Weitz, E.; Flynn, G. W. Ado. Chem. Phys. 1981, 47, Part 2, 185. (2) Flynn, G. W. In Chemical and Biochemical Applications of Lasers, Vol. 1, Moore, C. B., Ed.; Academic: New York, 1974. (3) Lemont, S.; Flynn, G. W. Annu. Rev. Phys. Chem. 1977, 28, 261. (4) McDonald, J. D. Annu. Rev. Phys. Chem. 1979, 30, 29. (5) Yardley, J. T. Introduction to Molecular Energy Transfer;Academic: New York, 1980. (6) Leone, S . R. Annu. Rev. Phys. Chem. 1984, 35 109. (7) Stewart, G. M.; McDonald, J. D. J. Chem. Phys. 1983, 78, 3907. (8) Stewart, G. M.; Ruoff, R.; Kulp, T. J.; McDonald, J. D. J. Chem. Phys. 1984,80, 5353. Kulp, T. J.; Ruoff, R.; McDonald, J. D. J. Chem. Phys. 1985, 82, 2175. (9) Lawrance, W. D.; Knight, A. E. W. J. Chem. Phys. 1982, 76, 5637. (10) Kittrell, C.; Abramson, E.; Kinsey, J. L.; McDonald, S. A.; Reisner, D. E.; Field, R. A,; Katayama, D. H. J. Chem. Phys. 1981, 75, 2056. ( I 1) Lawrance, W. D.; Knight, A. E. W. J . Chem. Phys. 1983, 77, 570. (12) Lawrance, W. D.; Knight, A. E. W. J . Chem. Phys. 1983, 79,6030. (13) Lawrance, W. D.; Knight, A. E. W. J. Phys. Chem. 1983, 87, 389. (14) Kable, S. H.; Thoman, Jr., J. W.; Knight, A. E. W. J . Chem. Phys to be submitted for publication.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 5, 1987 1005
Letters
!
I
4t k,
i
s"
0.42~10~
100
pDFB
I
I
I
200
300
400
I
,
Pressure (m torr)
Figure 1. Total decay rate ET for the level 53302plotted as a function of pDFB pressure. The line through the data corresponds to a linear least-squares fit weighted by the inverse of the variance of each data point. The collision-freerelaxation rate ko is given by the intercept at zero pressure of pDFB. 106x1 4
-1 '
"'1., 2
, 4
, 6
,
, 8
, -iI
1
10
12
,
I
1
1
14
Cumulative number of data points
Figure 2. Plot showing the behavior of the linear least-squaresestimate of the zero-pressure intercept (k,,), derived as shown in Figure 1, as cumulatively more data points are used to determine the estimate. The estimate is unreliable when only a few data points are included but settles quickly with additional points to nest within a range that is more compressed than that indicate by a traditional statistical estimate of error. The linear least squares (L.L.Sq.) estimate is included for comparison.
region, the range of the estimate is 0.36 < ko < 0.52 ps-l. This is a tighter estimate than that suggested by the standard error of the intercept obtained from the weighted least-squares fit. The weighted linear least-squares estimate is included in Figure 2 for comparison. Figure 3 summarizes the results for the four So levels 3,302, S23o2,53302,and 3,52302. Estimates from both forms of analysis discussed above are included, together with error bars. Estimates for the mean are essentially the same for both methods of analysis. The preferred results are ko = 0.2, 0.3, 0.4,, and 0.6 ps-l for the four levels, respectively.
Discussion The collision-free rates give lifetimes 70= 1/ ko that range from
4to ~ 1 . hs. 7 One must exercise caution in interpreting their meaning. We first establish that the measured lifetimes are unlikely to be pure radiative lifetimes of pDFB Sovibrational levels. We have measured the intensity of the strongest bands in the pDFB vapor infrared absorption spectrum as being a factor of 2-4 weaker than the strong 947-cm-' v3 fundamental of SF6. The radiative lifetime of this level in SF6 is 24 m ~ By . ~making use of the standard relationship between the integrated absorption coefficient and the radiative lifetime (for example, see ref 5 ) , we estimate that the radiative lifetimes of levels reached through these strong dipole-allowed absorption transitions in pDFB will be in the range 20-100 ms. The radiative rates of vibrational levels investigated here will be set by the sum of the squares of the transition moments for emission to each of the allowed destination states. Because of the v3 factor in the Einstein A coefficient, the
L
l 2000
2500
3000
Evle (cm.') Figure 3. Dependence of the collision-free relaxation rate ko on vibrational energy of the initially excited state in So pDFB. Estimates for ko and for the error ranges determined from both forms of analysis displayed in Figures 1 and 2 are shown, along with vibrational level assignments. Vibrational state collision-free lifetimes r0 (in ps) are given by the inverse of the value displayed for ko. The experimental upper limit for the diffusion rate kD is necessarily the slowest observed rate, i.e. kD 5 ko (3]302)and is displayed as a revised base line relative to which the data coresponding to the remaining three levels may be gauged.
dominant contribution to the radiative rate for the four levels studied, of type 3,5,302, will come from Au = f l quantum changes in IR active modes15J6 (symmetry species blu, b2", b3J that are accompanied by AIJ = -1 changes in one or both of the high frequency totally symmetric modes v3 and v5. Our estimates suggest that the radiative lifetimes of the four levels studied will lie in the range 0.2-0.5 s. We next assess the contribution to the observed lifetime that is attributable to diffusion of pDFB molecules out of the range of view during the observation time. A rough estimate based on the optical geometry and the thermal velocity of pDFB indicates that the contribution due to diffusion will be small but may contribute a little to the observed decay rates. Precise estimates are difficult to obtain. However, since the diffusion rate will not depend on the identity of the probed level, the slowest observed decay rate is necessarily an upper limit on the contribution to the observed decay rates due to diffusion. In Figure 3, this experimental upper limit for the diffusion rate kD is shown as a revised base line, i.e. where we have taken kD Iko (3,302). Using this upper estimate for kD, we may derive lower estimates for collision-free rates ko, and hence upper limits for 70, the corrected collision-free lifetimes. For the three states 52302,53302, and 3,5?302,we quote upper limits of 70 5 10, 4.3, and 2.5 ps, respectively. Clearly, these lifetimes are still a factor of =IO5 shorter than our estimates for the pure radiative lifetimes of the prepared states. In order to assess the significance of these measurements, we are led to consider the vibrational identity of the prepared states that are subsequently probed by using dispersed state-selected fluorescence and to discuss the implications of IVR. We shall argue that the most probable explanation for the relatively short collision-free lifetimes is intramolecular vibrational redistribution. The pump laser is coincident with strongly overlapped 'Qband heads in the $30; absorption. Roughly half of the thermally populated IJ,K) states are excited in the pump step," and a similar (J,K) population distribution is transferred via the dump step to create the vibrationally excited So "level". This initially prepared So "level" will in fact consist of a set of states, some of which will be true rotation-vibration molecular eigenstates, and hence stationary in time, and other subsets which will arise due to coherent (1 5) Herzberg, G. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand: New York, 1945. (1 6 ) Zimmerman, R. L.; D u m , T.M. J . Mol. Spectrosc. 1985, 110, 3 12. (17) Cvitas, T.; Hollas, J. M. Mol. Phys. 1970, 18, 793.
1006 The Journal of Physical Chemistry, Vol. 91, No. 5, 1987
preparation of small ensembles of anharmonically coupled rotation-vibration states. This latter situation must surely arise since the rotation-vibration level densities at these vibrational energies are in the regime where IVR state mixings have been identified in analogous circumstances. The SI state of pDFB is the nearest analogy. An intrinsic feature of our SEP-SVLF method is that the population of initially prepared molecules is monitored by using two steps of state selection, namely selective excitation by the probe laser tuned to the 30,50,30: transition and selective observation of a single band in the dispersed fluorescence, namely 30;. Accordingly, the probe will monitor only the 3,5,302 vibrational character of any initially prepared state. For example, consider the level prepared at tVib= 2884 cm-I. The probe will monitor the average (squared) coefficient of the zero-order state 5,302 in the set of states that are prepared via SEP. Other zero-order components of the mixed eigenstates will not be viewed by the probe. Hence, if some of the So pDFB molecules are prepared in nonstationary compound states, i.e. they are coherently pumped to small ensembles of anharmonically coupled rotation-vibration states, then the decay of these nonstationary compound states will contribute to the experimental measurement of the decay of “zero-order’’ s33o2character from the initially prepared So population at cvib = 2884 cm-I. In other words, the IVR rate will appear as a component of the decay rate. At lower pressures, as collisional relaxation becomes less significant, IVR will begin to dominate the decay rate. We are reminded that the vibrational density of states ranges from = 2 per cm-I in the region of the lowest level studied, i.e. 3,302, to =200 per cm-I near the highest level, 3,52302. IVR under these circumstances should display intermediate case behavior,7*19*22,23 whereby the time dependence of vibrational redistribution may be characterized loosely in terms of a “fast” component in the picosecond to nanosecond range together with a much slower component that could persist as long as a few hundredths of a second ,4.7.8,22.23 Of course, the large number of rotational states accessed in our experiment will dictate that there will be a wide variation in the composition of each nonstationary compound state formed through the coherent pumping of small ensembles of anharmonically coupled rotation-vibration states. However, we recognize that the sum of a relatively large number of quasi-exponential decays, (18) Kable, S. H.; Lawrance, W. D.; Knight, A. E. W. J . Phys. Chem. 1982, 86, 1244.
(19) Parmenter, C. S. Faraday Discuss. Chem. SOC.1983, 75, 7. (20) Fujii, M.; Ebata, T.; Mikami, N.; Ito, M.; Kable, S. H.; Lawrance, W. D.; Parsons, T. B.; Knight, A. E . W. J . Phys. Chem. 1984, 88, 2937. (21) Knight, A. E. W. In Excited States, Vol. 7, Lim, E. C. Ed.; Academic: New York, in press. (22) Bixon. M.: Jortner. J. J . Chem. Phvs. 1968.48. 715. 1969.50. 3284. Freed,‘K.; Nitzan, A. J . Chem. Phys. 1980: 73,4765. Mukamel, S.;Smalley, R. E. J . Chem. Phys. 1980, 73, 4156. (23) Coveleskie, R. A,; Dolson, D. A,; Parmenter, C. S . J . Phys. Chem. 1985,89, 655
Letters even with widely varying decay constants, will be quasi-exponential;24hence we are unlikely to observe the nonexponential character that would be expected in the decay arising due to the simultaneous vibrational dephasing of an ensemble of molecules in a variety of different nonstationary states. Nor is our time resolution or state selectivity anywhere near sufficient to resolve either the fast component due to initial dephasing or the modulation of the slow component due to quantum beats. The collision-free lifetimes that we have observed for So pDFB are in the regime 10”-10-5 s. They are consistent with what one would expect to observe for the slow component of IVR in a sparse-intermediate case system. However, we refrain from attaching too much quantitative significance to the data since these decay times are averages over a wide variety of initially prepared states. Nevertheless, we notice that the lifetimes decrease with increasing vibrational energy, although the decrease is not dramatic. Calculations carried out e l s e ~ h e r e l indicate ~ , ~ ~ that the set of background states of appropriate symmetry that will contribute most to state mixing does not alter dramatically as one proceeds through the four levels explored here. However, there will be some increase in the available background state density as tnb increases, and, moreover, the increase will be a little more marked as the vibrational complexity of the initially prepared state increases. The trends in the lifetime data are consistent with these guidelines, and as such we are reassured further that the measured collision-free decay rate are indicative of IVR rates. We have demonstrated that collision-free lifetimes of vibrational levels lying reasonably high in the So manifold of a polyatomic may be measured by SEP-SVLF spectroscopy. The advantage of this method of state preparation is that a variety of levels with widely varying vibrational composition may be accessed, thus facilitating a systematic study of collision-free lifetimes, and hence the dynamics of IVR, in regions of polyatomic manifolds that have been hitherto largely unexplored. Picosecond experiments using the SEP-SVLF method will surely reveal interesting new information concerning intramolecular vibrational relaxation in the ground states of polyatomic molecules.
Acknowledgment. Financial support has been provided by the Australian Research Grants Scheme. A travel grant provided through the US-Australia Agreement for Scientific and Technological Cooperation (National Science Foundation, U S A . and Department of Science, Australia) enabled J.W.T. to participate in this research. Andrew Rock has contributed substantially to the development of our laboratory computing facilities and his expertise and assistance is gratefully acknowledged. We have enjoyed stimulating interactions with Professor Jeffrey Steinfeld. (24) Knight, A. E. W.; Selinger, B. K. Aust. J . Chem. 1973, 26, 1, 499. Knight, A. E. W.; Selinger, B. K.; Ross, I. G . Aust. J . Chem. 1973, 26, 1159. Field, R. W.; Benoist d’Azy, 0.;Lavollee, M.; Lopez-Delgado, R ; Tramer, A. J . Chem. Phys. 1983, 78, 2838. (25) Whetten, N.; Lawrance, W. D., private communication.
