3533
J . Phys. Chem. 1986,90, 3533-3541
Mode Selectivity In Vibrational Predlssoclatlon: The p-Dlfluorobenzene-Ar Complex Kirk W. Butz, David L. Catlett, Jr., George E. Ewing,* Doug Krajnovich, and Charles S. Parmenter* Department of Chemistry, Indiana University, Bloomington, Indiana 47405 (Received: January 30, 1986; In Final Form: April 17, 1986)
The van der Waals complex between p-difluorobenzene and argon (pDFB-Ar) has been formed in a free jet expansion and studied by using the techniques of UV fluorescence spectroscopy. The mode selectivity of the vibrational predissociation (VP) process has been investigated by selectively pumping two SI pDFB-Ar levels, 3 and G,that lie well above the energy limit for VP and are separated by only 3 cm-I. Dispersed fluorescence spectra obtained after pumping these levels show that, in each case, >80% of the emission is accounted for by only three contributions: resonant complex fluorescence, and monomer Oo and 6l fluorescence following VP. Eleven other VP channels are energetically accessible but are not observed. The total VP rate is roughly a factor of 2 larger for 7than for 9. A more striking initial mode selectivity is observed in the 6I/O0 VP branching ratio. For 3 pump, 6l/Oo = 1, while for 3 pump, 6'/0° = 5. Several rationales are explored for the high initial- and final-state selectivities observed experimentally. Propensity rules known to describe SI level-to-level energy transfer in full pDFB + Ar collisions at 300 K fail miserably when confronted with the van der Waals results. A simple model for VP of a Morse oscillator can explain the efficiency of the 3 6' and 7 6' VP channels but not the production of monomer. By explicitly taking into account the possibility of Fermi resonances between the initially prepared intramolecular vibrational levels and near-isoenergetic combination levels involving large amounts of van der Waals stretching (and bending) excitation, the appearance of large energy gap VP channels such as G -,Oo can be qualitatively understood.
-
Introduction Over the years, R. A. Marcus has made many contributions to our understanding of vibrational energy flow in highly excited polyatomic molecules. Although much of this work is of recent vintage,' Marcus is perhaps best known for his contribution to the RRKM theory.2 With its assumption of rapid and statistical intramolecular vibrational energy flow at high excitation energies, RRKM theory remains the starting point for most discussions of unimolecular reaction kinetics. The problem of understanding vibrational energy flow received particular impetus in the early 1970s with the discovery of the phenomenon of infrared multiple photon dissociation of polyatomic molecules. The prospects of seeing mode-selective dissociations were initially considered to be p r ~ m i s i n g . In ~ the intervening years, however, we have learned how difficult it is to beat the statistical predictions of RRKM theory." There is one class of molecules, if the term is used broadly, where nonstatistical dissociation appears to occur routinely. Van der Waals molecules formed between a vibrationally complex polyatomic molecule and, say, an inert gas atom can be excited to selected vibrational levels of the chemically bound moiety by absorption of light. In the case of visible or UV absorption, an excited electronic state is produced as well. If the energy of the internal vibrational level exceeds that of the van der Waals bond, the excited van der Waals molecule can.dissociate by vibrational predissociation (VP). Many such VP processes have been observed. In a number of studies of electronically excited van der Waals complexes (including, e.g., s-tetra~ine-Ar,~,~ pyrimidine~
(1) See, for example: Noid, D. W.; Koszykowski, M. L.; Marcus, R. A. Annu. Rev. Phys. Chem. 1981, 32, 267. (2) Marcus, R. A. J. Chem. Phys. 1952, 20, 359. (3) Bloembergen, N.;Yablonovitch, E. Phys. Today, 1978, May, 23. (4) Schulz, P. A.; Sudbo, Aa. S.;Krajnovich, D. J.; Kwok, H. S.;Shen, Y. R.; Lee, Y. T. Annu. Rev. Phys. Chem. 1919, 30, 379. ( 5 ) (a) Haynam, C. A.; Brumbaugh, D. V.; Levy, D. H.J. Chem. Phys. 1984,80,2256. (b) Brumbaugh, D. V.; Kenny, J. E.; Levy, D. H.Ibid. 1983, 78, 3415. (c) Kenny, J. E.; Brumbaugh, D. V.; Levy, D. H.Ibid. 1979, 71, 4757. (d) Smalley, R. E.; Wharton, L.; Levy, D. H.; Chandler, D. W. Ibid. 1978,68, 2487. ( 6 ) (a) Langelaar, J.; Bebelaar, D.; Rettschnick, R. P.H. In Applications ofPicasecond Spectroscopy to Chemistry; Eisenthal, K. B., Ed.; Reidel; 1984; Dordrecht, The Netherlands, p 293. (b) Ramaekers, J. J. F.; van Dijk, H. K.; Langelaar, J.; Rettschnick, R. P.H. Faraday Discuss. Chem. Soc. 1983, 75, 183. (c) Ramaekers, J. J. F.; Krignen, L. B.; Lips, H.J.; Langelaar, J.; Rettschnick, R. P. H. Laser Chem. 1983, 2, 125. (d) Ramaekers, J. J. F.; Langelaar, J.; Rettschnick, R. P. H. In Picosecond Phenomena III,Eisenthal, K. B. et al., Eds.; Springer Verlag: West Berlin, 1982; p 264.
0022-3654/86/2090-3533$01.50/0
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Ar,N2,' benzene-He,Ar,8 and glyoxal-H2,D2,Ar,Kr9), the final vibrational states of the polyatomic fragment have been identified by dispersing the visible or UV fluorescence. Invariably one finds a strong bias to produce the polyatomic fragment in only a few of the many vibrational states that are energetically accessible. VP in these systems is decidedly nonstatistical. The selection of final vibrational states in a given system is highly sensitive to the vibrational level that is initially excited, and in this sense one could consider these dissociations to be mode selective. The concept is blurred, however, by the experimental circumstances. It is usually impossible to excite different initial vibrational levels in the van der Waals molecule that have the same set of final state VP possibilities. Comparisons have necessarily involved initial vibrational levels of rather different energies, so that the accessible set of final states also differs, often substantially. We are presently using UV +So spectroscopy to characterize the van der Waals molecule formed by p-difluorobenzene and argon (pDFB-Ar). The study is now sufficiently well advanced to provide estimates of the ground- and excited-state well depths, the geometry of the complex, the van der Waals stretching frequency, and the positions of a number of vibrational levels involving chemical bond modes in the complex. The spectroscopy also shows that it is possible to excite selectively either of two known SI complex levels that lie well above the energy limit for VP and are separated by only 3 cm-'. Since these levels are associated with precisely the same set of possible final VP states, the stage is set for a particularly instructive experimental inquiry into the extent to which the VP of the SIpDFB-Ar complex is truly mode-selective. Our results show that the predissociation lifetime and particularly the vibrational energy flow in the aromatic ring accompanying VP are distinctly sensitive to the identity of the SI ring mode initially excited. One other aspect of the pDFB-Ar complex is particularly appealing for study of VP. As we shall describe below, the flow of vibrational energy within SIpDFB in collision with Ar has been (7) Abe, H.; Ohyanagi, Y.; Ichijo, M.; Mikami, N.; Ito, M. J. Phys. Chem. 1985. 89. 3512. (8) (ai Stephenson, T. A.; Rice, S. A. J. Chem. Phys. 1984,81,1083. (b) Fung, K. H.; Seizle, H. L.; Schlag, E. W. Z. Naturforsch. 1981, 36A, 1338. (c) Beck S.M.; Liverman, M. G.; Monts, D. L; Smalley, R. E. J. Chem. Phys. 1919, 70, 232. (9) (a) Halberstadt, N.; Soep, B. J. Chem. Phys. 1984, 80, 2340. (b) Halberstadt, N.; Soep, B. Laser Chem. 1983, 2, 115. (c) Beswick, J. A,; Halberstadt, N.; Jouvet, C.; Soep, B. Ibid. 1982, I , 77. (d) Halberstadt, N.; Soep, B. Chem. Phys. Lett. 1982,87, 109.
0 1986 American Chemical Society
3534
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 Ar
F-F
F
~
8'30' 17' 30'
8' 30'
: i OL Figure 1. Energy level diagram for vibrational predissociation of SI pDFB-Ar complexes. The stack of pDFB monomer levels has been offset by the SI van der Waals binding energy of approximately 400 cm-I. Note that all pDFB monomer levels up to 8'302 are included (with the possible exception of the 16' level-see Figure 2 caption). However, only those complex levels are shown that have been studied experimentally.
studied extensively in 300 K bulbs. This system is thus unusually well suited for comparisons of vibrational energy flow within SI pDFB in full collisions (the 300 K bulb experiment) and in half-collisions (the van der Waals VP). A partial energy level diagram relevant to VP of S, pDFB-Ar is shown in Figure 1. In this figure, two stacks of vibrational energy levels corresponding to the complex and the monomer are shown in correct relationship to one another, being offset by the SIvan der Waals binding energy, D,' = 400 cm-'. The latter value was deduced from the following experimental observations. (These observations will only be outlined here to provide perspective. Full details will be included in a future publication.I0) First, each vibrational band in the SI So fluorescence excitation spectrum of the monomer is accompanied by a van der Waals band lying to the red. The displacement for the band and all but one other band is 30 f 2 cm-' from the parent band. (A bar is used to designate the complex.) Therefore, the van der Waals bond is 30 cm-' stronger in the excited electronic state than in the ground electronic state. Second, a lower bound to the Sovan der Waals binding energy, D,,", is set by our observation of the 221, sequence absorption in the complex. This result gives DO)'> uz{' = 348 cm-I. (We are assuming that pDFB-Ar complexes formed with u22/1 excitation would dissociate before reaching the laser crossing zone if DO)'< u22/1. This assumption is supported by our results concerning the magnitude of the VP rate in SI pDFB-Ar, to be discussed below.) Finally, we observe that excitation of the 61, complex absorption band produces emission from both the SI complex and the monomer formed by VP, so that D,' < v6' = 410 cm-'. Combining the above results gives 378 cm-' < DO)< 410 cm-I. For several reasons that we do not wish to go into here, these bounds must be interpreted somewhat loosely. Nevertheless, it is clear that DO'is at least close to 400 cm-I, and this value will
-
6
(IO) Butz, Kirk W. et al., to be published.
Butz et al.
be adopted for our present considerations. From Figure 1, the possibilities for vibrational level changes F are easily seen. For example, excitation of the SI complex level Oo cannot lead to vibrational predissociation. Excitation of the level 61 can produce the monomer, but only in its 0' level. These situations are consistent with spectroscopic observations. The levels nominally labeled 9 and 3 lying at 818 and 821 cm-' above the complex SI zero-point level are the two levels of particular interest in the present report. These levels involve known a l gmodes and may be mixed modestly by Fermi resonance." As can be seen in Figure 1, 13 known ring levels in the pDFB SI monomer can in principle participate in the vibrational state changes that accompany VP from either of these complex levels.
Experimental Procedure van der Waals complexes were formed by pulsing a 0.24% mixture of pDFB in argon through a 0.8-"diameter orifice using a commercially available solenoid valve.'* Optimum complex formation was achieved with nozzle backing pressures between 700-1000 Torr. The gas pulses (of approximately 1-ms duration) expanded freely into a small vacuum chamber evacuated by a 6-in. diffusion pump. UV light pulses were produced by doubling the output of a Lambda Physik excimer pumped dye laser in a KDP crystal. The UV pulses entered and exited the vacuum chamber through light baffles and crossed the gas jet at right angles. For the work reported here, the UV pulses crossed the gas jet approximately 12 mm (15 nozzle diameters) downstream of the nozzle orifice. At this distance, the pDFB monomer rotational temperature has essentially converged to its asymptotic value, but the gas density is still sufficiently high that residual collisions may be occurring in the jet. Collisional effects are, however, strongly discriminated against in our experiment because of the short time scale imposed on our measurements by the electronic fluorescence lifetime ( ~ f 10 ns). In fact, spectra measured at an even smaller nozzle-laser distance of 6 mm still looked very similar to those presented in this paper. Typical UV pulse energies were a few hundred microjoules per pulse (lower for excitation spectra to prevent photomultiplier saturation), with a bandwidth of -0.4 cm-' and a pulse duration of -20 ns (comparable to the pDFB fluorescence lifetime). Fluorescence was collected along two directions perpendicular to both the gas jet and the laser beam, Along one direction, an EM1 9813QA PMT was used to monitor the total fluorescence intensity and to record fluorescence excitation spectra. Along the other direction, fluorescence was imaged onto the entrance slit of our 1.7-m Czerny-Turner spectrometer (operated in fourth order), and the dispersed fluorescence was detected by a Hamamatsu R2079 PMT. The PMT outputs were integrated on a pulse-by-pulse basis by a home-built Gated Detection Systemi3 interfaced to an IBM PC. The fluorescence excitation spectra and dispersed fluorescence spectra were scanned under computer control and the data stored on floppy disks for later analysis. Experimental Results and Analysis Figure 2 shows a small segment of the S1-So fluorescence excitation spectrum of pDFB and of the pDFB-Ar complex in a free jet expansion. The segment is chosen to show the region of the 510 and 6*0 absorption bands. Note the 30-cm-I separation of the complex bands from the monomer bands and particularly the 3-cm-I separation of the two complex bands and 6 from each other. With our 0.4-cm-' laser bandwidth, it is easily possible to excite one complex band to the exclusion of the other. It is also clear from Figure 2 that the G:5IO intensity ratio is nearly identical with the 6 : 6 ' 0 ratio. In fact, similar comp1ex:monomer fluorescence intensity ratios obtain for all of the bands that we have studied in excitation, including Ooo. As we ( 1 1 ) Coveleskie, R. A,; Parmenter, C. S. J. Mol. Spectrosc. 1981,86, 86. (12) Series 9 High Speed Solenoid Valve, General Valve Corporation, Fairfield, NJ. ( 1 3 ) Ensman, R.; Knight, A. E. W . , unpublished design.
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 3535
Mode Selectivity in Vibrational Predissociation I
I
I
I
5:
I -30
I
I
I
-20
-10
0
I
Displacement from 6: band origin/cm-' Figure 2. Fluorescence excitation spectrum of pDFB and of pDFB-Ar in the vicinity of the 510 and 6'0 absorption bands. The monomer 6'0 band origin occurs at 37661 cm-' (vac). The rotational temperature is -2 K. The band at -20 cm-l displacement is an unassigned monomer band. A possible assignment is 1620. If this assignment turns out to be correct, then the 16' monomer level should also be included in Figure 1 as a possible VP channel for the 7and 3 van der Waals complex levels.
shall see, pumping the 7and 3 complex levels mainly results in monomer emission (due to VP), while 3 yields, of course, only complex emission. The fact that the comp1ex:monomer total fluorescence ratios are the same (within 50%) for all of these bands indicates that the fluorescence quantum yields and fluorescence lifetimes of the complex are very similar to those of the monomer. This fact will be useful later on. Dispersed fluorescence spectra have been obtained after pumping each of thecomplex - - Sl-So - -absorption bands leading to the complex levels Oo, 22l, 8*,6l, 5 l , and 3. Emission after pumping the 5 level can be fully assigned as being only from the complex. Each band is displaced about 30 cm-1 from the corresponding band in the zero-point monomer spectrum, showing that the ring vibrational frequencies are not perturbed more than 2 or 3 cm-I from those in the monomer. Weak satellite bands are observed 41.0 f 0.5 cm-I to the red of each strong peak in the $ fluorescence spectrum. These are assigned to the trantransition in the van der Waals stretching mode. The sition has also been observed in the fluorescence excitation spectrum, 41.0 f 0.5 cm-I to the blue of Thus, within experimental error, the van der Waals stretching frequency is the same in the ground and excited electronic states. We are here interested specifically in the dispersed fluorescence spectra obtained after selectively pumping each of the complex absorption bands 7and 3.(The spectra obtained from the other levels will be shown in a future paper.I0) The fluorescence spectrum following 7pumping is shown in the bottom panel of Figure 3. The monomer 5l fluorescence spectrum is also shown for comparison. Similarly, the 3 and 6* fluorescence spectra are compared in Figure 4. Each complex spectrum shows structure characteristic of the corresponding monomer level, appropriately red-shifted by 30 cm-', and this is readily assigned to resonance fluorescence from the van der Waals complex. But it is clear that, in both cases, resonance fluorescence accounts for only a small fraction of the total emission, and that the remaining emission is highly structured. The assignment of this structure is unambiguous on account of our extensive experience with simpler pDFB and pDFB-Ar fluorescence spectra when other levels" are pumped. In Figure 5 we display segments of the 7and 3 spectra on an expanded scale, aligned so that their respective features can be easily compared. The most striking similarity between the two spectra is that, in each case, nearly all of the structured emission is accounted for by just three levels: the level initially pumped (7or G), and the monomer levels Oo and 6l. Since v6 is a totally symmetric vibration, any quantum number change in this mode is allowed by symmetry in the S1-So electronic transition.
1
1
35,000
I
1
37,ooo
36,000
Frequency / cm? Figure 3. Dispersed fluorescence spectra obtained while pumping the 510 transition of the pDFB monomer (top panel) and the transition of the
pDFB-Ar complex (bottom panel). Spectrometer resolution: fwhm. I
-
12 cm-I
I
I
6; I
a
6.
1
I
35,000
I
36,000 Frequency /cm?
I
I
37,000
Figure 4. Same as Figure 3, except for 620 and 6Loexcitation.
Therefore, the 6' level yields an unmistakable fluorescence pattern consisting mainly of the 610, 6'1, and 612 transitions, along with strong fluorescence progressions involving the v5 and vj vibrations. This structure is easily picked out in both panels of Figure 5 . The assignment of the other structure to the monomer Oo level is slightly more hazardous, since a nontotally symmetric S, vibrational level with a small sequence shift could give a fluorescence spectrum nearly identical with that of the Oo level. Fortunately, the sequence shifts for all of the energetically accessible SI monomer levels are known." Only one level, 22l, has a sequence shift small enough to cause concern. (The 22', transition lies 4 cm-' to the blue of Ooo.) Since odd quantum number changes in the nontotally symmetric mode 22 are forbidden, the fluorescence spectrum of 22l is virtually identical with that of Oo except that all transitions
3536
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986
4
Butz et al.
J
I
1 35,000
I
1 35,400
I
I
1
35,800
I 36.200
I
I 36,600
I
I 37,000
,
37.400
Frequency /err-' Figure 5. Expanded view of the 3 and 3 dispersed fluorescence spectra. (Each spectrum is a 3-point sliding average of the raw spectra shown in Figures 3 and 4.) Common features in the two spectra due to the monomer Oo and monomer 6 , VP channels are connected by short- and long-dashed lines, respectively.
are blue-shifted by 4 cm-l. Although the experimental resolution was 12 cm-I for the spectra shown in Figure 5, we are confident from repeated measurements (including some at higher resolution) that we can locate the center frequencies of the fluorescence bands to better than 2 cm-'. The results indicate that the OO-like fluorescence spectrum in both panels of Figure 5 is in fact mainly due to Oo emission, although a minor contribution from 22l cannot be completely ruled out. We conclude that, for both initial complex levels, only two of the 13 energetically accessible monomer levels are populated with high probability in the VP process. The most striking difference between the two initial levels is that the 6':0° monomer ratio is much larger when 3 is pumped than when 3 is pumped, even though the two complex levels differ by only 3 cm-I in energy. We now want to dissect the 7and 3 spectra to obtain the fractional contributions of the three major fluorescence channels (resonant complex fluorescence, and fluorescence from Oo and 6l monomer following VP) to the integrated emission intensity between 37 700 and 34000 cm-'. These fractional contributions will then be used to calculate state-to-state VP rate constants, assuming identical fluorescence lifetimes for pDFB and pDFB-Ar. The procedure we followed is outlined below. (1) For each of the major channels, we chose a "diagnostic transition" that was well-resolved from othertransitions. For the 5l resonance emission channel, we chose the 6°,510transition. For the 3 resonance emission channel, we chose the 6*3 t r a n ~ i t i o n . ' ~
6
(14) The reason was not chosen as the diagnostic transition for 5 resonance emission is that this transition has an anomalously low intensity compared to the corresponding monomer transition. This may be seen in Figure 4: the relative intensities of all labeled transitions in the 6* and 3 spectra agree quite well with the exception of 6*,. The stronger 621intensity in the monomer spectrum may reflect more borrowing of intensity from the nearly coincident 6O,5lOtransition, due to a stronger 5'-.62 Fermi resonance in the monomer. (See ref 11.) This problem is not so important for the other 6' fluorescencetransitions. since they do not coincide with strong 5' transitions.
TABLE I: Major. Fluorescence Channels after Pumping the Levels of pDFB-Ar fraction of total fluorescence intensity accounted for bv
level pumped
5' 62
(A) complex resonance fluorescence
0.18 0.38
(B)
3 and 3
monomer 6' VP channel
(C) monomer 0' VP channel
(A) + (B) + (C)
0.31 0.47
0.33 0.10
0.82 0.95
For the monomer Oo and 6l VP channels, we chose the Ooo and 6l transitions, respectively. These diagnostic transitions have been shaded in Figure 5. ( 2 ) Next, we calculated the fraction of the total emission (following 3 or 3 pumping) between 37 700 and 34 000 cm-' due to each diagnostic transition. (3) Finally, the fractional contribution of each diagnostic transition was converted to the fractional contribution of the corresponding fluorescent channel by using independently measured fluorescence spectra of the Oo, 6 ' , 5l, a n d 62 monomer levels to determine accurately what fraction of the total fluorescence from each of these levels (between 37 700 and 34 000 cm-') is emitted at the diagnostic transitions Ooo, 6'1, 6O,5I0, and 623, respectively. (In this step, we make the reasonable assumption that the resonant 3 and 3 emission spectra closely follow the corresponding monomer spectra.I4) To illustrate the above procedure, consider the contribution of the monomer Oo VP channel to the 3 fluorescence spectrum. The Ooo diagnostic transition accounts for 7.0% of the total emission in the 3 spectrum between 37700 and 34000 cm-I. In the monomer Oo fluorescence spectrum, the Ooo transition accounts for 21.5% of the emission in this same frequency range. Therefore, the Oo VP channel accounts for 7.0/21.5 = 33% of the total
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 3531
Mode Selectivity in Vibrational Predissociation
7
fluorescence intensity following pumping. Proceeding similarly for the other channels, we obtain the results summarized in Table I. Note that the three major channels account for at least 80% of the total fluorescence intensity in the case of both 7 and 3 excitation. Therefore, the monomer to complex emission ratio, M / C , is well approximated by these three contributions. The result is as follows: for 3 pump, M / C = 3.6; for 3 pump, M / C = 1.5. To proceed further, we recall our earlier argument that the fluorescence quantum yields and fluorescence lifetimes of the complex and monomer are similar. Monomer fluorescence lifetimes and quantum yields have been reported by Guttman and RiceIs and by Volk and Lee.I6 Both quantities appear to decrease slowly and smoothly with increasing SI vibrational energy, but over the small energy range relevant to the present experiments (cvlb = 0-820 cm-I), the fluorescence lifetime and quantum yield may be regarded as essentially constant (within 20%). We therefore make the approximation that all levels under consid-_ eration (in particular, 62, 5l, 6l, Oo) have the same fluorescence quantum yield and the same fluorescence rate constant, which we take to bel5 kf = lo8 s-l. The fluorescence rate constant provides a built-in clock for the VP process. Using the results in Table I and the above kf value, it is easy to obtain the following state-to-state VP rate constants (for a caveat, see footnote 17):
-
-
kvp (5’
6’) = 1.7 X lo8 s-]
kvp(?
Oo) = 1.8 X lo8 s-I
kvp(G
6l) = 1.2 X lo8 s-]
kvp(G
Oo) = 0.26 X lo8 s-I
These values should be reliable to *50%. Note that the total VP rate constant is roughly 2X larger for 3 than for 3: k v ~ ( 7 ) ~ v P ( ?---* 6’,Oo) - 1.7 1.2 k v p ( 3 ) k v p ( a ---* 61,Oo)
+ 1.8 + 0.26
= 2.4
The results for the 6l vs. Oo VP branching ratio are as follows: for 7pump, 6’/0° = 1; for 3 pump, 6’/0° = 5. Finally, we consider briefly the residual fluorescence in the and 3 spectra. In both spectra there are numerous small peaks, particularly in the 36 450-36 800-cm-I region, that we believe are both real and not due to the three major channels. Since these peaks are weak and not very well resolved, and since we are unable to discern a fluorescence progression associated with any of these peaks, assignments are highly speculative. (Typically, there are two or more possible assignments for each peak, due to additional VP channels or to “relaxed” complex emission channels.) We do not consider it profitable to run through the possible assignments here. The point we wish to emphasize is that these additional channels, whatever their assignment, are minor; nearly all of the observed fluorescence is in fact accounted for by the three major channels as summarized in Table I.
7
-
These rate constants are conveniently of the same order of magnitude as the fluorescence rate constant, Le., lo8 S I . (b) The vibrational energy flow accompanying VP is highly selective among the 13 possible final levels. Each excitation leads to significant population of only the 6l and Oo monomer states. (c) The partitioning of the energy flow between these final states is very different for the two initial van der Waals excitation. The 6I/O0 ratio is about five for 3 initial state preparation and about one for 5i excitation. These points taken together comprise compelling evidence that VP in this molecule is not only highly selective among possible final states (common to all VP studies) but also highly modeselective with respect to the identity of the initially excited ring mode. The relative energies of the initial and final states have been essentially removed from consideration. W e now want to explore rationales for this specificity by examining models of VP. A complicating element would seem to exist in the application of models and that is the extent of the Fermi resonance (FR) between the complex levels 3 and 3. We will ignore the mixing altogether in the initial application of the models and see what predictions occur for the pure states. The presence of a real FR would lead to behavior that is a blend of the predictions for the pure states, and our predictions can be so treated. Vibrational Predissociation as a Half-Collision. It is difficult to avoid the temptation to consider VP as the second half of a full-collisional vibrational energy transfer, in this case within SI pDFB during collision with Ar. Within this context, the equilibrium geometry of the van der Waals molecule is one of the many possible collision geometries occurring during a full collisional experiment. The structure of pDFB-Ar is believed to be similar to that of s-tetrazine-Ar, with the argon symmetrically centered 3.0 to 3.5 A above the ring.’* As such, the van der Waals complex is a very special (and low energy) example of the transient complexes formed in a 300 K bulb experiment. We can specifically explore the extent to which VP mimics energy flow in full 300 K collisions since the latter has been characterized with Ar for each of seven initial SI pDFB levels,I9 including the levels 6l and 5l. The full collision transfers are also highly selective among possible final states. They are governed by a single set of propensity rules that works for transfer from every initial level. Since rules that approximately reproduce the 300 K collisional flow are known, we can use them in an attempt to model the VP experiments. The rules in their simplest form, as explored by Parmenter and Tang,20define the relative probability Pabof a vibrational energy transfer in which, say, only modes a and b undergo quantum changes as
Pab = Va2V?Z(AE)
(1)
The factors V 2 are dependent on the magnitude of IAul, the quantum change of each mode. For pDFB + Ar collisions we observe common factors for all modes except the lowest frequency mode V 3 0 . l ~ For these
v:
=
vb2=
... = (0.1)’”’
(2)
(0.6)lAul
(3)
Discussion The results reveal several important characteristics of VP from the SI pDFB-Ar levels 3 (cvib = 821 cm-I) and 3 (t,ib = 818 cm-I). (a) The VP rate constants for the two levels differ by about a factor of 2, with that for the lower level 7being the greater.
The factor Z(AE) is explicitly dependent on the energy AE transferred between vibrational and translational/rotational de-
(15) Guttman, C.; Rice, S. A. J. Chem. Phys. 1974, 61, 661. (16) Volk, L. J.; Lee, E. K. C. J . Chem. Phys. 1977, 67, 236. (17) In calculating these rate constants, we have assumed that the three major processes (resonant complex fluorescence, formation of Oo and 6l monomer by VP) are parallel and that each follows first order kinetics. If instead VP proceeds via an intermediate (“relaxed”) complex level, as suggested in the Discussion, then the true VP rate constants can only be determined by direct time- and wavelength-resolved fluorescence decay measurements. (See, for example, ref 6a.)
( 1 8) The structure of s-tetrazine-Ar has been determined very accurately by fitting high-resolution, rotationally resolved fluorescence excitation spectra (ref Sa). Using an asymmetric rotor band contour program (originally written by Prof. Louis Pierce and kindly provided to us by Prof. D. H. Levy), we have shown that our measured fluorescence excitation band contours of pDFB-Ar are at least consistent with this same structure. (Details will be given in ref 10.) (19) Catlett, David L. Jr., Ph.D. Thesis, Indiana University, 1985. (20) Parmenter, C. S.; Tang, K. Y. Chem. Phys. 1978, 27, 127.
For
~ 3 changes, 0
V302 =
3538 The Journal of Physical Chemistry, Vol. 90, No. 16, 1986
Butz et al.
TABLE 11: Comparison of Observed VP Energy Flow Probabilities and Rate Constants with Those Calculated by Using the Two Simple Models Described in the Text ~~
~~
~
final monomer state
cm-I
E,,,,'
81302
817
6' 17'30' 27I 303 22'
810 197 79 1 766 753 746 695 675 644 573 522 400
8' 8I3O1 171 302
8' 30' 00
A E , ~c m - ~ 4 11 24 30 55 68 75 126 146 177 248 299 42 1
full collision propensity rules 470 transfer 6* calcd (obsd) 5 ' calcd (obsd) 0.3
0.8
