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J. Phys. Chem. 1984,88, 2937-2940
Mode-Dependent Intramolecular Vibrational Redistribution in the S, State of Jet-Cooled p -Difluorobenzene Masaaki Fujii, Takayuki Ebata, Naohiki Mikami, Mitsuo Ito,* Department of Chemistry, Faculty of Science, Tohoku University, Sendai 980, Japan
Scott H . Kable, Warren D. Lawrance,j Terrence B. Parsons, and Alan E. W. Knight* School of Science, Griffith University, Nathan, Queensland, 41 1 1 , Australia (Received: April 25, 1984)
Fluorescence spectra of p-difluorobenzene cooled in supersonic expansions have been measured following laser excitation of a variety of discrete absorption features in the SI-So transition. The spectra reveal that the onset for SI state mixing, as gauged from the fraction of unstructured emission in the dispersed fluorescence, occurs in the vicinity of t ~ i b 1200 cm-'. Estimates of the fraction of unstructured emission from emitting levels containing excitation in the out-of-plane mode ~ 3 indicate that state mixing is more advanced for these levels, as has been concluded previously from dispersed fluorescence studies of p-difluorobenzene at 300 K. Comparisons between the 300 K data and the results obtained for jet-cooled p-difluorobenzene support the view that rotation-vibration state mixing contributes to the intramolecular redistribution of vibrational energy in regions of low-to-medium vibrational state densities. N
Introduction Intramolecular vibrational redistribution (IVR) in an isolated molecule has been a topic of considerable interest in recent years. The complete redistribution of vibrational energy prior to dissociation is a central assumption in the RRKM theory of unimolecular reactions. The successes of chemical rate theory in rationalizing experimental data for reactions conducted at large excesses of vibrational energy are well documented, hence verifying indirectly the assumptions of complete vibrational redistribution prior to reaction. The role of IVR in the low to intermediate regions of a vibrational manifold is open to a more-detailed examination and offers opportunities for characterizing the molecular factors that control vibrational energy redistribution. Previous studies have revealed onsets of IVR in a large variety of aromatic molecules in their So, SI,and S2electronic states to be dependent on the amount of excess vibrational energy and hence, at least qualitatively, on the background density of states (pVib).l-l4 Recently, data have begun to emerge which indicate that factors other than &b may influence IVR in this intermediate region. Zewail and co-workers1S*16 report quantum beats in the fluorescence decay of anthracene in selected regions of the SI manifold where the total background vibrational density of states is high enough to expect statistical limit behavior with respect to IVR. Kable et al.l0 observed a dependence of the extent of IVR not only on Pvib but also on the identity of the initially excited vibrational mode. There is evidence that rotations contribute to IVR by increasing the effective state density available for intramolecular vibrational m i ~ i n g . ~ J ~ J ' J ~ The issue of mode-sensitive state mixing is addressed further in this Letter. We provide additional evidence from supersonic free-jet dispersed fluorescence spectroscopy that the features of vibrational state mixing are dependent on the initially excited vibrational level. Independent experiments have been performed at Tohoku and Griffith Universities and the results from both centers are presented here. Kable et al.1° measured the dispersed fluorescence spectra of collision-free p-difluorobenzene (pDFB) in a bulb at 300 K. IVR (or more precisely, state mixing) was manifest as a broad, unstructured background underlying the discrete SVL fluorescence. The extent of state mixing was expressed as a ratio of unstructured to structured fluorescence intensity (U/S ratio). When the totally symmetric progressions in modes v3, v5, and v g were excited, the dispersed fluorescence spectra yielded U / S ratios that increased smoothly with vibrational energy. This confirmed the general *Currently Miller Institute Research Fellow, University of California, Berkeley, CA.
0022-3654/84/2088-2937%0 1SO10
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trend of increasing IVR with excess vibrational energy for pDFB. When levels involving one or more quanta of the low-frequency, 0 cvib(S1) 120 cm-') were popuout-of-plane vibration, ~ 3 (b3u, lated via sequence transitions, an enhancement of the extent of IVR was observed. Chemical timing, using Parmenter's O2 quenching method,3 showed that the U / S ratios for the 52301and 52302levels were reduced when the 02-limited "gate" was set at ca. 15 ps (corresponding to 3000 kPa of 02).10 These results from a bulb experiment have now been subjected to further scrutiny. We have obtained dispersed fluorescence spectra from a number of vibrational levels in S1pDFB following vibrational and rotational cooling in a supersonic free-jet expansion. These data provide confirmation that the out-of-plane mode, v30, plays a role in enhancing the extent of IVR, at least in the regions of relatively low vibrational state densities accessed in these experiments (evlb < 50 states/cm-'). The experimental apparatus used by each group has been described in detail e l s e ~ h e r e . ~ ~ ~ ~ ~ Any additional relevant experimental details are included in the appropriate figure captions. N
Results Figure 1 shows the SI-So fluorescence excitation spectrum of jet-cooled pDFB. The sequence-rich, 300 K absorption spectrum has collapsed to a series of sharp, clearly resolved progressions (1) Beck, S. M.; Monts, D. M.; Liverman, M. G.; Smalley, R. E. J . Chem. Phys. 1979, 70, 1062. (2) Hopkins, J. B.; Powers, D. E.; Smalley, R. E. J. Chem. Phys. 1980, 72, 2905, 5039, 5049. (3) Coveleskie, R. A.; Dolson, D. A.; Parmenter, C. S. J. Chem. Phys. 1980, 72, 5774. (4) Amirav, A.; Even, U.; Jortner, J. Opt. Commun. 1980, 32, 266. (5) Amirav, A.; Even, U.; Jortner, J. Chem. Phys. Lett. 1980, 71, 12. (6) Dolson, D. A.; Parmenter, C. S.; Stone, B. M. Chem. Phys. Lett. 1981, 81, 360. (7) Parmenter, C. S. J. Phys. Chem. 1982, 86, 1735. (8) Beck, S. M.; Hopkins, J. B.; Powers, D. E.; Smalley, R. E. J . Chem. Phys. 1981, 74, 43. (9) Hopkins, J. B.; Powers, D. E.; Smalley, R. E. J. Chem. Phys. 1981, 74, 6986. (10) Kable, S. H.; Lawrance, W. D.; Knight, A. E. W. J . Phys. Chem. 1982,86, 1244. (11) Smalley, R. E. J. Phys. Chem. 1982, 86, 3504. (12) Parmenter, C. S. Faraday Discuss., Chem. Soc. 1983, 75, 7. (13) Smalley, R. E. Annu. Rev. Phys. Chem. 1983, 34, 129. (14) Dolson, D. A.; Holtzclaw, K. W.; Lee, S. H.; Munchak, S.; Parmenter, C. Stone, B. M.; Knight, A. E. W. Laser Chem. 1983, 2, 271. (15) Lambert, W. R.: Felker, P. M.: Zewail, A. H. J . Chem. Phvs. 1981. 75, '5958. (16) Zewail, A. H.; Lambert, W. R.; Felker, P. M.; Perry, J.; Warren, W. J . Phys. Chem. 1982,86, 1184. (17) Stewart, G. M.; McDonald, J. D. J . Chem. Phys. 1983, 78, 3907. (18) Saigusa, H.; Forch, B. E.; Lim, E. C. J . Chem. Phys. 1983,78,2795. (19) Fujii, M.; Ebata, T.; Mikami, N.; Ito, M. Chem. Phys. 1983, 77, 191.
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The Journal of Physical Chemistry, Vole88, No. 14, 1984
2938
Letters
+
WAVENUMBER ( cm-1 )
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Figure 1. Sl-So fluorescence excitation spectrum of jet-cooled p-difluorobenzene (pDFB). pDFB was seeded in 3 atm of He and expanded through a nozzle orifice of 0.4 mm. The excitation source was the second harmonic of a N2 laser pumped dye laser (bandwidth = 1 cm-I). The laser beam crossed the supersonic free jet at X/D = 75. Source: Tohoku.
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ENERGY (crn'l
Figure 3. Dispersed fluorescence spectra of pDFB from the levels 3l and 3I3O2. pDFB was seeded in 0.5 atm of Ar and expanded through a nozzle with a 0.8-mmorifice. Excitation source (bandwidth 1 cm-I) was the first anti-Stokes Raman-shifted beam from the doubled output of a NdYAG pumped dye laser (dye: R6G R640). The excitation position is marked with an asterisk. Spectra were measured with a 2.5-m cosecant scanning Czerny-Turner monochromator. Spectral resolution was 2-3 cm-I. The laser beam crossed the molecular beam at X/D = 7. Source:
5; ( O o + 817 crn-'
)
32000
Figure 2. Dispersed fluorescence spectra of pDFB from the levels (a) Oo, (b) 302, (c) 5l, (d) 5I3O2, (e) 52, (f) 52302measured with a 0.75-m grating
monochromator. Spectral resolution was 8 cm-l for spectra (a)-(e), and 22 cm-' for (f). All spectra were measured with the laser beam crossing the molecular beam at X/D = 25. Source: Tohoku. in the totally symmetric modes v3, v5, and v6 (Evib(S1)= 1251, 817, and 410 cm-', respectively20,21). Also present is a complex array of weaker transitions that were camouflaged by the intense sequences in the 300 K spectrum. (The positions of some 300 K sequences are located in Figure 1). While the vibrational and rotational cooling afforded by a free-jet expansion facilitates the observation of these weaker transitions, the vibrational cooling, if substantial, precludes the use of sequence transitions such as 52,302 for populating S1 levels involving ~ 3 0 . Instead we turn to the symmetry allowed transitions X;l30; that occur as weak overtones built on the parent transitions Po(see Figure 1). Dispersed free-jet fluorescence spectra from the levels Oo, 302, 5l, 5'302, 52, and S2302are shown in Figure 2 and from the levels 3I and 31302in Figure 3. The levels populated span some 2000 cm-' in the low to intermediate regions of the S, manifold. The vibrational structure observed in all the spectra are in good agreement with expectations based on the previously published 300 K dispersed fluorescence spectra of Coveleskie and ParmenterSz0The fluorescence spectra from levels A"302 display the same vibrational structure, built on a 30; false origin, as from the corresponding parent levels, A", thus providing certain confirmation of the x",30; assignment. Slight differences in relative band intensities in transitions involving v5 may be attributed to exciting slightly different components of the 5'...62 Fermi resonance in S,.20 (20) Coveleskie, R. A,; Parmenter, C. S. J . Mol. Spectrosc. 1981,86,86. (21) Cooper, C. D. J . Chem. Phys. 1954, 22, 503.
Discussion Figures 2 and 3 demonstrate that emission from the levels 52302 and 3I3O2 are substantially more congested than emission from and 3l, respectively. In contrast, the level 5* which lies 140 cm higher than 31302shows substantially less congestion than does 3I3O2. In fact, 52 displays a degree of congestion that is only marginally more than that for 3l which lies 380 cm-' below it. In the 300 K spectra discussed by Kable et al.,1° there was a need to take into account contributions to congested fluorescence that might arise from thermal inhomogeneous broadening (TIB), i.e., emission arising from levels excited unintentionally, but unavoidably, because of overlapping sequence or hot band structure in the absorption spectrum. The jet excitation spectrum (Figure 1) shows that this complication does not arise under our jet expansion conditions. All the emitting levels discussed here may be accessed in the cold molecule by pumping absorption bands originating from the So zero point vibrational level that stand well clear from other structure. Moreover, the 30; sequences that are the strongest in the 300 K spectrum are barely observable in the jet excitation spectrum, hence other weaker sequence and hot bands will be of negligible intensity. Contributions due to TIB may therefore be neglected when discussing the spectra shown above in Figures 2 and 3. Kable et a1.I0 used the ratio U/S of unstructured to structured emission as a gauge for the extent of IVR. Here we choose to express the division of fluorescence into structured and unstructured portions by the ratio U/(U + S). This latter ratio translates as the fraction of unstructured emission that originates from a selected SI level. It provides a direct estimate for the extent of state mixing experienced by the zero-order Is) state that is optically accessible. The estimation and interpretation of U/(U + S) ratios is discussed in detail elsewhere.22 Briefly, the ratio U/(U + S) serves as a measure for the fraction
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[CP,21/ [a2+ CP3 J
J
(22) Dolson, D. A,; Holtzclaw, K. W.; Lee, S. H.; Munchak, S.; Parmenter, C. s.;Stone, B. M.; Rock, A. B.; Muller, D. J.; Lawrance, W. D.; Kable, S. H.; Knight, A. E. W. J. Phys. Chem., to be submitted. The fraction of unstructured emission is estimated from the area of emission that rises above the zero base line, but which does not appear as discrete bands, relative to the total area of fluorescence. The division between fluorescence that constitutes structure and that which does not requires a subjective estimate to be made of the degree of band overlap that contributes to the unstructured part. guidance from computer-synthesized spectra assists here. Discrete structure that may arise due to state mixing through large coupling matrix elements with a few levels is not included in our estimate of U, hence the fraction of U is inclined to be a conservative estimate.
The Journal of Physical Chemistry, Vol. 88, No. 14, 1984 2939
Letters
0.3 0.4
1
BULB
S23O2 3,301
,*3'5'.
!
to our observations in the beam, and the influence of ~ 3 on 0 state mixing is equally apparent. However, we draw attention to the absolute values of the U/(U + S) ratios in both cases of bulb and beam. Comparison between the two sets of data shows that the fraction of unstructured emission is always less in the case of the beam measurement. On the other hand, we see that the enhancement of the U/(U + s) fraction due to ~ 3 0 ,as measured in the beam, is roughly equal to the ~ 3 enhancement 0 of U / ( U S ) seen in the bulb. For example
S 5'302
h
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== 2.5 S)p2) 0.10 0.55 =2 0.27
=-
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S, VIBRATIONAL ENERGY (ern-')
Figure 4. Plot showing the ratio U/(U + S ) of unstructured to total emission (see text) observed in the dispersed fluorescence spectra for various vibrational levels in SI pDFB. The abcissa gives the S, excess vibrational energy content of each level. The lines and shading are for guidance only. Starred data points are from experiments carried out at Griffith. Circled points refer to data obtained at Tohoku. Exact coincidences of data (U/(U + s) = 0) occur for the levels 0' and 302. The inset shows analogous results obtained at Griffith for pDFB at 300 K under bulb conditions. These bulb data correspond to revised measurem e n t ~arising ~ ~ from the earlier study of Kable et a1.I0 The U/(U + S ) measurements were extracted from spectra measured with improved signal-to-noise relative to those described previously. Note that the present data for the levels 5l and 5'302 are less ambiguous than previously.lo There appears to be negligible state mixing and little, if any, effect due to u j 0 for E , , ~ 5 1100 cm-'. Other experimental details pertaining to the bulb data are given in ref 10.
A similar situation holds for the pair of levels 31302and 3l. We note, however, that the bulb measurement of U/(U + S) for 3A30: is less certain since the 3A30; absorption transition is overlapped with another band. Accordingly, it is excluded from the inset in Figure 4. Nevertheless, the pair of levels 3'30' and 3I provide a satisfactory representative comparison with the beam results. In this case
where a and flj are the mixing coefficients for the zero-order eigenstates Is) and (llj)) that comprise the vibrational molecular eigenstate 4:
These ratios of U/(U + S) fractions supply some comfort when it is appreciated that excitation of the levels 31302 and 52302is achieved via the absorption bands 3A30: and 5,230; in the case of the beam data, but via the sequence bands 3A30: and 5i30: in the 1000 case of the bulb measurements. For SI levels above cm-', it is evident that the increase in the degree of state mixing induced by presence of ~ 3 in 0 the initially excited level is similar under both bulb and beam conditions. This close accord between the ratios of U / ( U + S) fractions for the bulb and beam data provides reassurance. The inherently superior excitation selectivity in the beam measurements would highlight any anomalies in the bulb work should they be present. We therefore discard the proposition that the influence of v3,, observed in the bulb measurements arises due to complications from TIB. We re-emphasize, however, that the absolute magnitudes of the U / ( U S) ratios is depressed in the cold pDFB molecule relative to the 300 K molecule. In order to rationalize this observation, one must explore the mechanism for the onset of state mixing at vibrational energies of ca. 1000 cm-l in pDFB and enquire how temperature may alter the prevailing situation. There is a growing acceptance of the notion that vibrational state mixing in aromatics proceeds through both vibrational anharmonic coupling and through vibration-rotation coupling of different vibrational ~ t a t e ~ . ~The , ~details ~ , ~of ~these ~ ~two ~ , ~ ~ different mechanisms of state mixing are discussed in depth elsewhere.24 The central issue of concern to us here is that the involvement of the rovibronic state density, rather than just the vibronic level density, requires consideration of how the matrix elements that describe coupling between rovibronic zero-order basis states vary with the rotational quantum numbers J and K. We are assuming, implicitly, that the primary role of the cooling induced by the supersonic expansion is to dramatically alter the rotational population in So pDFB. Hence excitation from the So(u=O) level will originate in low J,K states. The strict rotational selection rules for electronic transitions will ensure that only states with low J',K'quantum numbers will be populated in the optically
Access to 4 is through the nonvanishing matrix element (slp10) and it is assumed that all the (1,lc~IO)are zero for absorption from the So zero point vibrational level. Obviously, for congestion to appear in emission, (ilhll,) # 0, where i denotes ground-state levels accessible via emission from 1,. Figure 4 displays the U / ( U + S) ratios extracted from the spectra shown in Figures 2 and 3. Included also are U / ( U + S) estimates for the levels shown in Figure 1, but measured from spectra recorded independently at Griffith (with 2-3-cm-' spectral resolution), including an additional level, namely, 3I5I. The Tohoku and Griffith data are in close agreement. Levels above -1000 cm-' that do not contain excitation in ~ 3 show 0 U/(U S) ratios that increase smoothly with excess vibrational energy. In contrast, the levels 31302 and 52302deviate sharply from the trend shown by the other levels. The fraction of unstructured emission for the levels 31302 and 52302are 0.22 and 0.25, respectively, commpared with 0.07 and 0.1 for the levels 3l and 52 (average of Griffith and Tohoku data). We may conclude therefore that these combination levels containing excitation in ~ 3 display 0 increased state mixing relative to their parent counterparts with no excitation in ~ 3 0 . This conclusion, based on fluorescence spectra observed from jet-cooled S , pDFB, is in accord with the conclusion drawn earlierIO on the basis of pDFB fluorescence spectra measured at 300 K. However, there are some further aspects that arise from a more detailed comparison that need to be highlighted. We reexamine the bulb result^'^.^^ for pDFB. Figure 4 (inset) also shows the U / ( U + S ) ratios obtained from 300 K spectra for all the levels studied under beam conditions. It is clear that the overall trend of increasing u / ( U s)with evib is analogous
+
+
(23) Lawrance, W. D. Ph.D. Thesis, Griffith University, 1983.
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(24) Lawrance, W. D.; Knight, A. E. W. J . Phys. Chem., to be submitted.
2940
J. Phys. Chem. 19M.88, 2940-2949
accessible SIvibrational molecular eigenstate under examination. Quantitative tests of these notions are now emerging.22-25Here we simply recount for example that the matrix elements for Coriolis mixing scale roughly with J (for low K ) for B,C axis coupling in a prolate symmetric top. Hence the extent of mixing will naturally be less among states with low J quantum numbers than states with high J quantum numbers. Admittedly, reduction in rotational temperatures results in a collapse of the rotational band contours and this collapse may be reflected in smaller U/(U + S) ratios in the beam measurements. However, the persistence of an appreciable unstructured contribution a t the lowest temperatures in the beam experiments for levels such as S2302,together with computer syntheses of the dispersed fluorescence spectra based on models of state mixing22v26argue that the overlap of rotational band contours provides an insufficient addition to the unstructured component to account for the differences between bulb and beam fluorescence spectra. Finally, we address briefly the question of why the mode ~ 3 0 in pDFB is effective in increasing the degree of state mixing in pDFB. There is evidence from the chemical timing studies of Holtzclaw and P a r m e ~ ~ t and e r ~ ~from the direct picosecond measurements of Moore et a1.28that the influence of ~ 3 persists 0 in the real-time observation of IVR associated with the dephasing of a packet of coherently pumped eigenstates. It should be emphasized that the SVL fluorescence spectra probe the overall state mixing associated with the optically accessed Is) state, and this mixing may include levels lying well outside a laser bandwidth. We discuss these differences between the real-time and static (25) Lawrance, W. D.; Kable, S. H.; Knight, A. E. W. J. Phys. Chem., to be submitted. (26) Dolson, D.A. Ph.D. Thesis, Indiana University, 1981. (27) Holtzclaw, K. W.; Parmenter, C. S., private communication.
fluorescence experiments elsewhere.24 Here it is sufficient to conclude that the role of ~ 3 with 0 respect to IVR in pDFB appears to be confirmed by Moore et a1.28and Holtzclaw's experiment^.^^ Kable et al.1° suggested that the vibrational potential for p3,, may contain higher-order anharmonic terms, Le., (a3/aQ3)oQ3and (a4//aQ')oQ', that were larger than those for other normal modes. If so, this would contribute to larger coupling matrix elements when the Is) state involved quanta of ~ 3 0 . However, it is our view now that this explanation alone cannot account for the observations. The arguments extend beyond the scope of this paper and the issue is addressed in full in a forthcoming p ~ b l i c a t i o n .The ~~ following conclusions emerge. The low-frequency of Y'~~.( 120 cm-') is instrumental in the overall pattern of state mixing; overtones and combinations in0 dominant among the (I1 ) ) volving ~ 3 are v30 may be coupled through a specihc rotation-vibration interaction with a subset of the (Ilj)) N
Acknowledgment. This work was supported by the Australian Research Grants Scheme and by the Japanese Ministry for Education. We are grateful to Mr. Geoffrey B. Edwards for his contributions to the construction of the supersonic jet apparatus at Griffith and for discussions initiated by him at Tohoku during his tenure in Japan as a Monbusho Fellow. A.E.W.K. is grateful for travel support from the US-Australia Agreement for Scientific Cooperation (National Science Foundation, USA, and Department of Science and Technology, Australia) that enabled him to discuss aspects of this work with Prof. C. S. Parmenter and Dr.K. W. Holtzclaw at Indiana University. Registry No. p-Difluorobenzene, 540-36-3. ~~~
~~
(28) Moore, R.; Doany, F. E.; Heilweil, E. J.; Hochstrasser, R. M. Faraday Discuss., Chem. Soc. 1983, 75, 331.
FEATURE ARTICLE Fourier Transform Infrared Spectra of HF Complexes in Solid Argon Lester Andrews Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901 (Received: December 8, 1983)
Hydrogen fluoride and base molecules ranging in strength from N, to N(CH3)3have been codeposited with excess argon at 12 K. Fourier-transform infrared spectra of the samples before and after sample warming to allow reagent diffusion and association provide identification of 1:1 and 1:2 hydrogen-bonded complexes. Strong v, and y absorptions of the HF submolecule in the complexes vary with the proton affinity of the base and characterize the strength of the hydrogen-bonding interaction. Base submolecule modes show small displacements from the base molecule spectrum, depending upon the structure of the complex. These matrix infrared studies of HF complexes are complementary to gas-phase infrared and microwave spectra.
Introduction The hydrogen-bonding phenomenon is of considerable importance in chemistry and biology. Simple molecular hydrogenbonded complexes can provide useful models for this phenomenon. Hydrogen fluoride is particularly useful for the study of hydrogen bonding because it forms strong hydrogen bonds to suitable bases and HF and D F are straightforward to synthesize in the absence of water; in addition, HF complexes give simple vibrational spectra and meaningful theoretical calculations can be done for low molecular weight species. 0022-3654/84/2088-2940$01.50/0
A number of physical experimental methods have been employed to study simple molecular HF complexes. Infrared spectra of gaseous mixtures reveal broad product absorption^,'-^ which have the advantage of observing hot-band fine structure but the disadvantage of spectral absorption by the reagent molecules. The (1) Couzi, M.; LeCalve, J.; Van Huong, P.; Lascombe, J. J. Mol. Struct. 1970, 5, 363. (2) Thomas, R. K. Proc. R. SOC.London, Ser. A 1971, 325, 133. (3) Thomas, R. K. Proc. R. SOC.London, Ser. A 1975, 344, 579.
0 1984 American Chemical Society
