J. Phys. Chem. 1082, 86, 3504-3512
3504
FEATURE ARTICLE Vibrational Randomization Measurements wlth Supersonic Beams R. E. Smalley Rice Quantum Institute and Department of Ctwmbby, Rlce Universny. Houston, Texas 77251 (Recdvd Aprll 15, 1082; In Final Form: June 18, 1082)
Through the use of ultraviolet laser excitation of a variety of large, ultracold molecules in collisionless supersonic beams, it has been possible to explore in depth the onset and ultimate dominance of intramolecular vibrational randomization (IVR)in excited polyatomics. Within molecules wit5 ordinary chemical bonds, the only effective barrier to rapid and complete IVR is an inadequate density of states. Even for abnormally well-localized initial vibrational excitations,this critical density of states is found to be on the order of lo3states per cm-' or less. Above this critical region, localized vibrational excitation randomizes on a subnanosecond time scale.
I. Introduction Intramolecular vibrational randomization processes (IVR), and their rate, and their degree of completeness have traditionally ranked high among the prime intellectual issues of chemical The most fundamental of these processes is that pertaining to the molecule itself, isolated and free from any outside perturbing influence. Unfortunately, as is common in so many other areas of science, this most fundamental process has also been the most difficult to study. From the viewpoint of experimental measurements the difficulty has resided chiefly in (A) an inability to cleanly deposit vibrational energy in a well-defined, localized portion of the molecule, and (B)an inability to subsequently probe the evolution of this localized excitation without perturbation. At the high vibrational state densities required for unimolecular IVR, even extremely long-range collisions can produce a substantial effect, and the correspondingly extreme vacuum necessary to prevent such collisions has presented a considerable problem in detection of the excited molecule. From the theoretical viewpoint, IVR is extremely difficult to deal with because the coupling responsible for the decay process is a sensitive function of the anharmonicities of the full potential energy hypersurface. The normal-mode approximation which is so useful in the currently welldeveloped theory of electronic radiationless transitions would forbid any and all vibrational radiationlesstransition from the outset. First principles prediction of the rates of even electronic radiationless transitions is still well beyond the abilities of theory. Prediction of IVR rates would not even be contemplated by current theorists were it not for the central importance these IVR rates have in chemistry. Recently a key issue has been whether there are any circumstances wherein vibrational excitation can remain localized for a chemically relevant time period. Is it possible for vibrational energy to be localized for a time sufficient to permit chemistry to occur only on the side or portion of the molecule initially excited with a laser? If so, a dramatically different chemistry would be possible, unlike anything currently done by thermal or ordinary photochemical means. If not, laser chemistry would be restricted to a more ordinary molecule-or isotopespecificity (which can be quite impressive, even so). For most currently available lasers the relevant time scale for 0022-3654/82/2086-3504$0 1.2510
depositing the initial excitation is >1 ns. For most known unimolecular reactions, the relevant time scale is also rather long: the time needed for energy to rattle around the acceeeible phase space of even a relatively small portion of a molecule before it finds a reactive channel is usually >1 ns unless extremely high excess energiea are used.= Of coime, a highly specific laser chemistry would be assured if one could pump directly along a reaction coordinate, but this is generally prohibited by negligible vibrational overlaps for the relevant optical transition. For picosecond excitation lasers, mode- or region-specific chemistry would conceivably still be possible since the up-pumping rate could compete with even very rapid IVR, but here the laser flux would have to be so high that other processes such as multiphoton ionization, dielectric breakdown, and photolysis of products would severely limit the yield of desired products. So for laser chemistry the issue of unimolecular vibrational randomization on a nanosecond time scale is particularly relevant. (1) Noid, D. W.; Korrzykowski, M. L.; Marcus, R. A. Annu. Reu. Phys.' Chem. 1981,32, 267. (2) Rice, S. A. Adu. Chem. Phys. 1981,47, 117. (3) Jortner, J.; Levine, R. D. Adu. Chem. Phys. 1981,47, 1. (4) McDonald, J. D. Annu. Reu. Phys. Chem. 1979,30,29. (5) Brumer, P. Adu. Chem. Phys. 1981, 47, 201. (6) Flynn, G. W. Acc. Chem. Res. 1981,14,334. (7) Golden, D. M.; h i , M. J.; Baldwin, A. C.; Barker, J. R. Acc. Chem. Res. 1981,14,56. (8)Oref, I.; Rabinovitch, S. Acc. Chem. Res. 1979, 12, 166. (9) Freed, K. F. Adu. Chem. Phys. 1980, 42, 207. Acc. Chem. Res. 1978,11,74. (IO) Reddy, K. V.; Heller, D. F.; Berry, M. J. J. Chem. Phys. 1982,76, 2814. (11) Stannard, P. R.; Gelbart, W. M. J. Phys. Chem. 1981,85, 3592. (12) (a) Parmenter, C. S. J. Phys. Chem. 1982,86,1735. (b) Coveleskie, Dolson, D. A,; Paramenter, C. S. J. Chem. Phys. 1980, 72, 5774. (13) Wolf, R. J.; Hase, W. L. J. Chem. Phys. 1980, 73, 3779. (14) Thiele, E.; Goodman, M. F.; Stone, J. Chem. Phys. 1980,69, 18. (15) Kay, K. G. J. Chem. Phys. 1980, 72, 5955. (16) Schulz, P. A,; Sudbo, Aq. S.;Krajnovich, D. J.; Kwok, H. S.; Shen, Y. R.; Lee, Y. T. Annu. Rev. Phys. Chem. 1979,30,379. (17) Bloembergen, N.; Yablonovich, E. Phys. Today 1978,31, 23. (18) Heller, E. J. Acc. Chem. Res. 1981, 14, 368. (19) Levine, R. D. Adu. Chem. Phys. 1981,37, 239. (20) Miller, C. M.; McKillop, J. S.; Zare, R. N. J.Chem. Phys. 1982, 76, 2390. (21) Zare, R. N.; Bemstein, R. B. Phys. Today 1980,33, November. (22) Lin, S. H., Ed.'Radiationless Transitions";Academic Press: New York, 1980. (23) Robinson, P. J.; Holbrook, K. A. 'Unimolecular Reactions"; Wiley-Interscience: New York, 1972.
0 1982 American Chemical Society
Feature Article
Over the past several years at Rice we have explored this issue of nanosecond IVR with the new capabilitiesafforded by collisionless, ultracold supersonic molecular beams and narrow-band, tunable pulsed lasers. We have used ultraviolet absorptions involving electronic transitions, letting the UV transition moment function pick out for us just a few vibrations from the many available in a large polyatomic. The extreme cooling of the supersonic beam permitted large, floppy molecules to be studied so that IVR was a real possiblity even for a single quantum excitation in the laser-pumped mode. We have searched for cases where IVR would be expected to be abnormally slow: molecules where the UV transition moment selects modes involving motion on only one side, the other side of the molecule continuing its cold, zero-point nuclear motion. As discussed below, monocyclic aromatic rings substituted with long alkyl side chains have provided some excellent examples. Here there are a variety of ring-centered vibrational modes which are active in single-quantum transitions in the UV spectrum. Some of these spectrally active modes are particularly well isolated in the aromatic ring because they do not involve motion of the carbon to which the alkyl chain is attached. Vibrational energy in such a case is forced to decay from a fairly rigid, low-amplitude, high-frequency motion localized in the ring into extremely large-amplitude, very low-frequency torsional and bending modes of the chain. In some of the cases we have studied, the frequency mismatch between the excited "system" mode in the ring and the "bath" modes in the chain ultimately receiving the energy is greater than 50 to 1. It would be hard to find a chemically bound molecular system wherein IVR will proceed slower than in these ring + chain cases. This article is organized as follows. Section 11deals with IVR measurements in the S1excited electxonic state of the ring + chain molecules including experiments where predissociation of a van der Waals complex competes with the IVR. Section I11 discusses an experiment with alkylbenzenes where IVR is measured in the So ground electronic state for some of the same localized modes studied previously in the excited S1state. Section IV looks at probes of IVR occurring in isolated molecules following an electronic radiationless transition from a higher electronic state-in this case IVR within triplets produced by intersystem crossing from S1.Section V then extends this discussion to internal conversion and summarizes the implications of such IVR results to conventional and laserdriven photochemical processes. 11. IVR in S1Excited States For many aromatic molecules the first excited electronic singlet state, S1,has a potential energy surface that is much like that of the ground state. The TU* excitation which gives rise to this S1state produces only a slight reduction of bonding within the ring with most vibrational modes reduced in frequency by less than 20%. Vibrational energy flow on this upper S1surface should therefore be quite similar to that on the ground So surface, except that-due to fluorescence-motion on the S, surface is much easier to monitor. In this section a variety of experiments are reviewed where aromatic ring + chain molecules cooled in a supersonic beam are laser excited to a particular vibrational level in the S1state. The subsequent time evolution of this vibrational energy on the S1surface is then monitored by the spectral nature of the dispersed fluorescence from these excited molecules as they travel in the absence of collisions down the molecular beam. A . Alkylbenzenes. The most extensively studied ring + chain molecules have been the alkylbenzenes them-
The Jwrnal of phvsical Chemktry, Vol. 86, No. 18, 1982 9505
selves.24 Under the supersonic expansion conditions routinely attainable with current techniques, intense beams of the alkylbenzenes are readily prepared with all internal degrees of freedom effectively depopulated. Generally only transitions originating in the ground vibration quantum level are observed and the entire rovibronic bandwidth is usually less than 1 cm-', corresponding to a rotational temperature of less than 1 K. The cooling during the expansion is, however, sufficiently sudden (Atmh I lo5 s) that the various conformations of the alkyl chain do not have time to equilibrate. At every carbon-carbon bond in the chain (except the first and the last) there are two gauche conformations and one trans conformation. The gauche conformers are slightly less stable than the trans and the potential barrier to interconversion is believed to lie in the range of 1000-1500 cm-'. At room temperature in the supersonic nozzle roughly equals numbers of molecules will be found in the gauche and trans potential wells for any particular C-C bond, and this population ratio tends to persist throughout the course of the supersonic expansion and in the subsequently collisionless molecular beam. The ultraviolet absorption spectrum of these alkylbenzenes is beautifully simple in the cold supersonic beam.24a Only a few ring modes are found to be active in progressions and combinations, and several of these modes are found to be extremely insensitive to changes in the nature or length of the alkyl chain. These substituent insensitive active ring modes have long been known from studies of the infrared spectra of monosubstituted benzenes: they are in-plane ring distortion modes which do not affect the site to which the substituent is attached. In the alkylbenzenes the most active modes in the UV spectrum are 6b' (530 cm-') and 12' (932 cm-') whose frequencies are found to vary by less than 1part in 500 over the entire series from methylbenzene to octylbenzene. Clearly then, these are vibrational modes which must be very well isolated in the ring section of the molecule. Since they are strongly active modes in the spectrum, it is quite straightforward to tune a pulsed ultraviolet laser so as to generate a sample of S1excited molecules which are cold in all vibrational degrees of freedom except one of these simple harmonic motions (6b' or 12l) in the ring. The dispersed fluorescence spectrum will then reveal the fate of this localized Figure 1,for example, shows the fluorescence spectrum of 6b' excited alkylbenzenes as a function of chain length from methyl through heptyl. In order to ensure the 6b' excitation is distinctly on one "side" of the molecule, the laser excited only those molecules in the beam which are trans (actually best termed anti) with respect to the bond between the first and second carbon atoms of the chain (countingout from the ring). Once the conformation about this bond is set, the rest of the chain is forced to extend out away from the benzene ring and all significant ringchain interactions are constrained to pass through the first methylene unit of the chain. Luckily, this distinction is easily made by the excitation laser in the UV absorption process since all molecules which are not trans in this C1-Cp bond have a UV spectrum shifted to the red by roughly 60-70 cm-l due to an intramolecular solvation effect. For the first few members of the alkylbenzene series, the fluorescence spectrum consists of a simple set of sharp bands each assignable to a transition originating from the (24) (a) Hopkins, J. B.; Powers, D. E.; Smalley, R. E. J . Chem. Phys. 1980, 72,6039. (b)Ibid. 1980, 72,5049. (c) Ibid. 1980, 73,683. (d) Ibid. 1981, 74, 745. (e) Mukamel, S.; Smalley, R. E. Ibid. 1980, 73, 4156.
S500
Smaliey
The Journal of phvsicel Chemistry, Vol. 86, No. 18, 1982 1
M E T H Yl. 17’
METHYL
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FREQUENCY
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Flgwe 1. Dispersed fluorescence spectra from alkylbenzenes In a supersonic beam. Initial excitatbn was performed by a pulsed laser tuned to the 6b: vibronic band of the SI So ultraviolet absorption band. The nuclear displacements of the 530cm-’ ringkcallzed vibrational mode are shown In the molecular diagram on the left. The broad red-shifted pattern seen In the fluorescence spectrum of the longer chain akylbenrenes shows that the 6b’ chain vibrational relaxation has proceeded quickly compared to the fluorescence llfe-
--
time.
6b1 vibrational level in the fluorescing S1state. By n-butylbenzene, however, a distinctly different type of fluorescence spectrum begins to be seen as well. It is a broadened, slightly red-shifted version of the fluorescence one expects from a cold alkylbenzene molecule having no vibrational excitation in the ring. For n-pentylbenzene this broadened spectrum is more prominent, and by n-hexylbenzene, it is the only spectrum observed. This broadened spectrum is the pattern expected from an alkylbenzene molecule whose vibrational energy has relaxed. It has drained into the bends and torsions of the chain. These low-frequency chain modes are not active in the UV spectrum: in the S1 So transition they follow quite welJ a Au = 0 propensity rule. Such Au = 0 transitions are termed sequences and the observed broadening is due to the same phenomenon that causes sequence broadening in the SI So absorption spectrum of room temperature molecules. In the supersonicbeam case, each S1fluorescing molecule has 530 cm-l of vibrational energy distributed over the various torsional and bending degrees of freedom of the chain. For any particular chain motion, the potential surface is only slightly different in the S1 excited state from the corresponding surface for the Soground state. If the surfaces were identical, all sequence transitions would occur at the same frequency, but the slight difference in the two surfacea produces a shift in the sequence transition frequency (the %equence shift”) which depends on the amount of excitation involved in the relevant mode. Since there are many ways of distributing the 530 cm-l among the various chain modes, there are many sequence shifts and the distribution of these sequence shifta produces the sequence broadening observed in the fluorescence spectrum. Completeness. Although it is a bit difficult to discern from Figure 1 reproduced as small as it must be in this article, there is a remarkably uniform tendency for the “relaxed” fluorescence spectrum of the 6b1 excited alkyl-
-
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1000 2000 3000 4000 FREQUENCY (CM-’)
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Flgwe 2. Dispersed fluorescence spectra from alkylbenzenes in a supersonic beam. In this case inRiai excitation was to the 12; band of the S, So absorption spectrum. Compare with Figure 1 where a lower energy ring mode was excited.
benzenes to become progressively narrower and less red shifted as the alkyl chain length is increased. Figure 2 shows this same phenomenon more clearly. Here the 12l ring-centered mode has been excited. Since the available vibrational energy has now almost doubled (from 530 to 932 cm-’), the IVR process is found to onset at much lower chain lengths. Already for ethylbenzene a substantial fraction of the fluorescence intensity is in a very markedly broadened and red-shifted pattern. In the case of such a short chain molecule, the bending and torsional modes involve atoms which are, of course, quite near the benzene ring. Although the m*excitation on the ring will not drastically affect the force constants for torsions and bends of the chain, there will be at least some difference in the frequencies of these modes between the S1 and So states. The closer a particular bend or torsion is to the benzene ring, the larger will be the frequency difference upon excitation to SI.So in the case of ethylbenzene where all chain modes are close to the ring, it is quite readily understandable that large sequence shifts arise from the excitation of these modes with a resulting large red shift and broadening of the fluorescence spectrum. In the progressively longer chain molecules an increasing fraction of the available chain modes are localized far from the benzene ring where their is little change in the potential surface due to a?r* excitation on the ring. As shown in Figure 2, the dispersed fluorescence spectrum reflects this fact by becoming sharper and less red shifted as the chain length is increased. The most interesting aspect of this whole discussion is that this narrowing phenomenon would not have been observed at all were it not for the fact that the vibrational energy initially deposited in the ring has migrated throughout the full length of the chain. The extent of the red shift and broadening of the “relaxed” fluorescence is therefore a measure of the completeness of the IVR process. Consider, for example, the case of n-heptylbenzene initially excited in the 12l ring mode. Flow of vibrational energy out of the 12l mode would be seen as a loss of intensity of fluorescence in sharp bands such as 12;) 12; 6b7, 12:, etc.-a pattern similar to that shown for methylbenzene in Figure 2. Suppose, however, that the vibrational randomization process were not complete: in-
Feature Article
stead of flowing the entire length of the alkyl chain, the vibrational energy hung up in a few of the bends and torsions of the first few linkages of the chain. Since these linkages are close to the benzene ring, the resultant fluorescence spectrum would look much like that seen for ethyl- or propylbenzene in Figure 2. After a sufficiently long time period the energy would flow throughout the entire chain and the fluorescence spectrum would evolve in time to a considerably sharper and less red-shifted pattern. Since we do not know the exact frequencies of the bends and torsions as a function of chain length, we cannot predict the spectrum for a fully random distribution of 530 or 932 cm-' worth of vibrational energy in an alkylbenzene. We do know, however, that the observed spectrum continues to sharpen as the chain length increases-the vibrational energy distribution is responding to additional units being added to the chain. Another known datum is that the fluorescence patterns shown for the seven alkylbenzenes in Figures l and 2 are the same in the first nanosecond as they are 100 ns after the moment of laser excitation.24cThere is no nanosecond time scale evolution of the fluorescence pattern, only a simple single exponential decay with a time constant of roughly 80 ns. For the long chain alkylbenzenes, therefore, the IVR process is over on a time scale of
