J . Phys. Chem. 1989, 93, 4083-4091 4083

be delocalized in the three oxygen atoms of NO,' like the reso- nance structure 111, which may be less electrophilic and less reactive. In the condensed phase, NO,' is reported to be a Y- shaped structure,36 in which an unpaired electron is localized on one oxygen atom like the canonical structures I and 11. This radical center is quite reactive and electrophilic. This change of the electronic distribution may also be one of the causes for the medium effect.

For the reaction of NO,' with phenol in the gas phase,,' it is assumed that the addition of NO,' to the benzene ring occurs first followed by the elimination of phenolic hydrogen. In the case of

(36) Gundu Rao, T. K.; Lingam, K. V.; Bhattacharya, B. N. J. Magn.

(37) Atkinson, R.; Aschmann, S. A,; Winer, A. M. Enuiron. Sci. Technol. Reson. 1974, 16, 589.

1987, 21, 1123.

aryl aldehydes in acetonitrile, although direct evidence for the formation of a cyclohexadienyl radical was not observed by our flash photolysis experiments, the smaller values in log A and E , suggests the complex formation between NO,' and *-bonds in the phenyl ring or/and the C=O group in the transition state.

Acknowledgment. We are thankful for a Grant-in-Aid (No. 62540314 and 63550676) for Scientific Research from the Ministry of Education, Science and Culture of Japan.

Registry No. K,(Ce(NO,),), 17126-44-2; NO;, 12033-49-7; HCHO, 50-00-0; CH3CH0, 75-07-0; PhCHO, 100-52-7; (CH3)2CO, 67-64-1; PhH, 7 1-43-2; PhCN, 100-47-0; PhOCH3, 100-66-3; CHICH2CH0, 123-38-6; (CH,),CHCHO, 78-84-2; (CH3)3CCHO, 630-19-3; p - NO2C6H4CHO, 555-16-8; m-NO2C6H4CHO, 99-61-6; p-CNC6H4CH0, 105-07-7; m-CNC6H4CH0, 24964-64-5; m-CIC6H4CH0, 587-04-2; p-CIC,jH4CHO, 104-88-1; p-CH,C,H,CHO, 104-87-0; p - CH3OC6H,CHO, 123-1 1-5.

Acetone Photophysics in Seeded Supersonic Molecular Beams

Hanna Zuckermann, Bernhard Schmitz, and Yehuda Haas*

Department of Physical Chemistry and The Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91 904, Israel (Received: September 26, 1988)

The fluorescence decay characteristics of acetone-h6 and acetone-d6 upon excitation of the SI ]A2 state were studied in a supersonic molecular jet. It is shown that both internal conversion (Sl-So) and intersystem crossing (&-TI) take place in the isolated molecule. At theorigin, the rate of internal conversion is 11.5 X IO5 and 2.3 X lo5 s-l for acetone-h6 and acetone-d6, respectively. The decay time of acetone increases gradually as the excitation frequency increases, due to better coupling with TI . This trend reverses at an excess energy of about 2250 cm-I, where a very rapid decrease in the decay time as a function of energy is observed. The sudden change is ascribed to the onset of dissociation on the TI surface, and a barrier of 93.5 kcal/mol (above the ground state) is found for this process. The results are consistent with a radiative lifetime of about 10 K S for SI, as deduced from absorption measurements. The low fluorescence yield is accounted for, in the isolated molecule, by internal conversion or intersystem crossing. In bulk systems, these intramolecular processes alone do not accoun$ for the observed decay times, and collisional quenching must be taken into account.

Introduction According to Calvert and Pitts' classic textbook,' "the photo-

chemistry of ketones is the most thoroughly studied of any class of compounds". This comment refers to the chemical events initiated by light absorption at the n r * transition centered around 280 nm. Being the simplest ketone, acetone is probably the best studied molecule of this group. Some aspects of its photochemistry are well-established. The most important primary reaction is believed to be the homolytic cleavage to form an acetyl and methyl radical: CH3COCH3 - C H 3 C 0 + CH, AHo = 81 kcal/mol (1)

The quantum yield has been carefully measured and is reported to rise with the temperature to a maximum of 100% at 130 OC in the gas phase.2 The confidence level in these results is reflected by the fact that the system is often used as an actinometer in the UV. The triplet state is considered an important participant in this reaction, a feature common to all carbonyl compounds. The fluorescence quantum yields and lifetimes have been reported for both the gas3q4 and the liquid4s5 phases. The results have been interpreted as indicating very efficient intersystem crossing to TI.

Nevertheless, many aspects of acetone photochemistry remain to be elucidated. Some important parameters need to be ex-

( I ) Calvert, J . G.; Pitts, J. N. Photochemistry; Wiley: New York, 1966;

(2) Cundall, R. B.; Davies, A. S. Proc. R . SOC. London, A 1966,290, 563. (3) Hansen, D. A.; Lee, E. K. C. J . Chem. Phys. 1975, 62, 183. (4) Halpern, A. M.; Ware, W. R. J . Chem. Phys. 1971, 54, 1271. (5 ) Dalton, J. C.; Turro, N. J . J . Am. Chem. SOC. 1971, 93, 3569.

p 319.

perimentally measured, and discrepancies between different reports need to be settled. Thus, some of the rates and energy barriers relevant to the photochemistry of acetone, listed in a recent review: are admittedly estimates or guesses. A well-known anomaly is recorded in the literature concerning the radiative lifetime of acetone. Using integrated absorption measurements, one arrives at a lifetime of about 10 ~ s , ~ 3 ~ 9 ~ while a determination based on the ratio of the measured lifetime to the measured quantum yield leads to 1-2 bs.33498

In recent years the photophysical properties of many isolated molecules have been extensively studied with pulsed lasers as light sources and molecular beams as a means to ensure collisionless conditions. In particular, considerable efforts were dedicated to the study of simple a l d e h ~ d e s , ~ - l ~ leading to a much better un- derstanding of the primary photochemical processes. The ab-

(6) Nicholson, A. J. C. Can. J . Chem. 1983, 61, 1831. (7) Worden, E. E., Jr. Spectrochim. Acta 1966, 22, 21, reports on oscillator

and 3.64 X lo4 for acetone-h, and acetone-d6, re-

(8) Turro, N. J . Modern Mechanistic Photochemistry; Benjamin: Ndw

(9) Michel, C.; Tramer, A. Chem. Phys. 1979, 42, 315. (IO) Moore, C. B.; Weisshaar, J . C. Annu. Reo. Phys. Chem. 1983, 34,

strength of 4.14 X spectively.

York, 1978.

525. (11 ) Henke, W. E.; Selzle, H. L.; Hays, T. R.; Schlag, E. W.; Lin, S. H.

(12) Noble, M.; Lee, E. K. C. J . Chem. Phys. 1984,80, 134. (13) Noble, M.; Lee, E. K. C. J . Chem. Phys. 1984, 81, 1632. (14) Dubs, M.; Muhlbach, J.; Bitto, H.; Schmidt, P.; H u h , J. R. J . Chem.

J . Chem. Phys. 1982, 76, 1327, 1335.

Phys. 1985, 83, 3755. (15) Muhlbach, J . ; Huber, R. J. J . Chem. Phys. 1986, 85, 4411.

0022-3654/89/2093-4083$01.50/0 0 1989 American Chemical Society

Zuckermann et al. 4084 The Journal of Physical Chemistry, Vol. 93, No. 10, 1989

sorption spectrum of acetone is very congested a t elevated tem- peratures, due mostly to many low-frequency vibrational modes. The method of seeded supersonic molecular beamsi6 thus offers a distinct advantage for this molecule. Indeed, cooling in a su- personic jet leads to a vibrationally resolved ~ p e c t r u m ’ ~ and allows the study of single vibronic level behavior in isolated molecules. We report herewith some results of a study of acetone and its perdeutcrated analogue under jet conditions. The spectral reso- lution allowed only the separation of different vibrational levels, in distinction with work on some aldehydes performed with ro- tational-state r e s o l u t i ~ n . ~ - ~ ~ Even so, significant progress is achieved by comparison with previous studies of acetone. The roles of internal conversion and intersystem crossing in the isolated molecules can be assessed. The threshold for a rapid radiationless process taking place on the triplet surface is accurately determined. Circumstantial evidence is presented, supporting the hypothesis that this process is due to reaction 1. The decay characteristics are discussed in terms of radiationless transition theory of in- termediate-sized molecules. It is shown that the decay time of the singlet, measured in the bulk, reflects the dephasing time of the initially prepared state. Thus, the lifetime “anomaly” is due to comparison of two unrelated properties. A direct measurement of the decay time of an isolated vibrationless (CD,)*CO molecule leads to a lifetime of 3 ps, much longer than that of (CH&CO but still significantly shorter than the calculated radiative one. The radiationless process responsible for this increased decay rate is proposed to be internal conversion.

Results The experimental apparatus used in Jerusalem was described

in a previous communication,’* so only a brief description is given. Acetone was seeded i n helium or argon, and the mixture was expanded through a pulsed nozzle into a vacuum chamber maintained a t lo-’ Torr. The molecular beam was crossed by a frequency-doubled tunable dye laser beam, the resulting fluorescence being viewed through a cutoff filter and detected by a photomultiplier. The signal was digitized, averaged by an on-line computer, and recorded as either a decay curve or a time-resolved excitation spectrum.

Acetone Seeded in Helium. A portion of the excitation spec- trum obtained upon using a mixture of 0.1% acetone i n 5 atm of helium, expanded through a 0.35-mm nozzle is shown in Figure 1 . It is seen to be quite similar to the spectrum reported pre- viously” i n an argon-seeded beam, although some differences in peak locations and intensities can be discerned. As noted by Baba et a1.,I7 the spectrum becomes more and more congested as the excitation frequency increases. This trend was confirmed by us for both argon and helium. Thus, observing the fluorescence a t a delay time of 200 ns after the laser pulse, the excitation spectrum becomes severely congested around 3 13 nm, and concurrently the intensity of the emission is significantly reduced. Tuning the laser to individual peaks, rotational contour envelopes could be de- termined. (The 0.2-cm-’ resolution available in these experiments precluded the observation of individual rotational lines). In the low-energy region, the contours were very similar to those reported by Baba et aI.,l7 thus establishing that the rotational temperature was about 5 K. At higher energies some spectra displayed complex rotational contours, as shown in Figure 2.

The time evolution a t several excitation energies was deter- mined. Below about 2000-cm-’ excess energy, the decay could be fit quite well with a single exponential. Several attempts to check for rotational dependence of the decay rate were made by tuning the excitation frequency across the rotational contour. Within the precision of the measurements, the observed decay rates for a given vibronic band were identical. It should be remembered that the spectral resolution did not allow the excitation of a single

(16) Levy. D. H . ; Wharton, L.; Smalley, R. E. I n Chemical and Eio- chemical Appliralions of Lasers; Moore, C . B., Ed.; Academic: New York. 1977; Val. 2, p I .

(17 ) Baba, M.: Hanazaki, I . ; Nagashima. U. J . Chem. Phys. 1985, 82, 3938.

(18) Anner, 0.: Haas, Y. Chem. Phys. Lerr. 1985, 119, 199.

i 314.3 302 308.1

I I 314.3 316.1 317.9

I I 317.9 319.5 321.1

Wavelength (nm) Figure 1. Part of the fluorescence excitation spectrum of acetone-h6 seeded in helium, taken with 0.2-cm-l spectral resolution.

J level. The overall trend observed was a decrease of the decay rate upon increasing the excess energy, AE, over the range 0-2000 cm-I. Thus, in the case of (CH,),CO one obtains 1.25 X lo6 s-’ a t the origin and 4 X lo5 s-’ with AE = 1500 cm-’. However, the decrease is not entirely monotonic, as shown in Figure 3.

At high energies, this relatively long decay component was preceded by a much faster one whose decay time could not be determined with our temporal resolution of 10 ns. This “spike” was observed previously in room-temperature samples,19 as well as in other similar sized molecules in the jet.14,15.20 Compared to bulk conditions, the energy onset of the spike can be determined with much higher accuracy in the jet. The amplitude ratio of the

(19) Greenblatt, G. D.; Ruhman, S.; Haas. Y . Chem. Phys. Lett. 1984,

(20 ) Matsumoto, Y . : Spangler, L. H.; Pratt, D. W. Lnser Chem. 1983, 2, 112. 200.

91.

Acetone Photophysics in Seeded Supersonic Molecular Beams The Journal of Physical Chemistry, Vol. 93, No. IO, 1989

I 17'

314 9 315 2 31x 6 3 I R.8

1085

321 7

Figure 2. Rotational contours of some vibronic bands of acetone-hG in a seeded supersonic beam. Assignment is according to ref 17.

spike to that of the long-lived component is found to increase with excitation energy in both acetone-h6 and acetone-d6. The excess energy a t which the spike becomes clearly observable is about 600 cm-I for acetone-d6 and 1200 cm-' for acetone-h6.

The time dependence of the long-lived component can be represented faithfully by a single-exponential form even after the appearance of the spike. The decay time increases slowly with energy. The results for both isotopic species are collected in Table I. Beyond a certain energy, the trend reverses, and the decay time shortens very rapidly. Figure 3 shows results obtained under several different expansion conditions. The onset of the lifetime shortening takes place a t about AE = 2250 and 2550 cm-' for acetone-h6 and acetone-d6, respectively. A larger diameter leads to better rotational cooling, and such a nozzle was used to probe the transition region and perhaps measure an even sharper change. However, it proved impossible to obtain a well-defined transition region with the larger (0.35 mm) diameter nozzle, since a per- sistent emission with a decay time of about 600 ns was observed at energies beyond the transition zone found with the small nozzle. This emission is tentatively assigned to clusters, probably acetone dimers or higher oligomers, which form easily when a large nozzle is used. At the energy range considered, excitation of these clusters results in their dissociation, leading to the formation of the electronically excited fragment responsible for the persistent fluorescence. It is noted that, at lower excitation energies, dimers appear to be nonemissive, as the fluorescence signal decreases upon

using large diameter nozzles. This observation is consistent with the proposed assignment, if the emitting fragment is chosen to be monomeric acetone: only beyond a certain energy (determined by the binding of the dimer in the ground and the excited state) is an electronically excited monomer expected to be formed. A discussion of clustering is deferred to a separate report.

It was attempted to reduce the cluster formation probability by diluting the sample. However, a limit was set by the number of repetitions practical in our system (16O00) at a dilution of about 1:2000. At this dilution ratio, the signal assigned to clusters was still too strong to be ignored.

Acetone Seeded in Argon and Krypton. With these heavier carrier gases, it was found that the excitation spectra were identical in their location and relative intensity to those obtained with helium decay. The rotational envelopes were also practically identical, as shown in Figure 4. However, the decay profiles of the emission were found to be qualitatively different. Except for the very low energy vibronic levels, the decay could not be represented by a single exponent. Figure 5 shows examples of some decay plots and attempted analyses. The results obtained with argon as a carrier gas could be reasonably well fitted with a biexponential expression of the type I ( t ) = a , exp(-k,t) + a2 exp(-k,t). I t turns out that the second exponent is longer lived than the ones found for helium-seeded molecules excited with identical energies. A similar trend was found with krypton, in which even longer decays were observed.

4086 The Journal of Physical Chemistry, Vol. 93, No. 10, 1989

30 0 ACETONE - he In hel ium, 0 35 mm nozzle I" I

', 008" I' 1 1

1 1 I I

I /

" 003 " "

0 ACETONE- d, in argon , 0 35 " " 0'

A " " " " 008 " " ,A 1

Zuckermann et al.

" 003 " " ,I ,I

= I a

0 0

0

0 0 0

00

0 0

0

00 0 0 0

0 0 m

0

0 .

Cb

0

.?q A

I I 1 I IO00 2000

A E ( c m - l )

01

Figure 3. Fluorescence decay rate constant of acetone& and acetone-d6 in a supersonic beam. The plotted values refer to the long-lived com- ponent, in cases where the spike appears. See text for details.

TABLE I: Decay Rate Constants of the Long-Lived Component of Acetone"

CH3COCH3 seeded in He CD3COCD3 seeded in Ar A E , cm-I k . lo6 s-I AE, cm-' k . IO6 s-I

0 1.26 0 I74 1.10 579 304 1.24 608 335 0.85 65 1 347 0.95 683 37 1 1.32 705 47 1 0.90 814 625 1.06 91 1 675 1 . 1 1 925 747 0.87 967 757 0.63 1016 830 0.85 1034 885 0.81 1092 899 0.88 1120

I034 0.82 1 I69 1172 0.76 1226 1293 0.71 1278 1417 0.74 1531 I528 0.63 1641 I789 0.57 2010

a A€ is the excess energy over Si origin.

0.31 0.21 0.20 0.20 0.24 0.28 0.25 0.20 0.21 0.19 0.18 0.16 0.16 0.17 0.15 0.18 0.16 0.25 0.24 0.25

Decay of Isolated Molecules-A Resume The pattern revealed in the decay kinetics of acetone is similar

to that observed in many other similar-sized molecules. Recent detailed studies are for example those of butynal,15 pyrazine,2iv22 and other^.^^-^^ Three states are commonly considered to be involved: the ground electronic state So, the first excited singlet Si, and the first triplet TI . A schematic energy level diagram is

(21) Frad, A.; Lahmani, F.; Tramer, A.; Tric, C. J . Cfiem. Pfiys. 1974.60,

(22) Amirav, A. Cfiem. Pfiys. 1986, 108, 403. (23) van der Werf, R.; Schutten, E.; Kommandeur, J . Cfiem. Pfiys. 1975,

(24) van der Werf, R.; Kommandeur, J . Cfiem. Pfiys. 1976, 16, 125. (25) Spears, K. G.; El-Manguch, M. Cfiem. Pfiys. 1977, 24, 165. (26) Spenser, S.; Pfeiffer, W. F; Atkinson, G. H. Cfiem. Pfiys. Lett. 1982,

4419.

11, 281.

93. 480.

AE = 373 cm-' 7-- - - - - ._

I o tm Krypton

, I

I 5 olm Helium

I

/r i? ----, 1 r

4 2 0 -2 - 4 Fpequency Sh: * t lcm-1)

Figure 4. Comparison of the rotational contours of fluorescence excita- tion vibronic bands of acetone seeded in helium and in krypton.

~~ A E = I429 cm-I A E = 680 cm-'

I 2 3 4 I 2 3 LIFETIMES L I F E T I M E S

k : I I a 106s-I k = 7 4 ~ 1 0 ' s - ~

T i m e T i m e

Figure 5. Examples of the fluorescence decay kinetics for acetone seeded in helium, argon, and krypton. The derived rate constants (in s-I) for a biexponential decay in krypton were k , = 2 X IOs, k2, = 8 X IO4 and in argon k , = 8 X I O 5 , k 2 = 6 X IO4.

Born 0ppenheiT.er Scheme

of Acetone

- - 1 S O

Figure 6. Schematic representation of the energy level diagram of ace- tone for levels accessible by photon absorption. The nomenclature is explained in the text.

shown in Figure 6, similar to that discussed in ref 15 and 19. We shall use the results and the nomenclature of Huber et

a1.i4915 to analyze the data. The properties of acetone are expected to somewhat resemble those of butynal (in terms of level spacings and coupling constants), making their work a suitable starting point. It should be. noted that we were not able to observe quantum beats in our system, and thus some aspects of the interactions cannot be discussed at the elegant detail level of ref 15. However, it seems that even with the lower resolution available, the salient features can be outlined. Initial excitation is to a rovibronic state

Acetone Photophysics in Seeded Supersonic Molecular Beams

belonging to SI , depicted as b ) in Figure 6. It is coupled to a number of states in T I (depicted as [ I ) ) and possibly also in So, shown in Im). The molecular eigenstate, which may be described as a superposition of all these, is denoted by Ik). The number of 11) or Im) states coupled to an initial b ) state is determined by the excitation energy and by the spectroscopic resolution. At

The Journal of Physical Chemistry, Vol. 93, No. IO, 1989 4087

coupling matrix elements may be used, so that the probability of intersystem crossing rises roughly with p .

Formulas describing the resulting decays were given by Muhlbach and Huber,Is who find that the diagonal elements in the damping matrix are

(3) high excess energies, the density of 11) states increases rapidly, Ykk = lcjk12rjj + ~ ~ ~ i k ~ 2 ~ l i

making the coupling to b ) more probable. The density of Im) states is very high, and should they be strongly coupled to b ) one expects to get very weak fluorescence. It appears, however, that only a very small number of them can couple to b), and the overall process is inefficient, as discussed below.

The decay pattern depends, among other parameters, on the excitation conditions. In our case the spectroscopic resolution AusP is 0.2 cm-I, and the coherence width Auc for transform-limited pulses is 0.006 cm-I. In practice, the pulse is not transform limited, and AuC is probably of the order of 0.1 cm-’. Near the origin of SI, the average spacing between adjacent Ik) states is bigger than Au,. Thus, excitation prepares several “coherent subsets” each containing only one eigenstate Ik). In general, this eigenstate may be represented by a linear superposition of the three Born-Op- penheimer states So, T I , and SI:

Ik) = c,kb) + ccikll) + cc mk Im) ( 2 )

where the summations are over all T I or So states within the coherence width Auc that are coupled to the initial SI state !j).

The time development of this state will depend on the number of these coupled states and the coupling constants. In the case of acetone, near the origin of SI, the density of states of So is very large27 ( - 1O1O states/cm-’) so that the molecule is within the statistical limit with respect to internal conversion. However, like in other carbonyl systemslO-ls the coupling is weak and only high-energy vibrations and specific promoting modes can effec- tively convert the electronic energy into nuclear motion. Thus, modes related to the C-H bond are expected to be involved in the process and this is the probable cause of the observed isotope effect. Once in So, intramolecular vibrational relaxation (IVR) degrades the energy to a large number of smaller vibrational quanta, making internal conversion a practically dissipative mode. Thus, the conversion into So may be described by an effective width r s that is equivalent to a decay rate constant. The overall decay of the state is thus determined by two dissipative decay constants, the radiative one rr and rss0.

The density of triplet levels near the origin is much smaller. Assuming that the T i origin is at 28000 cm-’, it is about 80 states/cm-’ near the origin of SI, rising to 800 states/cm-’ at about AE = 1000 cm-l. Thus, acetone is an intermediate molecule as far as intersystem crossing is concerned. The coupling between SI and TI states is much stronger than between Si and So states. Quantum beats measurements typically reveal matrix elements of 1-10 MHz,Is while level anticrossing experiments on glyoxal show that values as high as 500 M H z ~ ~ are also important. Moreover, the triplet state cannot be considered as truly dissipative; rather, the time development of the initially prepared state may show quantum beats as found for many similar systems. This behavior holds, of course, for energies below the dissociation barrier of T , .

I n the case of acetone, spectroscopic information is not yet available to the detailed extent of smaller molecules such as p r ~ p y n a l ’ ~ or glyoxal.28 It will therefore be assumed that inter- system crossing may be represented by a golden rule formula of the type p E vsT2p where p is the transition probability, uST the coupling matrix element, and p the triplet density of states. Near the origin, p is small, and this approximation may be too crude. At higher excitation energies, it will be assumed that some average

(27) Ground-state vibrational frequencies (from: Shimanouchi, T. Tables of Molecular Vibrational Frequencies; U S . National Bureau of Standards: Washington, DC, 1972; Consolidated Vol. I, NSRDS-NBS 39) were used for So and also for T, except for u3 (C=O stretch) and u23 (out-of-plane CO deformation). They are listed in Table 11.

(28) Pebaye, Peyroula, E.; Jost, R.; Lombardi, M.; Dupre, P. Chem. Phys. 1986, 102, 417.

Here r,, is the decay rate of the SI state (r, + rss, in our notation) and rli is the decay rate (radiative, dissociative, and coupling to So) of the triplet level. ril, whose magnitude mayfluctuate due to changes in the different decay parameters, is thus a function of energy. Near the origin, I’,, is small and the fluorescence intensity can be represented fairly accurately by a single-expo- nential decay with a rate constant Tkk, provided the coupling between SI and TI is small enough. In practice, several Ik) states will be excited by the laser pulse, and the total fluorescence intensity consists of a linear superposition of emission from all the states:

(4) In = x I k ( t ) = xGe-y&‘

Since the ykk’s of adjacent states (all are withjn the spectral width of 0.2 cm-I in our case) may be similar, particularly since the random coupling approximation2’ is expected to hold, the actual decay may still be very nearly exponential. Different hyperfi7e levels may, however, display different decay rates.

If the triplet is coupled to SI, the decay will be more compli- cated. Near the origin, as long as the triplet density of states is small, quantum beats may be observed. The modulation depth depends on the relative magnitudes of the Tl-So and Sl-So os- cillator strengths. In the case of acetone, the former is of the order of 10-7-10-830 compared to f - 3 X lo4 for the So-SI transition. The fact that many Ik) levels are excited simultaneously leads to “smearing out” of the beats, as each maximizes a t a slightly different time.

When the number of coupled triplet levels increases, even ex- citation of a single Ik) state leads to running out of phase of the beat oscillations.1s This arises from the fact that the oscillation period is slightly different from different 1’s. Thus, only the first part of each oscillation survives, and a fast decay (spike) results. The temporal behavior of this spike may often be ap- proximated by an exponential which is much faster than the slow decay that follows.

If the density of coupled states p is large enough, the rate constant for the dephasing process is given by the Fermi Golden Rule expression which involves intramolecular coupling. As in other intramolecular processes, it is thus not expected to be strongly influenced by collisions. It may, however, depend on the rotational energy.

Following the spike, a much slower component appears; it is due to the Ik) state which contains an appreciable triplet con- tribution, and its decay rate constant is given approximately by

Y k k (many triplet levels) = rll/N + r l l ( N / N - 1) ( 5 )

where N is the number of triplet levels effectively coupled to b ) (compare eq 3). The amplitude ratio of the fast component to the slow one is given by

In the case a t hand, several Ik) states are initially populated. Each will show the behavior described in the previous paragraph, and the overall response will be similar: the decay will consist of a spike followed by a longer decay. In a supersonic jet, only a small number of states are thermally populated, so that the overall energy spread of the optically prepared b ) states will be small, the Sl-Tl coupling remains nearly constant, and the number of triplet levels coupled to each of them is expected to be about the same.

(29) Heller, E. J.; Rice, S. A. J . Chem. Phys. 1974, 61, 936. (30) Estimated from the radiative lifetime of triplet acetone. See: Bork-

man, R. F.; Kearns, D. R. J . Chem. Phys. 1966, 44, 945.

4088

Data Analysis Acetone Seeded in Helium. Helium is expected to form fewer

clusters than heavier carrier gases, and thus seeded beams in helium are the best medium to study isolated molecule behavior. Rotational cooling was not complete, particularly with small nozzle diameters. However, acetone-acetone cluster formation appears to be so efficient that small nozzles had sometimes to be used when possible cluster interference had to be avoided.

At the origin, the decays of both acetone-h6 and acetone-d6 are represented by a nearly exponential decay with rate constants 1.25 X lo6 s-I for acetone-h6 and 3.3 X lo5 s-l for acetone-d,. Assuming for the moment that coupling to the triplet is negligible, these rates represent Y k k and are given by r, + rsso.

The nonradiative coupling between two electronic states whose origins are widely apart is known to be strongly enhanced by high-frequency vibrations. This has been demonstrated for a large variety of systems, including aromatic hydrocarbon^,^' rare-earth

and also carbonyl compounds.10~'2-15~34~3s Theory accounts of this trend by invoking the energy gap law3,-the nonradiative transition probability decreases roughly exponentially with AE/hw, where 1E is the energy gap between the origins of the two states and (I: is a characteristic frequency of the molecule. In the case of acetone, the observed decay rate constant in the deuterated molecule is 2-3 times greater than the calculated radiative one. while in the case of the protonated molecule, this ratio is 6.1 or 8: 1 , depending on the method used to calculate k,. Choosing a radiative rate constant of los s - I , ~ and assuming that the only nonradiative process is internal conversion, we find kSSo = 11.5 X 10, and 2.3 X 10, s-l for acetone-h6 and acetone-& respectively. These rate constants appear to be reasonable, on the basis of comparison with formaldehyde,l" propynal,14 acetaldehyde,l* and but ynal. I

The slow decrease in the decay rate constant upon increasing the excitation energy has been attributed to increase in the coupling strength between SI and T I . Thus, the triplet component of the k states increases in percentage, effectively leading to a longer decay time. However, other decay processes may become im- portant, such as intersystem crossing to S0,37938 making the overall kinetic behavior fairly complicated.

In order to check the validity of these arguments, and to extract some rate constants, we proceed as follows. In an energy range for which b' is large enough so that N - 1 s.1 N , eq 5 becomes

The Journal of Physical Chemistry, Vol. 93, No. 10, 1989 Zuckermann et al.

rll is the lifetime of a single triplet level a t the energy of interest. It may be written, in the absence of dissociation or collisions, as

where Trad(T) is the triplet radiative lifetime and rTSo the ISC rate constant. Over a relatively small energy range, both are not expected to change much with energy. Similarly, rj, would be fairly constant over a span of 1000 cm-l assuming constant internal conversion rates. We can thus use eq 7 to extract TI, and ra by plotting Y k k (the observed decay rate) as a function of the density of states ([/A'). This procedure involves the statistical assumption that the number of coupled triplet states to a given SI state is proportional to the density of states.

The plot for the interval 800-1800-cm-' excess energy in SI is shown in Figure 7 . Despite a considerable scatter, particularly for acetone-h6, an obvious correlation does emerge. The numerical

(31) Hutchison, C. A.; Mangum, B. W. J . Chem. Phys. 1960, 32, 1261. (32) Kropp, J. L.; Windsor. M. W. J . Chem. Phys. 1965, 42, 1599. (33) Haas, Y . ; Stein, G. J . Phys. Chem. 1971, 75, 3677. (34) Zittel, P. F.; Lineberger, W. C. J . Chem. Phys. 1977, 66, 2972. (35) Borkman, R. F.; Kearns, D. R . J . Chem. Phys. 1966, 44, 945. (36) Avouris. P.; Gelbart, W. M.; El-Sayed, M. A. Chem. Rec. 1977, 7 7 ,

793. (37) In the case of isolated molecules, the decay times of vibrationally

excited molecules are often reported to be significantly shorter than those of the vibrationaless state. In the absence of an open reactive channel, this phenomenon has been assigned to intersystem crossing (see ref 38).

(38) Smalley, R. E. Adc. Laser Spectrosc. 1983, 2, 135.

3 l -

L ~

I I l 2 : 4 0 6C 82

I V Y 103cn

Figure 7. The measured decay rate, k ( E ) , of acetone plotted as a func- tion of I / N ( E ) , N ( E ) IS the average calculated density of triplet states The energy interval I S 800-1800 cm-l above the origin of SI

TABLE 11: Vibrational Frequencies (in cm-') of Acetone-B, and Acetone-d,a,b assignt CH __ , OCH, CD,COCD, approximate type of mode

a , u, 3019 2264 CHI degenerate stretch v 2 2931 2123 CH, (CD,) sym stretch u3 1731 1732 CO stretch u4 1435 1080 CH, (CD,) sym deformation u5 1364 1035 CD3 degenerate deformation v6 1066 887 CH, (CD,) rock y7 777 689 CC stretch "8 385 321 CCC deformation

u l o 1426 1021 CH, (CD,) degenerate deformation Y,, 877 669 CH, (CD,) rock

105 75 torsion "12 Y,, 3019 2264 CH, (CD,) degenerate stretch

u I s 1410 1004c CH, (CD,) degenerate deformation u I 6 1364 1035 CH3 (CD,) sym deformation Y , ~ 1216 1242' CC stretch u 1 8 891 724 CH, (CD,) rock ui9 530 475 CO in-plane bend

u2, 1454 1050 CH, (CD,) degenerate deformation u22 1091 960 CH, (CD,) rock u2, 484 405 CO out-of-plane bend u24 109 79 torsion

_-

a2 ug 2963 2219 CH, (CD,) degenerate stretch

b, u I 4 2937 2123 CH, (CD,) sym stretch

b2 i,20 2912 2227 CH, (CD,) degenerate stretch

a Source: Shimanouchi, T. Tables of Molecular Vibrational Frequencies; U S . National Bureau of Standards: Washington, DC, 1972; NSRDS-NBS 39. bThe following frequencies are changed in the nrr*(SI) states, as re- ported in ref 17 (values are given for CHJOCH, and CD,COD,, respec- tively): u3 = 1124 and 1124 cm"; v7 = 757 and 684 cm'l; v I 7 = 1294 and 131 I cm-l; ~ 2 3 = 343 and 300 cm-l. cThese two numbers were apparently accidentally interchanged in Shimanouchi's table.

parameters deduced from these plots are rll = (1.3 f 0.2) X lo5 and (2.2 f 0.5) X lo5 s-I for acetone-d, and acetone-h6, re- spectively. These values are much greater than the radiative rate constant ( - I O 2 s-l) and must thus be assigned to intersystem crossing into So.

The slope in Figure 7 for acetone-h6 is about 3 times larger than for acetone-d,, namely, (9.6 f 1) X lo7 and (3.3 f 0.5) X lo7 cm/s, respectively. In order to deduce rate constants, we need to know the dilution f a c t ~ r , l ~ ~ ~ ~ defined as the fraction of triplet states coupled to an Si state. The fact that ratio between the slopes (2.9) is similar to the ratio between the measured decay rate constants a t the origin (4.1) could be fortuitous, but it may also

(39) Amirav. A.; Jortner, J. J . Chem. Phys. 1986, 84, 1500

Acetone Photophysics in Seeded Supersonic Molecular Beams The Journal of Physical Chemistry, Vol. 93, No. IO, I989 4089

indicate that over this limited range eq 7 provides an acceptable approximation. Assuming that this is the case, and using the values 1.2 X 10, and 0.3 X 10, s-l for the decay rate constants of ace- tone-h, and acetone-& respectively, we arrive at the dilution ratios of 80 and 110 for these two molecules. These values seem rea- sonable by comparison with b ~ t y n a 1 . l ~ It may be noted that, in butynal and p r ~ p y n a l , ' ~ - ' ~ similar isotopic effects were measured. It was argued there that the C-H wagging vibration plays an important role in the internal conversion process. The conclusion was reached by computing the theoretical ratio using a displaced harmonic oscillator model. The required spectroscopic constants are not yet available for acetone. Nevertheless, the similar isotopic ratio on the one hand and the availability of similar vibrational modes (for instance, CH3 rock; cf. Table 11) suggest that vibronic interaction dominates internal conversion.

In summary, the photodynamics of isolated acetone molecules upon excitation into SI, keeping the excess energy below 2000 cm-l, can be accounted for by assuming coupling to So and TI. The radiative rate constant is taken as about lo5 s-l, and the observed faster decay at the origin due to internal conversion, with rate constants of (11.5 f 0.3) X lo5 and (2 f 0.2) X IO5 s-I for acetone-h6 and acetone-d,, respectively. Above the origin, mixing with TI states becomes progressively more important, leading to a gradual decrease in the observed decay rate. Inspection of Figure 3 shows that the decrease in the decay constant as the excess energy is increased is not quite monotonic, particularly for ace- tone-h6. These fluctuations are likely to reflect specific interac- tions, in which some vibrations promote internal conversion or intersystem crossing better than others.40 A similar trend was reported in the case of pr0pyna1.l~

Evidence for Unimolecular Dissociation. Figure 3 shows that the measured decay rate increases rather abruptly a t about 2250- and 2500-cm-' excess energy for acetone-h6 and acetone-d6, re- spectively. This signifies the onset of a new dissipative channel, which is proposed to be dissociation of the triplet surface. Other alternatives are ( I ) dissociation on the S, surface, (2) sudden increase of Sl-So coupling, (3) a different chemical change (for instance enolization), and (4) a sudden increase in intersystem crossing efficiency. The first alternative may be ruled out as the fast component (the spike) is observable at much higher energy levels, showing that dissociation from SI is not a very fast process. The second is possible and has been considered as an option to account for the famous "channel three" problem in b e n ~ e n e . ~ ' , ~ ~ It was advanced, however, only after convincing evidence ruling out the possibility of a chemical reaction was brought together. Alternatives 3 and 4 are plausible and need to be further con- sidered in view of the available experimental findings.

Dissociation on the triplet surface was discussed by many au- t h o r ~ . ~ , ~ ~ - " ~ The estimated barrier heights for reaction 1 on the T I surface range between 6.4 and 15 kcal/mol. Placing the origin of TI at 28 000 ~m-~, ' " these values translate to 0-2800-cm-' excess over the origin of SI. Assuming that the sharp change in the decay rate is due to this dissociation process, we find for acetone-h, 2250 f 50 cm-' and for acetone-d6 2500 f 50 cm-l, both within the quoted range. It is noted that these values are consistent with barriers observed for formaldehyde4* and a ~ e t a l d e h y d e . ~ ~

Further support can be deduced by considering the isotope effect. The onset of the new radiationless process occurs a t a

(40) Behlen, F. M.; Rice, S. A. J . Chem. Phys. 1981, 75, 5672. (41) Callomon, J. H.; Parkin, J. E.; Lopez-Delgado, R. Chem. Phys. Lett.

(42) Callomon, J. H.; Somers, L. W. Chem. Phys. Lett. 1988, 144, 463,

(43) Cundall, R. B.; Davies, A. S. Proc. R. SOC. London, A 1966,290, 563. (44) O'Neal, H. E.; Larson, C. W. J . Phys. Chem. 1969, 73, 1011. (45) Gandini, A.; Hackett, P. A. J . Am. Chem. SOC. 1977, 99, 6195. (46) Copeland, R. A,; Crosley, D. R. Chem. Phys. Left . 1985, 115, 362. (47) Based on the known separation between S, and T, in acetaldehyde

(2500 cm-I: Moule, D. C.; Ng, K. H. K. Can. J . Chem. 1985,63, 1378) and assuming the same value for acetone.

(48) Chuang, M.-C.; Foltz, M. F.; Moore, C. B. J . Chem. Phys. 1987,87, 3855.

(49) Horowitz, A,; Kershner, C. J.; Calvert, J. G. J . Phys. Chem. 1982, 86, 3094. Horowitz, A.; Calvert, J. G. J . Phys. Chem. 1982, 86, 3105.

1972, 13, 125.

and references therein.

A c e ' o n e - h g n helium

l i n e 39

W A V E L E N G T H (nm)

Figure 8. Rotational contours of line 7 (Ai3 = 373 cm-I) as a function of the dilution. As the acetone concentration increases, the rotational contour broadens.

higher energy in the deuterated isomer. If it were due to a regular process involving coupling between two different Born-Oppen- heimer surfaces, such as internal conversion or intersystem crossing, an important factor would be the density of states, which is higher in acetone-d6. Thus, it is expected that such a process will take place at lower energy for the deuterated isomer. Re- actions involving directly the hydrogen atom, such as enolization or dissociation of a C-H bond, are expected to be strongly affected by deuteration. The observed effect may be, in fact, too small for this process. Considering reaction 1, isotopic substitution is likely to shift the barrier as the zero-point energy of acetone-h6 is higher than that of acetone-d,,. In this reaction, six vibrational modes are converted to translational or rotational degrees of freedom. The most likely candidates are the C-C asymmetric stretch ( v 1 7 ) , two CH3 rocking modes ( v , , and vZ2) , the out-of-plane C O deformation ( v 2 4 , and the two torsion modes (vi2 and v t 4 ) . These frequencies were chosen on the basis of chemical intuition and by comparing the frequencies of acetone to those of the products, CH3 and CH,CO. Since a normal-mode analysis for the latter is not available, the known modes of CH3CN were used for the correlation analysis. From Table I1 we find that the difference in the zero-point energies (of these six vibrations) between acetone-h, and acetone-d6 is 212 cm-I. The similarity of this value to the observed energy separation of the onset of the fast decay between acetone-h6 and acetone-d6 lends support to the proposed interpretation.

Accepting this interpretation, we may try to check whether it conforms with a statistical calculation of the rate constant. An RRKM calculation shows that the rate constant for dissociation on the T I surface exceeds IO8 s-I even with an excess energy of only 1 kcal/mol over the barrier. Referring back to eq 5, this means that Y k k - r,, (rl1 >> rJ), and thus the very steep change shown in Figure 3 is compatible with a statistical-type dissociation on the triplet surface. I t may be noted in passing that a similar calculation on the So surface leads to a much smaller rate constant (IO s-l at 1 kcal/mol excess energy) in view of the much larger density of vibrational states.

The RRKM calculation performed for the TI surface indicates a much steeper change in the rate constant than observed ex- perimentally. Although the more gradual trend may be due to experimental difficulties (for instance, insufficient cooling), it

4090 The Journal of Physical Chemistry. Vol. 93, No. 10, 1989 Zuckermann et al.

should be noted that R R K M considerations were never properly tested, for a polyatomic molecule, a t energies very near to the barrier. Due to some inevitable roughness of the potential surface, one expects to observe deviations from a complete statistical behavior. Some vibrational motions may be more inclined to lead to bond dissociation than others. These effects are probably too small to affect the overall rate with large excess energy but could be important close to the barrier.

Rotational Effects. The data used to deduce the dissociation threshold energy were taken with a small nozzle diameter in order EO avoid cluster formation. However, reducing the nozzle diameter resulted in less extensive rotational cooling, as shown in Figure 8. Since the spectral resolution was limited to 0.2 cm-I, several rotational states were simultaneously excited. It was found that the fluorescence decay behavior was indeed affected by the ro- tational temperature. In general, longer decay times were observed as the rotational temperature increased. This points to increased S,-T, coupling due to molecular rotations. The rotational effects on radiationless transitions have been discussed by many authors. In formaldehyde, intersystem crossing is strongly affected by the rotational motion, apparently due to chance coincidence with triplet levels.50 The dissociation quantum yield was also found to be affected by the rotations in an apparently random manner.” However, Henke and co-workers” showed that, a t least for some levels of formaldehyde, rotational effects could be accounted for systematically by considering centrifugal effects and vibration- rotation couplings. Recently, McDonald and co-workerss2 showed that state mixing between the C-H stretching mode and lower frequency modes in norbornadiene depends on the rotational energy. Their data show that the number of interacting states scales linearly with J . This trend is consistent with a statistical model that assumes equal coupling between all the zeroth-order rovibrational states having the correct energy and symmetry. The same argument may apply in the present case since the only difference is that the spin-orbit coupling operator is used in the formalism, instead of the Coriolis or Fermi coupling.

In acetone, internal rotations may also play a central role. Barriers for the torsion and for the out-of-plane CO wagging are low (740 and 460 cm-l, respectively1’). The large-amplitude motion that becomes possible above this barrier may increase the spin-orbit coupling. However, a systematic study of these effects requires considerable more work.

Coming back to the sudden change observed in the decay rate (Figure 3). rotational motion is not expected to be of a major importance. The small residual uncertainty in the energy threshold may be partly due to the excitation of different rotational levels. Fast rotation may actually hamper the dissociation somewhat, due to a centrifugal barrier. It is thus concluded that the value of the threshold determined here is not expected to be modified significantly should rotationally colder molecules be probed.

Acetone Seeded in Argon and Krypton. As shown in Figure 5 , the decay pattern obtained upon seeding acetone in argon or krypton differed from that observed in helium. In particular, the long-lived component can no longer be fitted properly by a sin- gle-exponential decay. Several possible mechanisms may account for this observation. Cluster formation was mentioned and is expected to take place in the heavier gases. In fact, evidence that acetone-argon clusters are formed is rather convincing, as detailed in a separate report. However, at relatively low excess energy (below AE = 1500 cm-I), the rotational contours observed in helium and argon arc practically identical. Yet, the decay rate obtained upon excitation into these bands are distinctly different. We also note that the effect was observed under conditions that strongly disfavor cluster formation, small nozzle diameters, and I O N backing pressures.

( 5 0 ) Weisshaar. J . C.; Moore, C. B. J . Chem. Phys. 1979. 70, 5135; 1980, 72. 2 8 7 5 , 541 5

(51) Shibuga, K . ; Fairchild. P. W.; Lee. E. K . C. J . Chem. Phys. 1981. 7.5, 3397. F:iirchild. P. W.: Shibuga. K . ; Lee. E. K . C . J . Chem. Phys. 1981. 7 5 , 3407

( 5 2 ) Minion. T. K . : K im. H . L . : McDonald, J . D. J . C h e m Phys. 1988. XR, 1 5 3 9

It is suggested tentatively that the nonexponential decay is due to in-beam collisions between acetone and carrier gas atoms. The number of effective collisions in a supersonic expansion was discussed recently by Lubman, Rettner, and Zare.53 Using their equations and a collision cross section of 100 A2, we find that under our typical experimental conditions a molecule experiences 1-2 collisions in a microsecond. The effectiveness of these collisions in causing intersystem crossing increases in the sequence helium, argon, krypton. It is proposed that the longer decay component observed in the heavier carrier gas is due to states reached by these collisions, in which the contribution of the triplet is bigger than in the initially prepared energy interval. This interpretation requires that the decay pattern be dependent on the location a t which the laser beam crosses the molecular beam. The number of collisions is expected to decrease as the molecules travel downstream.

Discussion In this work we showed that the photophysical behavior, in

particular the fluorescence time dependence, of acetone is qualitatively similar to that of similar-sized aldehydes. Radia- tionless transition theory provides an adequate framework for accounting for the gross features of the fluorescence decay. Being “floppier” than most aldehydes, cooling i s less efficient and in the present work we were not able to study single rovibronic states. However, the available resolution leads to the following conclu- sions.

I . Near the origin of SI, SI - So coupling is stronger in acetone-h, than in acetone-d,. The nonradiative rate constant associated with this transition is about 2 X IO5 s-I for acetone-d6 and 11.5 X I O 5 s-l for acetone-h,.

2. Intersystem crossing and its dependence on the state density are revealed by the lengthening of the decay time as the vibronic energy in S, is increased. Qualitatively, eq 5 accounts for this trend. The radiative rate constant of SI is about lo5 s-’.

3. A sharp increase in the nonradiative rate constant a t about 32 700 cm-’ is interpreted as signaling the onset of dissociation on the triplet surface.

4. Acetone clusters appear to be emissive, if excited to a sufficiently high energy.

The Acetone Lifetime “Anomaly”. The results can be used also to address an issue concerning acetone photophysics in bulk systems, which has as yet not been properly settled. The radiative lifetime of singlet acetone may be calculated in two ways. One is based on the relationship between the Einstein A and B coef- ficients. Experimentally, the oscillator strength is determined from the integrated absorption spectrum, and the decay rate constant of the excited state is deduced from it.’ The result for acetone. as for most simple ketones, is8 k, - I O 5 s-l. Alternatively, one may measure directly the observed lifetime T and the absolute quantum yield q!~ and deduce k , from the relation k, = @/T. The experimental result in this case is8 4-5 times larger than obtained by the other method.

The findings reported in this paper (jet results) and in a previous oneL9 (bulk) cast some doubt as to the validity of the second procedure in the case of acetone. In the bulk, and particularly in liquid solutions, emission is from the thermalized singlet (or triplet state). I t was shown19 that the spike is observable even under practically collision-free conditions upon excitation at 330 nm. nominally a lower energy than the 0-0 transition. As the present work shows, this must be due to the thermal population of high rotational or vibrational states, since in the jet the spike is observed only when the vibrational energy in SI exceeds - 1400 cm-I. Most liquid solution measurements were taken at 313 nm or at lower excitation wavelengths, corresponding to sufficiently large excess vibrational energies that causes strong S-T coupling on a time scale shorter than s. The observed “decay constant” under these conditions is likely to be a convolution of the actual decrease in the spike intensity and some quenching by the solvent.

______ ( 5 3 ) Lubman. D. M,: Rettner. C . T.: Zarc, R . N . J Ph.k.7. Chrm. 1982.

R6. 1129.

Acetone Photophysics in Seeded Supersonic Molecular Beams The Journal of Physical Chemistry, Vol. 93, No. 10, 1989 4091

Solvent molecule motion is likely to cause rapid vibrational re- laxation in either the singlet or triplet manifold. Furthermore, once the molecule is vibrationally relaxed, coupling to the triplet is expected to be more efficient than in the gas phase even near the origin of SI. Solvent motion provides the required broadening so that the number of TI levels coupled to each SI states is large enough to cause rapid dephasing, leading to the spike appearance.

One is thus led to the conclusion that the discrepancy reported between the radiative lifetimes of acetone obtained by the two methods could be due to neglecting the effect of rapid intramo- lecular coupling. It appears that the value based on the absorption coefficient is to be preferred.

This conclusion can be carried over to other ketones as well. In the bulk, direct lifetime measurements for many small ketones are in the range of 2-4 ns.8954*55 In the jet, we found that the fluorescence of cyclobutanone, cyclopentanone, 2-pentanone, and 3-pentanone consisted of only the very short lived component. In the case of 1-butanone, the only ketone for which a long-lived component could be observed, the amplitude ratio between the short-lived component and the long-lived one was much larger than in acetone. These preliminary results are consistent with the kinetic scheme proposed for acetone, provided a decay channel is open for these ketones at a lower energy. A possible route for ethyl ketones (and ones containing longer side chains) is formation of ethylene and a carbonyl compound, for i n ~ t a n c e ~ ~ ~ ~ ~

CH3CHZCOCH3 - CHZ=CHZ + CH3CHO AHo = 38.8 kcal/mol (9)

Thus, this reaction is energetically allowed a t the SI origin, if the barrier is smaller than 50 kcal/mol. For the cyclic ketones, cleavage to yield smaller fragments is energetically possible. Thus, the barriers for reactions 10 and 11 in cyclobutanone are probably

c-C4H60 - C o + CH3CH=CH2 AHo = 12 kcal/mol (10)

c-C4H60 - C2H4 + C H 2 C 0 ( 1 1)

quite low, 58 and 52 kcal/mol, r e s p e c t i ~ e l y . ~ ~ ” ~ Reaction 11

AHo = 22 kcal/mol

(54) Hemminger, J. C.; Lee, E. K. C. J . Chem. Phys. 1972, 56, 5284. (55) Yang, N. C.; Hui, M. H.; Shold, D. M.; Turro, N. J.; Hautala, R.

R.; Dawes, K.; Dalton, J . C. J . Am. Chem. Soc. 1977, 99, 3023. (56) The enthalpy for this reaction was based on heats of formation given

by ref 57 and a heat of formation of -66 kcal/mol of 2-butanone. This value was calculated from the heat of combustion quoted in the Internarional Critical Tables, 1929 (736 kcal/mol).

(57) Benson. S. W. Thermochemical Kinetics; Wiley: New York, 1976.

is believed to take place on the triplet surface. The low barrier makes this surface dissociative at any excitation frequency into SI. It follows that &-TI coupling results in immediate dissociation and only a short-lived emission is expected, in agreement with the experimental results. Similar pathways are open for all higher ketones.

Singlet or Triplet Type Reactions. Another feature of acetone photochemistry is related to the different reaction patterns assigned to singlet or triplet acetone.61 For instance, it has been stated that the triplet can cause cis-trans isomerization while the singlet leads to oxetane formatiod2 when a ketone is irradiated in the presence of 1,2-dicyanoethylene. According to the present analysis, initial excitation of acetone leads to the formation of a “mixed” state a t a rate faster than any collision-induced process. The d!fference between singlet and triplet reactivities must thus be assigned to reactions of the vibrationally relaxed species. In addition, some excitation wavelength dependence may be observed. Upon excitation to high vibronic states, the bimolecular reaction assigned to S,, and actually originating with the “mixed” state, must compete with vibrational relaxation by the solvent. This fact is also in line with the usually small yields (<5%) of “SI” reactionsS6’

Acknowledgment. This research was supported by Grant 84- 0037 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. B.S. is grateful to the Minerva Foundation for a research fellowship. We are indebted to Dr. A. Tramer for a most helpful discussion and to Dr. G. D. Greenblatt for his contribution to the early part of the project.

Registry No. CH3COCH3, 67-64-1; D, 7782-39-0; He, 7440-59-7; Ar, 7440-37-1; Kr, 7439-90-9.

(58) Brewer, G. M.; Lewis, R. S.; Lee, E. K. C. J . Phys. Chem. 1975, 79,

(59) Tang, K. Y.; Lee, E. K. C. J . Phys. Chem. 1976,80, 1833. (60) McGee, T . H.; Schleiffer, A. J . Phys. Chem. 1972, 76, 963. (61) Turro, N. J. Modern Molecular Photochemistry; Benjamin: Menlo

(62) Dalton, J. C.; Turro, N. J. Annu. Reo. Phys. Chem. 1970, 21, 499. (63) Donaldson, D. J.; Leone, S. R. J . Chem. Phys. 1986,85, 817. Wo-

odbridge, E. L.; Fletcher, T. R.; Leone, S. R. J . Phys. Chem. 1988, 92, 5387. (64) Sivakumar, N.; Hall, G. E.; Houston, P. L.; Burak, I.; Hepburn, J .

W. J . Chem. Phys. 1988, 88, 3692. (65) Bamford, D. I.; Filseth, S . V.; Foltz, M . F.; Hepburn, J. W.; Moore,

C. B. J . Chem. Phys. 1985.82, 3032. (66) Imre, D.; Kinsey, J. L.; Sinha. A,; Krenos, J . K. J . Phys. Chem. 1984,

88, 3596. (67 ) Hall, G. E.: Ogorzalek, Loo, R.; Harri, H. P.; Sivakumar, N.; Chawla.

G. K.; Houston, P. L.; Chandler, D. W.; Hepburn, J.; Burak, I. Ber. Bun- sen-Ges. Phys. Chem. 1988, 92, 281.

(68) Chawla, G. K.; McBane, G. C.; Houston, P. L.; Schatz, G. C. J . Chem. Phys. 1988, 88, 5481.

1985.

Park, 1978.