J . Phys. Chem. 1988, 92, 5425-5432 grateful to Drs. Dean R. Guyer, Herbert Bitto, and Mei-Chen Chuang for the low-resolution molecular beam spectra and to William H. Green for insightful discussions. W.F.P. thanks the National Science Foundation and Chevron U.S.A.for predoctoral fellowships. C.B.M. thanks the Miller Institute for Basic Research in Science at the Universtiy of California, Berkeley, for a Research
5425
Professorship. Over the years we have greatly benefitted from exchanging results and from discussing puzzles and conclusions with Ed Lee. His keen interest in science and his delight in sharing it provide continuing inspiration. Registry No. D$O, 1664-98-8.
Single Rovibronic Level Fluorescence Lifetimes of Jet-Cooled Formaldehyde-d, Joan K. Frisolit and C. Bradley Moore* Department of Chemistry, University of California, Berkeley, California 94720 (Received: March 28, 1988)
Single rovibronic level fluorescence lifetimes are measured for 2l4l, 2143,l14I, 9 , 214261,2241,4251,2243,2'5l, 2341,2I4,5l, and 112143bands of jet-cooled DzCO by laser-induced fluorescence. Lifetimes in the 112441and 2641bands are obtained from spectral line widths. Lifetimes generally decrease with increasing vibrational energy, with somewhat longer lifetimes observed for levels involving CD stretching excitation. The order of magnitude of the fluctuations in the lifetime with rotational quantum number found earlier for 4O and 4l narrows to a factor of 2 or 3 as S1 vibrational energy increases to 4000 cm-'. Within these fluctuations lifetimes are seen to decrease on average by 5% for each unit increase in J .
Introduction Formaldehyde is a particularly attractive molecule for the study of photophysics because it combines theoretical tractability with the interesting photophysics and photochemistry of a polyatomic. Hence formaldehyde spectroscopy,' photophysics,2 and photochemistry3 have been the subjects of many experimental and theoretical investigations. The spectroscopy and photochemistry are well understood and provide the background necessary for a study of the photopbysics. Upon excitation to the 'A2 state (SI),formaldehyde can either radiate or undergo internal conversion to high vibrational levels of the ground electronic state (So) followed by dissociation to molecular (H, and CO) or radical ( H HCO) products. Vibrational and rotational spectra of SI HzCO and D 2 C 0 have been analyzed for vibrational energies as high as 4000 cm-'.' Rotational constants are also known for low vibrational levels in So.' The energy level structure of highly vibrationally excited levels of So has been elucidated by Stark tuning experiment^.^.^ These levels are broadened by coupling to the dissociative continuum. Near the S1origin the So* levels are narrower than the average spacing, forming a "lumpy continuum"! Stark spectra also show that this structure smooths out at higher energies. Nonradiative decay rates from single SI rovibronic levels (SRVLs) fluctuate randomly according to the chance overlaps with "lumps" in the continuum.6 Lin and Schlag have predicted explicit rotational quantum number dependences of the nonradiative decay rate;'** these effects might be observable as the So* continuum becomes smooth at higher energies. In formaldehyde kmd< k,,, and the observed fluorescence decay rate, k = krad+ k,,, is a measure of the nonradiative rate. So far, SRVL fluorescence decay rates have been measured at low vibrational energies in both HzCO and DzCO and to higher energies in H2C0.6,"* In all of these studies random fluctuations in lifetimes mask any predicted systematic dependence of fluorescence lifetimes (inverse decay rates) on rotational quantum number. In going from SI to So H,CO, the C-O bond length decreases, and the molecule goes from a bent to a planar equilibrium geometry. Thus SIvibrational states with CO stretch ( u z ) and out-of-plane bend (u.,) excitation have greater Franck-Condon overlap with So than states that do not contain u2 or Although
+
'Present address: Wellman Laboratory, Massachusetts General Hospital, Boston, MA 02114.
early single vibronic level (SVL) workI4 showed no dependence of the radiationless transition rate on vibrational motion, Lee has reported that HzCO levels with CH stretching excitation exhibit slower decay rates than do 2"4" levels of comparable energy.I5 In the vibrational bands studied to date, the systematic dependence of nonradiative decay rates on quantum number has not yet been clearly revealed. In this work fluorescence lifetimes are measured for single, well-resolved rotational levels in a variety of DzCO vibrational bands.
Experimental Section Lifetimes of single J', K:, K : states of S1 DzCO in a molecular beam were measured by laser-induced fluorescence. A complete description of the narrow-band pulsed laser system and the method of acquiring high-resolution molecular beam spectra have been published.I6J7 Details particular to these measurements appear here. This technique was used to obtain lifetimes for states with vibrational energies from 1241 cm-' for 2l4' through 3917 cm-I for 112143. (1) Clouthier, D. J.; Ramsay, D. A. Annu. Rev. Phys. Chem. 1983,34, 31, and references therein. (2) Moore, C. B.; Weisshaar, J. C. Annu. Rev. Phys. Chem. 1983,34525. ( 3 ) Sodeau, J. R.; Lee, E. K. C. Rev. Chem. Intermed. 1980, 4, 259. (4) Weisshaar, J. C.; Moore, C. B. J . Phys. Chem. 1980, 72, 2875. (5) Polik, W. F.; Guyer, D. H.; Moore, C. B., to be submitted for publication in J. Chem. Phys. (6) Weisshaar, J. C.; Moore, C. B. J. Chem. Phys. 1979, 70, 5135. (7) Kono, H.; Lin, S.H.; Schlag, E. W. J . Chem. Phys. 1982, 77,4474. (8) Henke, W. E.; Selzle, H. L.; Hays, T. R.;Schlag, E. W.; Lin, S. H. J . Chem. Phys. 1982, 76, 1335. (9) Selzle, H. L.; Schlag, E. W. Chem. Phys. 1979, 43, 11 1. (10) Henke, W. E.; Selzle, H. L.; Hays, T. R.; Schlag, E. W.; Lin, S. H. J . Chem. Phys. 1982, 76, 1327. (1 1) Bamford, D. J. Ph.D. Thesis, University of California at Berkeley, 1984. (12) Shibuya, K.; Fairchild, P. W.; Lee, E. K. C. J . Chem. Phys. 1981, 75, 3397. (b) Apel, E.; Lee, E. K. C. J . Phys. Chem. 1985.89, 1391. (13) Freed, K. In Topics in Applied Physics; Fong, F. K., Ed.; SpringerVerlag: New York, 1976. (14) Yeung, E. S.; Moore, C. B. J. Chem. Phys. 1973,58, 3988. (15) Miller, R. G.; Lee, E. K. C. J . Chem. Phys. 1978,68, 4448. (16) Polik, W. F.; Guyer, D. R.; Moore, C. B. Proc. SPIE.-Int. SOC.Opt. Eng. 1988, 922, 150. (17) Frisoli, J. K.; Polik, W. F.; Moore, C. B. J. Phys. Chem., preceding
paper in this issue.
0022-3654f 88f 2092-5425$01 S O f 0 0 1988 American Chemical Society
5426
I 0
-
Frisoli and Moore
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988
1
0.5
I
1.0
1
1.5
I
2.0
Time (pis)
Figure 1. Observed fluorescence decay and fit to the transition PPI(5)o (404 5,5) at 30686.326 cm-I in the 2241band of D2CO; 7 = 290 ns.
A pulsed laser excites a skimmed molecular beam of DzCO in H e to the 'A2 state. A photomultiplier tube (EM1 9813QB) collects fluorescence at right angles to both the laser and molecular beam. The signal is amplified (Pacific Instruments 2A50) and sent to a transient digitizer (Tektronix 7912AD) equipped with a 7A16 amplifier and a 7B90 time base. The fastest time scale used in these experiments, 10 ns/division, does not approach the limit of the digitizer configured with these plug-ins; most measurements require a resolution of only 100-500 ns/division. Measurement of short lifetimes is limited by the laser pulse width of 10-ns full width a t half-maximum (fwhm). An IBM PC-XT interfaced to the 79 12AD controls data acquisition and manipulation. Typically, the addition of 256 signal traces and subtraction of an equal number of background traces result in an excellent signal-to-noise ratio. Decay curves are least-squares fitted to single-exponential decays or, in a few cases, double-exponential decays. A sample decay curve and fit are shown in Figure 1. For the vast majority of measurements, refitting a given decay trace results in at most a 1% variation in lifetime. This number increases to &5% for lines with poor S/N. Similarly, transitions that terminate in the same upper state yield lifetime measurements that often agree within 1% but occasionally differ by as much as lo%, with the magnitude of the discrepancy determined primarily by SIN. Measurements of a given transition on separate days are also reproducible to &5%. Therefore, single-exponentialdecays are accurate to within 3 ~ 5 % . Most double-exponential decays result from lines that are not resolved in the spectrum, and these rates may differ by 30% from fits to single-exponentialfluorescence decays from the same levels excited on well-resolved transitions. The rates derived from fitting biexponential decays are accurate to -25%, and the amplitude ratio, Zf/Zs, to -30%. At higher energies, fluorescence lifetimes of both DzCO and HzCOare derived from line widths observed in the molecular beam spectra. These experiments can be done straightforwardly when lifetime broadening is greater than both the laser line width and the Doppler width of the molecules in the molecular beam. At high energies where the lifetimes are short enough to measure this way, signal-to-noise becomes a problem because the fluorescence quantum yield is proportional to the observed lifetime. The short wavelength filter cutoff was shifted from 380 to 360 nm (Schott G G 1) to increase signal. The number of molecules and therefore the signal can also be increased by removing the skimmer from the beam. However, this broadens the Doppler width to ==0.10cm-' and is useful only for measuring lifetimes shorter than 50 ps. Spectra of individual lines were accumulated as in ref 17. Rhodamine 6G (Exciton) was used in the ring laser and pulsed dye amplifier to scan from 284 to 290 nm. Since the 699-29 scans continuously while the data are being accumulated, the scan speed was set to ensure that the spectral line shapes were not distorted. Data were accquired at 50 MHz intervals with a scan speed of 10 MHz/s, corresponding to one point every 5 s. The lasers were fired at 20 Hz, and 100 shots were averaged per data point. Spectra were stored on the Apple computer that controls the 699 and transferred to an IBM PC-XT for analysis. The Doppler width of D 2 C 0 in the skimmed beam was determined as a function of distance between the nozzle aperture
TABLE I: Lifetimes and Term Values for Rotational Levels of 2l4' E ,",, cm-I J' K6 K: T", fits E,, cm-' J' KL K: 21.7619 4 1 3 0 0 0 1.12 0.0000 4 1 4 1.7418 1 0 1 1.39 20.2505 5.4196 1 1 0 0.094 31.8175 4 2 3 5.2684 1 1 1 1.14 49.8314 4 3 1 4 3 2 2 0 2 0.99 49.8307 5.2206 9.0542 2 1 1 1.08 25.9603 5 0 5 2 1 2 0.77 30.8256 5 1 4 8.6006 5 1 5 19.6364 2 2 0 1.39 28.5603 5 2 4 19.6316 2 2 1 0.54 40.5133 5 3 2 3 0 3 0.34 58.5531 10.4267 14.5029 3 1 2 1.13 58.5504 5 3 3 36.2477 6 0 6 3 1 3 0.93 13.5958 24.8796 3 2 1 1.18 41.6870 6 1 5 6 1 6 0.35 38.5197 24.8558 3 2 2 7 1 7 42.8578 3 3 0 0.86 50.1229 42.8577 3 3 1 0.86 69.0266 6 3 3 17.3461 4 0 4 0.48 81.2373 7 3 5)
DzCO 7". M S
0.78 0.88 1.36 0.67 1.68 1.03 0.52 0.53 1.85 1.21 1.56 0.59 1.09 0.49 0.64" 0.59* 1.43
'Uncertainty f25%. bTransitions not resolved.
TABLE II: Lifetimes and Term Values for Rotational Levels of 2143 DZCO E,,, cm-l J' K: K', q, NS E,,, cm-I J' K', K', rn,NS 0.000 0 0 0 3.24 30.6925 4 2 2 0.76 1.7413 1 0 1 1.49 30.6273 4 2 3 0.90 5.1054 1 1 0 2.73 47.3218 4 3 2 0.69 4.9667 1 1 1 0.45 25.9618 5 0 5 1.21 5.2192 2 0 2 0.65 30.4167 5 1 4 1.95 8.7265 2 1 1 0.23 28.3383 5 1 5 0.46 8.3103 2 1 2 0.53 39.4721 5 2 3 1.00 18.4483 2 2 0 0.79 39.3209 5 2 4 0.98 18.4439 2 2 1 1.11 56.0417 5 3 2 0.50 10.4249 3 0 3 2.67 56.0393 5 3 3 0.87 14.1549 3 1 2 1.83 66.5104 6 3 3 0.91 13.3227 3 1 3 1.08 36.2552 6 0 6 1.60 23.6889 3 2 1 1.10 41.2375 6 1 5 1.23 23.6671 3 2 2 1.29 38.3315 6 1 6 1.21 40.3498 3 3 0 0.81 50.0428 6 2 4 0.77 40.3497 3 3 1 0.81 49.7435 6 2 5 0.81 1.81 49.9737 7 1 7 1.33 17.3448 4 0 4 21.3868 4 1 3 1.25 63.2583 8 1 8 1.18 20.0002 4 1 4 1.46 Unassigned Lines freq, cm-'
rn, NS
30 165.779 30 173.920
4.95 3.19
and skimmer by measuring line widths at 30 540 cm-' and correcting for the approximately 450O-cm-' change in frequency. The measured Doppler widths (fwhm) were ~ 7 0 % of the observed line widths. The Doppler component of the broadening is Gaussian, and the lifetime broadening gives rise to a Lorentzian. The convolution of these line shapes is a Voigt profile. To determine the contribution due to lifetime broadening, we fitted the observed fwhm to a Voigt profile:'* Z(W)
= CJ
eXp[-(U'
- W0)~/0.366W~~]
(w - w')2
+ (y/2)2
dw'
where wo is the center frequency, 6wD = 0.012 cm-' is the Doppler fwhm, and y is the fwhm of the Lorentzian. The lifetime is given by T = 1/2ny. The signal-to-noise ratio varies greatly; some line-width measurements are reproduced to within 5%, while the standard deviation for noisy spectra is 25%.
Results Nonradiative decay rates have been measured for single rotational states in 2l4', 2143, 114', 5l, 2'4261, 2241,4'5', 2243, 2'5', 2341,214251,and 1'2143bands of SI DzCO by directly measuring the fluorescence decay rate. The data are inspected for trends with rotational quantum number and for dependence on vibrational (18)Demtroder, W.Laser Spectroscopy; Springer-Verlag: New York, 1982.
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988 5427
Fluorescence Lifetimes of Jet-Cooled Formaldehyde-d2 TABLE III: Lifetimes and Term Values for Rotati0~1Levels of 1'4' DZCO E, cm-l J' K: K: Tfl, ps E,,, cm-l J' K', K: 0.0000 0 0 0 1.50 21.8670 4 1 3 20.3217 4 1 4 1.7562 1 0 1 1.98 31.8115 4 2 2 5.3786 1 1 0 2.74 4 2 3 5.2240 1 1 1 2.35 31.7360 26.1699 5 0 5 2 0 2 1.78 5.2636 3 1.0122 5 1 4 9.0456 2 1 1 1.12 2 1 2 1.40 28.6961 5 1 5 8.5818 40.6812 19.4517 2 2 0 1.42 5 2 3 40.5062 5 2 4 19.4466 2 2 1 1.78 6 0 6 36.5376 3 0 3 1.49 10.5123 6 1 5 41.9714 3 1 2 1.55 14.5430 6 1 6 38.7335 3 1 3 0.72 13.6155 54.7355 7 1 6 3 2 1 1.01 24.7403 7 1 7 50.4283 3 2 2 1.18 24.7151 17.4874 4 0 4 1.50
78, ps
1.65 1.56 1.86 1.61 1.18 1.07 1.69 0.99 1.18 1.25 1.14 1.36 1.56 1.44
TABLE I V Lifetimes and Term Values for R o t a t i o ~ Levels l of 5' D X O
1.7515 5.4268 5.2697 5.2492 9.0868 8.6156 19.6461 19.6409 10.4830 14.5735 13.6312 24.9212 24.8955
1 1 1 2 2 2 2 2 3 3 3 3 3
0 1 1 0 1 1 2 2 0 1 1 2 2
1 0 1 2 1 2 0 1 3 2 3 1 2
2.28 2.92 3.33 2.14 2.01 1.88 2.28 2.35 1.53 1.51 1.62 1.45 1.47
42.8794 17.4375 21.8826 20.3128 3 1.9742 31.8975 26.0930 31.0085 28.6556 40.8212 38.6541 51.4805 50.3021
3 4 4 4 4 4 5 5 5 5 6 6 7
3 0 1 1 2 2 0 1 1 2 1 2 1
1 4 3 4 2 3 5 4 5 3 6 4 7
2.46 2.03 1.55 1.45 1.81 1.53 3.17 1.82 2.57 2.13 1.99 1.60 1.99
Unassigned Lines freq, cm-'
30 548.30 30 547.796 30551.538 30 564.544 30 564.936 30 565.458 30565.580 30 566.097 a
Tfl, PS
0.751 1.79 1.64 0.321,1.59O 1.52 1.91 2.47 3.67
freq, cm-l 30 566.465 30 570.994 30 572.700 30 573.363 30 574.094 30 575.603 30 576.938 30 579.680
Tfl, ps
1.43 1.77 0.790 1.17 1.84 0.855 0.999 1.10
Double exponential due to unresolved lines in the spectrum.
TABLE V Lifetimes and Term Values for Rotational Levels of 2'4z61 DzCW E, cm-' J K: Kb T", ns E,,, cm-l J K: K: Tn, ns 3 2 1 0 0 0 511 25.0629 26 1 o.oO0o 25.0378 3 2 2 815 1 0 1 553 1.7411 749 5.4688 21.8263 4 1 3 1 1 0 543 20.2634 4 1 4 1 1 1 1420 674 5.3124 32.0722 4 2 2 484 5.2180 2 0 2 763 31.9972 4 2 3 477 2 1 1 402 9.1072 5 1 4 877 2 1 2 143 30.8963 8.6381 392 28.5538 5 1 5 19.8199 2 2 0 671 909 19.8148 2 2 1 1170 40.8628 5 2 3 841 41.7632 6 1 5 10.4204 3 0 3 462 14.5612 38.4881 6 1 6 3 1 2 498 731 3 1 3 529 13.6231 "Unassigned lines are listed in Table IV.
TABLE M: Lifetimes and Term Values for Rotational Levels of 2241 DzCO E, cm-' J' K', K: Tfl, ns E,,, cm-' J' K: K: Tn. ns 0.0000 0 0 0 682 21.6144 4 1 3 534 1.7258 1 0 1 500 20.1234 4 1 4 534 5.4242 1 1 0 1090 31.8139 4 2 2 560 5.2751 1 1 1 1040 31.7452 4 2 3 550 5.1728 2 0 2 770 25.7265 5 0 5 413 5 1 4 629 9.0249 2 1 1 535 30.5943 8.5774 2 1 2 1065 28.3593 5 1 5 467 19.6748 2 2 0 427 40.5216 5 2 3 245 19.6702 2 2 1 506 40.3621 5 2 4 235 10.3318 3 0 3 328 35.9236 6 0 6 600 3 1 2 547 41.3556 6 1 5 310 14.4229 13.5280 3 1 3 520 38.2306 6 1 6 607 24.8698 3 2 1 471 50.6935 6 2 5 478 24.8468 3 2 2 429 49.7317 7 1 7 608 295 17.1889 4 0 4 TABLE W: Lifetimes and Term Values for Rotational Levels of 4%' DzCO E,,, cm-I J' K', K: Tn, ps E,,, cm-I J' K', K', Tfl, ps 4 0 4 1.46 1.95 17.4232 0.0000 0 0 0 4 1 3 1.81 1.7499 1 0 1 1.29 21.7698 1.33 20.2382 4 1 4 5.3460 1 1 0 2.54 1.06 31.6439 4 2 2 2.03 5.1928 1 1 1 1.79 31.5693 4 2 3 5.2445 2 0 2 1.22 4 3 1 1.63 1.45 49.1737 8.9989 2 1 1 49.1729 4 3 2 1.35 2 1 2 1.16 8.5392 5 0 5 1.76 1.52 26.0730 19.3306 2 2 0 .53 30.8780 5 1 4 1.87 19.3256 2 2 1 10.4739 3 0 3 ..14 28.5825 5 1 5 1.43 5 2 4 1.39 1.31 40.3059 14.4748 3 1 2 2.03 41.7920 6 1 5 1.44 13.5556 3 1 3 6 1 6 1.45 24.5996 3 2 1 2.07 38.5827 51.1227 6 2 4 1.40 3 2 2 1.55 24.5747 1.27 54.5020 7 1 6 42.1654 3 3 0 1.21 50.2329 7 1 7 1.22 3 3 1 1.21 42.1653 Unassigned Lines freq, cm-'
freq, cm-l
T", NS
30925.295 30926.219 30 928.079 30930.543 30932.052 30933.654 30 934.064 30934.391
1.09 0.724 0.967 0.348 1.14 1.09 0.724 0.58
T",
30936.383 30937.782 30939.719 30940.301 30945.733 30945.936 30946.871
0 K = O
ps
0.243 0.945 0.865 0.731 1.31 0.889 0.704
8
AK: I
OK:2 0
A
0
0
0
0
0
't
01
b
'
0
A 1
1
1
2
4
6
8
J'
energy and vibrational mode. Tables I-XI1 list the lifetimes, quantum numbers, and rotational term values for rotational states within each vibrational band. The upper-state quantum numbers are derived from rotational analyses for all bands except for 2341, which has not been a n a l y ~ e d . ' ~Rotational ~ ' ~ ~ ~ ~ term values are calculated from the spectroscopic constants for the unperturbed bands. The term values for the three perturbed bands, 2243,214251, (19)Job, V. A.;Sethuraman, V.;Innes, K. K. J . Mol. Specrrosc. 1965, 30,365. (20)Sethuraman, V.;Job, V. A.; Innes, K. K. J . Mol. Specrrosc. 1970, 33, 189.
Figure 2. Decay rates 2398 cm-').
(Tn-')
as a function of J'for 2*4l D 2 C 0 (Evib=
and 112143,are calculated from the observed transition frequencies and the known ground-state constants.' Fluorescence lifetimes from the widths of individual lines in 112441and 2641bands are shown in Table XIII. Rotational Energy Dependence. The lifetimes in Tables I-XI1 sample states with K' = 0-3 and J' = 0-7. For the narrow range of K states observed, the decay rates in some cases show a possible slight dependence on the J or K quantum number, but for the most part the scatter in lifetimes masks any underlying trend. Figure
5428
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988
TABLE VIII: Lifetimes and Term Values for Rotational Levels of 2243 DzCO E,," c n i ' J' K : K', T", ns E,,,'cm-' J' K : K : T", ns 0.013 0 0 0 212 38.986 3 3 1 296 1.741 1 0 1 159 17.214 4 0 4 220 4.866 225 21.025 1 1 0 4 1 3 226 4.731 162 19.683 1 1 1 4 1 4 212 5.189 20 1 2 0 2 29.862 4 2 2 134 8.459 2 1 1 24 1 30.035 4 2 3 223 8.057 2 1 2 181 45.736 4 3 I 162 2 2 0 222 45.738 17.659 4 3 2 188 17.700 2 2 1 372 25.764 5 0 5 170 10.354 3 0 3 184 29.970 5 1 4 166 3 1 2 13.849 212 27.975 5 1 5 169 13.042 3 1 3 153 35.979 6 0 6 159 3 2 1 22.881 197 37.915 6 1 6 124 3 2 2 22.989 275 49.488 7 1 7 102 38.984 3 3 0 252b freq, cm-I 31 283.295 3 1 284.263 31 284.854 31 291.921 31 294.227 31 295.644 31 296.780 31 302.955 31 303.156
Unassigned Lines freq, cm-I
711,ns
1168 712 1160 827 875 123, 365 536 746 578
31 304.129 31 310.964 31 311.400 31 315.338 31 316.293 31 316.327 31 316.631 31 319.817 31 316.161
ns
T ~ ,
796 231 926 225 270 366 678 376 203
Term values are calculated from the observed transition frequency and So rotational constants. *This state shows a single exponential for 330/331
when they are not spectrally resolved and different lifetimes when they are resolved.
TABLE I X Lifetimes and Term Values for Rotational Levels of 2'5l DzCO E,,, cm-I J' K', K : 78, ns E,,, cm-' J' K', K : T", ns 1.7396 1 0 I 258 20.2401 4 1 4 184 5.4697 1 1 0 192 32.0608 4 2 2 252 5.3113 1 1 1 233 31.9838 4 2 3 188 19.8186 2 2 0 155 25.9133 5 0 5 334 19.8135 2 2 1 131 30.8921 5 1 4 240 10.4115 3 0 3 377 28.5191 5 1 5 174 14.5598 3 1 2 225 40.6677 5 2 4 118 13.6095 3 1 3 233 36.1741 6 0 6 401 25.0569 3 2 1 253" 41.7581 6 1 5 297 25.0312 3 2 2 222 38.4405 6 1 6 298 17.3181 4 0 4 403 49.9982 7 1 7 278 21.8234 4 1 3 352 frea. cm-I 31 704.715 31 705.575 31 721.620 31 722.621 31 723.692 31 726.260 3 1 727.803 31 728.591 31 729.135
Unassigned Lines freu. cm-I 243 31 733.002 258 31 734.634 263 31 741.418 312 31 745.254 328 31 747.893 197 31 749.170 31 749.656 110 31 750.948 88 102
in. ns
Tn. ns 99 102 131, 571 267 428 103 237 87 1
Frisoli and Moore TABLE X Lifetimes and Line Positions for 2 ' 4 l frea. cm-' 31 823.301 31 829.136 31 829.385 31 829.534 31 833.024 31 834.157 31 838.996 31 839.139 31 839.705 31 840.160 31 840.835 31 840.904 31 841.487 31 841.536 31 841.775 31 842.502 31 842.890 31 844.027 31 844.697 31 845.909 31 846.368 31 847.193 31 847.616 31 847.827 31 847.042 31 853.786 31 869.705 3 1 848.099 31 848.292 31 848.500 31 850.541 31 851.484 31 852.215 31 852.533 31 853.294 31 854.854 31 855.261 31 858.530 31 858.734 31 858.942 31 859.145 31 859.607 31 860.058 3 1 860.223 31 860.344 31 860.660 31 860.905 31 861.611 31 867.039 31 867.527
Tn.
DICO ns
96 81 177 89 93 84 130 144 535 85 149 90 1140 104 141 414 414 570 49 1 149 107 141 143 250 189, 1040 ( F / S = 3.3) 120, 383 ( F / S = 0.9) 203, 534 ( F / S = 2.8) 150 186 278 493 136 47 1 130 140 301 435 207 192 297 305 193 303 150 177 373 300 179 188 218
"f35-ns uncertainty.
2 illustrates the range of decay rates observed for 2*4l (Evib= 2398 cm-') as a function of J', and Figure 3 shows data for 112143 (Evib= 3917 cm-I). A very slight trend of increasing decay rate is observed as a function of J'. Least-squares fits show that T decreases about 5% with each quantum of J'in 7 out of 10 bands. In two bands the trend of decreasing T with J'is not significant compared to the uncertainty, and the tenth band, 2I5l, showed a slight but not significant increase in T with J'. Least-squares fits of T as a function of K'also indicate a small but significant decrease in T with K'(negative slope) in some cases. Three bands out of ten, 2143, 2l5', and 214251show a 15-2075 decrease in lifetime with additional quanta of KL, and in a fourth (112143) T decreases by an average 8% with each KL. In 50% of the vibrational bands scatter obscures any trend with Kra,perhaps
3t
0 K
I 01
=O
AK= I O K - 2
uK=3
0
4
2
6
8
d
Figure 3. Decay rates (?,,-I) as a function of J for 112143D,CO (Evib= 3917 cm-'). Decays corresponding to the three shortest lifetimes in Table XI1 are not shown.
because the range of K' states obtained in the beam is too small to demonstrate a trend. In just one case, 2*4), lifetimes increase with KB by roughly 10%. Median fluorescence lifetimes, the mean log 7,and standard deviation of log T values for each vibrational band are listed in
Fluorescence Lifetimes of Jet-Cooled Formaldehyde-d, TABLE XI: Lifetimes and Term Values for Rotational Levels of 2'4'5' DZCO
E,A,, cm-' 0.018 1.746 5.346 5.201 5.200 8.967 8.523 19.353 19.334 10.368 14.383 13.495 24.570 24.536 42.190 42.182 17.250 21.613 20.110 49.136 49.094 30.631 28.378
m, ns 28 1 310 247 165 180 193 20 97 125 132 194 210 200 39 46, 143 46, 143 158 113 30 41, 256 41, 256 29 1 144
J' K'. K'? 0 0 0 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 5 5
0 1 1 0 1 1 2 2 0 1 1 2 2 3 3 0 1 1 3 3 1 1
1 0 1 2 1 2 0 1 3 2 3 1 2 0 1 4 3 4 1 2 4 5
Unassigned Lines freq, cm-' 32085.488 32087.009 32 086.384
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988 5429 TABLE XIV: D2C0 SI Vibronic Lifetimes as a Function of Vibrational Energy (em-')'
vib band 2'4l 2143 1'4' 5' 2'4*6' 2241 425 I 2243 2'5l 2)4' 214251 1'2'4)
median 7 , p s
EVib 1241 1845 2144 2239 2257 2398 2619 3006 3428 3542 3797 3917
0.912 1.07 1.48 1.99 0.525 0.537 1.46 0.240 0.191 0.158 0.158 0.166
log -6.09 -5.99 -5.84 -5.70 -6.23 -6.29 -5.83 -6.71 -6.62 -6.67 -6.90 -6.88
(T)~"
7maxl7min
f 0.25
20 14 4 2 10 5 2 4 9 13 10 5
0.23 0.12 f 0.1 1 f 0.21 0.17 f 0.09 f 0.12 f 0.15 0.28 f 0.34 f 0.22
*
*
*
'Column four lists the mean of the log of the lifetimes and the standard deviation about the mean. 06
05 04
03 02 Y)
01
G
o
[L
% 03
ns 83 106 103
7,1,
02
E
01
0
TABLE XII: Lifetimes and Term Values for Rotational Levels of 1'2143 D X O
E,,, cm-'
J' K', K: 0 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 5 6 6
0 0 1 1 0 1 1 2 2 0 1 1 2 2 3 3 0 1 1 2 2 3 3 1 1 2 2 3 1 1
0 1 0 1 2 1 2 0 1 3 2 3 1 2 0 1 4 3 4 2 3 1 2 4 5 3 4 3 5 6
48.856
6
2
5
49.639
7 1 7
0.004 1.756 4.803 4.680 5.213 8.376 8.019 17.500 17.492 10.385 13.747 13.027 22.733 22.717 38.738 38.746 17.285 20.883 19.699 29.724 29.680 45.708 45.700 29.787 28.024 38.498 38.402 53.614 40.447 38.01 1
713, ns 165 172 166 183 152 152 125 172 166 185 95 166 100 199 36 36 173 139 183 151 90 169 163 102 24, 172' 142 168 165 72 179 164 164
5 k / 2.5) in 2*4' and three in 1'2'4) are not shown.
"There is only one transition here. TABLE XIII: Lifetimes from Line Widths vib band fres, cm-l gun, cm-' 112'41 34976.88 0.0122 34 979.60 2641 35 175.17 0.0123 35 206.06
y, cm-l
0.005 0.005 0.007 0.005
ns 1.09 1.06 0.76 1.10
7,
Table XIV. In addition, the ratio of longest to shortest lifetime for each vibrational band in Table XIV illustrates the maximum fluctuation of SRVL lifetimes, which is quite conspicuous even for vibrational energies as high as 3917 cm-'. At low vibrational energy but above the barrier for dissociation to molecular products, = 1241 cm-I) fluctuate by as much lifetimes in the 2'4' band (Evib as a factor of 20, and 1 standard deviation is 45% of the mean. Judging from the standard deviations, there appears to be little change in the magnitude of lifetime fluctuation as vibrational energy is increased from 1241 to 3917 cm-I. The standard deviation of 7 is 54% for 214251and 26% for 1'2143. The bulk of the measurements in these two bands fall within a factor of 3 of each other; a few lie outside this range. In 112143,for example, 96% of the data fall in the range 95-195 ns, and a single lifetime is 36 ns. This narrowing of the range of decay rates with increasing Evibis illustrated in Figure 4. The overwhelming majority of assigned SRVL lifetimes in 4251,2243,and 2l5' also vary only within a factor of 3 for each vibrational state. This is not true when the unassigned lines are included. For 4,5' in particular, the unassigned lines have lifetimes that are systematically shorter by a factor of 2. The rotational structure in 2341is not assigned, and there appear to be two complete sets of rotational lines. The lifetimes in Table X include all reasonably intense lines and show significant fluctuations. Asymmetry Doublet Levels. Within each vibrational band, it was possible to measure lifetimes for both asymmetry components of several J'K'states. Table XV lists calculated level splittings and observed lifetime ratios. Level splittings for the perturbed bands 2243, 2l4,5I, and 112143are obtained from the observed transition frequencies and calculated So rotational lines. Only the levels with the smallest calculated splittings, 1 X IO4 cm-',
5430 The Journal of Physical Chemistry, Vol. 92, No. 19, 1988
TABLE X V Asymmetry Doublet Splitting8 m d Ufetisre Ratio@ rot levels 2’4’ 2143 1I4l 51 214261 b 4.307
Frisoli and Moore
2241
1.08
C
3.167 2.22 2.265 0.98 1.511 0.88 0.907 1.22 0.454 2.57
0.151 0.08
0.024 3.33 0.005
2.57
2.906 1.02 2.078 4.23 1.387 0.86 0.832 1.69 0.4 16 0.44 0.299 0.96 0.151 1.02 0.139 6.03 0.065 0.84 0.022 0.85
0.004 0.71 0.002
3.238 0.84 2.316 0.63 1.545 1.06 0.928 2.15 0.464 0.80
3.275 1.15
2.353 0.71 1.570 1.07
0.942 0.93 0.471 1.07
2.343 2.24 1.563 1.11 0.938 0.941 0.469 2.81
0.175 0.85 0.155
1.17 0.075 1.15 0.025 0.86 0.005 0.80
0.571 0.077 1.18 0.026 0.99
0.156 0.38 0.075 1.01 0.025 0.32
0.005
0.005
0.97
0.57
0.88
3.125 0.51 2.235 1.35 1.491
1.oo 0.105
1.05 0.448 0.502 0.160 1.04 0.149 1.05
0.069 1.02 0.023 1.08 0.005 1.05
4251 4.269 0.96 3.209 0.99 2.295 1.31 1.532 1.36 0.919 0.64 0.460 1.25
2243
2I5I 3.318 1.oo 2.373 1.38 1.583 1.91 0.950 0.966
1.995 0.98 1.341 1.11 0.807 1.39 0.402 1.33
0.153 2.41 0.075 1.13 0.0249 1.34
0.82 0.077 1.34 0.026 1.14
0.005
0.135 1.39 0.173 0.60 0.108 0.71 0.040
0.99
0.60
1.18
0.158
0.005
2I4’5’
2.253 2.02 1.504 3.77 0.888
0.92 0.445 9.65
0.145 1S O 0.035 5.13 0.019 0.78
112143 2.436 0.40 1.76 0.60 1.184 0.76 0.720 0.57 0.356 1.21 0.096 0.84 0.123 0.91
0.044 1.68 0.016 0.50 0.008
1.04
0.58
0.0007 2.50 0.0001 1.oo
0.0001 1.00
0.002 0.86 0.001
0.0001 1.oo
0.042 6.25
0.008
0.008
0.008 1.oo
1.04
3.11 “Splittings for 2243,214251,and 112143are measured. bThis row of numbers is the level splitting (cm-I). CThisrow gives the ratio of the lifetimes, for example, ~ l l o / ~ l l l . uniformly exhibit the same lifetime; otherwise there is no obvious correlation between level splittings and lifetimes of asymmetry doublet pairs. For almost every vibration the calculated separation of levels 330 and 331 is only lo4 crn-’. Transitions to these levels, however, are difficult to resolve spectroscopically. For example, the transitions ‘R2(2)e and ‘R2(2)o terminate in 331 and 330 but are not resolved even in the high-resolution spectrum. At the spectral feature corresponding to these two transitions a single exponential was observed in all but one case, 214251. It is interesting to note that in the 2243spectrum a 273-11s single exponential was measured for ‘R2(2)e,0,but the lifetimes for 330 and 331observed from the resolved ‘Q2(3)e and o transitions were 253 and 296 ns, respectively. This band is perturbed,” and these levels may be separated by more than lo4 cm-’. Since the molecular beam laser-induced fluorescence spectra reported previously are accurate to 0.005 cm-l, level splittings smaller than 0.01 cm-’ cannot be measured. It is also difficult to identify double-exponential behavior when the two components are similar. Vibrational Energy Dependence. Figures 5 and 6 show the range of decay rates observed for single rovibronic states and the average for each vibrational band. These data are summarized in Table XIV. For comparison, Figure 5 includes published SVL decay rates,l5 ranges of molecular beam SRVL measurements,lO~ll and high-energy line-width measurements.2’ The decay rates increase with vibrational energy in S1. Although the SVL rates are generally faster than the average rates for SRVLs, many fall within the SRVL range of measurements. The exceptions are 1l4I, 9,4251,and 2I5l bands. Since the SRVL measurements access only low J’K’states in the molecular beam and the SVL experiments were done at room temperature, a slight trend of increasing decay rate with rotational energy would result in a slower average rate for the beam measurements. Some SVL rates may be increased by collisions. The reported SVL rate for 5l is close to the observed SRVL rate for 244261;the spectra of these two bands overlap at room temperature. (21) Baranovski, A.
1976, 60, 111.
P.;Hartford, A.; Moore, C. B. J . Mol. Spectrosc.
0.85
I21
I
I
2’4’
! 4
0
1000
2000
3000
4000
4
Vibrationol Energy (crn- ’ )
F i p e 6. Average decay rates and ranges, this work. Filled and open circles denote states with and without one quantum of CD stretch. Data shown for 4O, 4l, and 43 are from ref 6, 9, and 11.
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988 5431
Fluorescence Lifetimes of Jet-Cooled Formaldehyde-dz
Discussion A complete understanding of formaldehyde photophysics requires an accurate description of the states involved in both the radiationless transition, SI So*, and the dissociation process, So* D2 CO. The radiationless transition is also governed by the S1-So coupling matrix elements. Stark experiments give a clear picture of So* levels near the SI origin. In the vicinity of 4O and 4', individual states in So are resolved, only a few states are resolved at energies near 4' (&b = 125 cm-'), and none are completely resolvable above 43 (Evib = 667 cm-'). Recent Stark effect measurements in 4251(&ib = 2619 cm-') and 2243DzCO (Eab = 3006 cm-') show a few sharp features that are attributed to coupling with triplet levels (TI) and some broad structure over a 0.2-cm-' scan range.5 At higher energies, one can estimate the lumpiness of So* from calculated line widths and state densities. The D 2 C 0 D2 + C O dissociation rates extracted from measured So* line widths near the threshold range from 2 X lo7 to 5 X lo8 s-I, and place the barrier height at 80.6 f 0.8 kcal mol-', almost isoenergetic with the S1 origin (80.9 kcal mol-').5 Calculated unimolecular dissociation rates give line widths that agree with experiments near the SI origin (28 304 cm-l) and predict average level widths of , ~ ~density of So* states at about 0.03 cm-' at 32 000 ~ r n - ' . ~The 28 304 cm-' is =437/cm-', or 5 times greater than predicted by a direct count of anharmonic oscillator^.^ At 32 000 cm-I, where the density is 830/cm-', the So line widths are 25 times greater than the average line spacing, and the continuum should be almost smooth. The lifetime variations observed indicate that some broad structure exists here and at even higher energy. Rotational Quantum Number Dependence. Lifetime fluctuations at low vibrational energies in SI H 2 C 0 and DzCO are well documented and u n d e r ~ t o o d . ~Rotational ~ states Is) in S1 are coupled to a sparse manifold of So states, Il), which are broadened by coupling to the dissociative continuum thereby acquiring widths rl. The radiationless decay of state Is) is then described by
-
-
+
-
k", = (1/~)XIV,,l2r,/[(Es - E,)2 + ( r , / W l I
(1)
where Vs,is the coupling matrix element between Is) and ll), and (E, - E,) is the difference in their energies (or energy gap).24 This is the "weak coupling limit", Le., lVsrl
